A two equation VLES turbulence model with near-wall delayed behaviourApplied CCM Pty Ltd
Turbulence is a phenomenon that occurs frequently in nature and is present in almost all industrial applications. Despite significant increase in computational power in modern processors, Reynolds averaged Navier-Stokes (RANS) simulations are still the dominant approach to turbulence modelling of high Reynolds number flows. Hybrid LES/RANS approaches [1] are currently used to offset the cost of Large Eddy Simulation (LES) computations by retaining the RANS characteristics in boundary layers while using the LES model away from walls. The hybrid approach embodied in the Detached Eddy Simulation (DES) methodology has been used with success in industrial flow simulations. However, it should be noted that the DES approach still requires LES-like mesh resolution away from walls. This is a simple consequence of the fact that the DES model defaults to LES at large distances from the walls. This may prove prohibitively expensive in simulations where large turbulent structures persists over most of the computational domain.
In this work, a delayed two equation very large eddy simulation (VLES) model based on three length scales is introduced. The resolution control function used to rescale the Reynolds stresses is based on the ratio of the resolved to unresolved turbulence spectrum. The model constants are selected so that the Smagorinsky subgrid-scale model is recovered in the limit of grids approaching the resolution required for LES computations. The near wall RANS behaviour of the proposed model is obtained using blending functions. The objective was to implement this model using the open source library Caelus [2] and validate the results against two test cases involving turbulent vortex shedding from a bluff-body. The test cases used were flow past a square cylinder at a Reynolds number of 21,400 [3] and the Rudimentary Landing Gear benchmark case for Airframe Noise Computations (BANC) [4].
The numerical simulations were carried out using a transient solver based on the open source computational mechanics library Caelus. The pressure-based solver with second-order bounded spatial discretisation and second-order bounded implicit time marching scheme was applied to obtain a time-accurate solutions. Compressibility effects were negligible for the Mach numbers under consideration and the flow was treated as incompressible. Results from the simulations indicate close agreement between the proposed model and available experimental and numerical results.
Boundary Feedback Stabilization of Gas Pipeline FlowMartinGugat
The isothermal Euler-equations are a model of gas flow through pipelines. This is a hyperbolic system of pdes, so in general the regularity of the solution can decrease in finite time. We show that with sufficiently small initial data and a suitable boundary feedback law, this does not happen, so the solution keeps the regularity of the initial data. In fact, the feedback law stabilizes the system state exponentially fast to a stationary state.
Our research is part of the Transregio 154, Mathematical Modelling, Simulation and Optimization Using the Example of Gas Networks.
PROGRAMMA ATTIVITA’ DIDATTICA A.A. 2016/17
DOTTORATO DI RICERCA IN INGEGNERIA STRUTTURALE E GEOTECNICA
____________________________________________________________
STOCHASTIC DYNAMICS AND MONTE CARLO SIMULATION IN EARTHQUAKE ENGINEERING APPLICATIONS
Lecture Series by
Agathoklis Giaralis, Ph.D., M.ASCE., P.E. City, University of London
Visiting Professor Sapienza University of Rome
A two equation VLES turbulence model with near-wall delayed behaviourApplied CCM Pty Ltd
Turbulence is a phenomenon that occurs frequently in nature and is present in almost all industrial applications. Despite significant increase in computational power in modern processors, Reynolds averaged Navier-Stokes (RANS) simulations are still the dominant approach to turbulence modelling of high Reynolds number flows. Hybrid LES/RANS approaches [1] are currently used to offset the cost of Large Eddy Simulation (LES) computations by retaining the RANS characteristics in boundary layers while using the LES model away from walls. The hybrid approach embodied in the Detached Eddy Simulation (DES) methodology has been used with success in industrial flow simulations. However, it should be noted that the DES approach still requires LES-like mesh resolution away from walls. This is a simple consequence of the fact that the DES model defaults to LES at large distances from the walls. This may prove prohibitively expensive in simulations where large turbulent structures persists over most of the computational domain.
In this work, a delayed two equation very large eddy simulation (VLES) model based on three length scales is introduced. The resolution control function used to rescale the Reynolds stresses is based on the ratio of the resolved to unresolved turbulence spectrum. The model constants are selected so that the Smagorinsky subgrid-scale model is recovered in the limit of grids approaching the resolution required for LES computations. The near wall RANS behaviour of the proposed model is obtained using blending functions. The objective was to implement this model using the open source library Caelus [2] and validate the results against two test cases involving turbulent vortex shedding from a bluff-body. The test cases used were flow past a square cylinder at a Reynolds number of 21,400 [3] and the Rudimentary Landing Gear benchmark case for Airframe Noise Computations (BANC) [4].
The numerical simulations were carried out using a transient solver based on the open source computational mechanics library Caelus. The pressure-based solver with second-order bounded spatial discretisation and second-order bounded implicit time marching scheme was applied to obtain a time-accurate solutions. Compressibility effects were negligible for the Mach numbers under consideration and the flow was treated as incompressible. Results from the simulations indicate close agreement between the proposed model and available experimental and numerical results.
Boundary Feedback Stabilization of Gas Pipeline FlowMartinGugat
The isothermal Euler-equations are a model of gas flow through pipelines. This is a hyperbolic system of pdes, so in general the regularity of the solution can decrease in finite time. We show that with sufficiently small initial data and a suitable boundary feedback law, this does not happen, so the solution keeps the regularity of the initial data. In fact, the feedback law stabilizes the system state exponentially fast to a stationary state.
Our research is part of the Transregio 154, Mathematical Modelling, Simulation and Optimization Using the Example of Gas Networks.
PROGRAMMA ATTIVITA’ DIDATTICA A.A. 2016/17
DOTTORATO DI RICERCA IN INGEGNERIA STRUTTURALE E GEOTECNICA
____________________________________________________________
STOCHASTIC DYNAMICS AND MONTE CARLO SIMULATION IN EARTHQUAKE ENGINEERING APPLICATIONS
Lecture Series by
Agathoklis Giaralis, Ph.D., M.ASCE., P.E. City, University of London
Visiting Professor Sapienza University of Rome
PROGRAMMA ATTIVITA’ DIDATTICA A.A. 2016/17
DOTTORATO DI RICERCA IN INGEGNERIA STRUTTURALE E GEOTECNICA
____________________________________________________________
STOCHASTIC DYNAMICS AND MONTE CARLO SIMULATION IN EARTHQUAKE ENGINEERING APPLICATIONS
Lecture Series by
Agathoklis Giaralis, Ph.D., M.ASCE., P.E. City, University of London
Visiting Professor Sapienza University of Rome
PROGRAMMA ATTIVITA’ DIDATTICA A.A. 2016/17
DOTTORATO DI RICERCA IN INGEGNERIA STRUTTURALE E GEOTECNICA
____________________________________________________________
STOCHASTIC DYNAMICS AND MONTE CARLO SIMULATION IN EARTHQUAKE ENGINEERING APPLICATIONS
Lecture Series by
Agathoklis Giaralis, Ph.D., M.ASCE., P.E. City, University of London
Visiting Professor Sapienza University of Rome
Importance sampling has been widely used to improve the efficiency of deterministic computer simulations where the simulation output is uniquely determined, given a fixed input. To represent complex system behavior more realistically, however, stochastic computer models are gaining popularity. Unlike deterministic computer simulations, stochastic simulations produce different outputs even at the same input. This extra degree of stochasticity presents a challenge for reliability assessment in engineering system designs. Our study tackles this challenge by providing a computationally efficient method to estimate a system's reliability. Specifically, we derive the optimal importance sampling density and allocation procedure that minimize the variance of a reliability estimator. The application of our method to a computationally intensive, aeroelastic wind turbine simulator demonstrates the benefits of the proposed approaches.
Landslides of any type, and particularly soil slips, pose a great threat in mountainous and steep terrain environ- ments. One of the major triggering mechanisms for slope failures in shallow soils is the build-up of soil pore water pressure resulting in a decrease of effective stress. However, infiltration may have other effects both before and after slope failure. Especially, on steep slopes in shallow soils, soil slips can be triggered by a rapid drop in the apparent cohesion following a decrease in matric suction when a wetting front penetrates into the soil without generating positive pore pressures. These types of failures are very frequent in pre-alpine and alpine landscapes. The key factor for a realistic prediction of rainfall-induced landslides are the interdependence of shear strength and suction and the monitoring of suction changes during the cyclic wetting (due to infiltration) and drying (due to percolation and evaporation) processes. The non-unique relationship between suction and water content, expressed by the Soil Water Retention Curve, results in different values of suction and, therefore, of soil shear strength for the same water content, depending on whether the soil is being wetted (during storms) or dried (during inter-storm periods). We developed a physically based distributed in space and continuous in time model for the simulation of the hydrological triggering of shallow landslides at scales larger than a single slope. In this modeling effort particular weight is given to the modeling of hydrological processes in order to investigate the role of hydrologi- cal triggering mechanisms on soil changes leading to slip occurrences. Specifically, the 3D flow of water and the resulting water balance in the unsaturated and saturated zone is modeled using a Cellular Automata framework. The infinite slope analysis is coupled to the hydrological component of the model for the computation of slope stability. For the computation of the Factor of Safety a unified concept for effective stress under both saturated and unsaturated conditions has been used (Lu Ning and Godt Jonathan, WRR, 2010). A test case of a serious landslide event in Switzerland is investigated to assess the plausibility of the model and to verify its perfomance.
Numerical Study of Forced Convection in a Rectangular Channel
Original Research Article
Journal of Chemistry and Materials Research Vol. 1 (1), 2014, 7–11
Salim Gareh
DYNAMIC RESPONSE OF SIMPLE SUPPORTED BEAM VIBRATED UNDER MOVING LOAD sadiq emad
In this thesis, an experimental and numerical study of dynamic deflection and dynamic bending stress of beam-type structure under moving load has been carried out. The moving load is constant in magnitude and travels at a uniform speed. The dynamic analysis of beam-type structure is done by taking three different concentrated loads (4, 6 and 8) kg , each one of them travels at three different uniform speeds (0.15, 0.2 and 0.25) m/s .
(May 29th, 2024) Advancements in Intravital Microscopy- Insights for Preclini...Scintica Instrumentation
Intravital microscopy (IVM) is a powerful tool utilized to study cellular behavior over time and space in vivo. Much of our understanding of cell biology has been accomplished using various in vitro and ex vivo methods; however, these studies do not necessarily reflect the natural dynamics of biological processes. Unlike traditional cell culture or fixed tissue imaging, IVM allows for the ultra-fast high-resolution imaging of cellular processes over time and space and were studied in its natural environment. Real-time visualization of biological processes in the context of an intact organism helps maintain physiological relevance and provide insights into the progression of disease, response to treatments or developmental processes.
In this webinar we give an overview of advanced applications of the IVM system in preclinical research. IVIM technology is a provider of all-in-one intravital microscopy systems and solutions optimized for in vivo imaging of live animal models at sub-micron resolution. The system’s unique features and user-friendly software enables researchers to probe fast dynamic biological processes such as immune cell tracking, cell-cell interaction as well as vascularization and tumor metastasis with exceptional detail. This webinar will also give an overview of IVM being utilized in drug development, offering a view into the intricate interaction between drugs/nanoparticles and tissues in vivo and allows for the evaluation of therapeutic intervention in a variety of tissues and organs. This interdisciplinary collaboration continues to drive the advancements of novel therapeutic strategies.
Seminar of U.V. Spectroscopy by SAMIR PANDASAMIR PANDA
Spectroscopy is a branch of science dealing the study of interaction of electromagnetic radiation with matter.
Ultraviolet-visible spectroscopy refers to absorption spectroscopy or reflect spectroscopy in the UV-VIS spectral region.
Ultraviolet-visible spectroscopy is an analytical method that can measure the amount of light received by the analyte.
THE IMPORTANCE OF MARTIAN ATMOSPHERE SAMPLE RETURN.Sérgio Sacani
The return of a sample of near-surface atmosphere from Mars would facilitate answers to several first-order science questions surrounding the formation and evolution of the planet. One of the important aspects of terrestrial planet formation in general is the role that primary atmospheres played in influencing the chemistry and structure of the planets and their antecedents. Studies of the martian atmosphere can be used to investigate the role of a primary atmosphere in its history. Atmosphere samples would also inform our understanding of the near-surface chemistry of the planet, and ultimately the prospects for life. High-precision isotopic analyses of constituent gases are needed to address these questions, requiring that the analyses are made on returned samples rather than in situ.
Deep Behavioral Phenotyping in Systems Neuroscience for Functional Atlasing a...Ana Luísa Pinho
Functional Magnetic Resonance Imaging (fMRI) provides means to characterize brain activations in response to behavior. However, cognitive neuroscience has been limited to group-level effects referring to the performance of specific tasks. To obtain the functional profile of elementary cognitive mechanisms, the combination of brain responses to many tasks is required. Yet, to date, both structural atlases and parcellation-based activations do not fully account for cognitive function and still present several limitations. Further, they do not adapt overall to individual characteristics. In this talk, I will give an account of deep-behavioral phenotyping strategies, namely data-driven methods in large task-fMRI datasets, to optimize functional brain-data collection and improve inference of effects-of-interest related to mental processes. Key to this approach is the employment of fast multi-functional paradigms rich on features that can be well parametrized and, consequently, facilitate the creation of psycho-physiological constructs to be modelled with imaging data. Particular emphasis will be given to music stimuli when studying high-order cognitive mechanisms, due to their ecological nature and quality to enable complex behavior compounded by discrete entities. I will also discuss how deep-behavioral phenotyping and individualized models applied to neuroimaging data can better account for the subject-specific organization of domain-general cognitive systems in the human brain. Finally, the accumulation of functional brain signatures brings the possibility to clarify relationships among tasks and create a univocal link between brain systems and mental functions through: (1) the development of ontologies proposing an organization of cognitive processes; and (2) brain-network taxonomies describing functional specialization. To this end, tools to improve commensurability in cognitive science are necessary, such as public repositories, ontology-based platforms and automated meta-analysis tools. I will thus discuss some brain-atlasing resources currently under development, and their applicability in cognitive as well as clinical neuroscience.
Comparing Evolved Extractive Text Summary Scores of Bidirectional Encoder Rep...University of Maribor
Slides from:
11th International Conference on Electrical, Electronics and Computer Engineering (IcETRAN), Niš, 3-6 June 2024
Track: Artificial Intelligence
https://www.etran.rs/2024/en/home-english/
Earliest Galaxies in the JADES Origins Field: Luminosity Function and Cosmic ...Sérgio Sacani
We characterize the earliest galaxy population in the JADES Origins Field (JOF), the deepest
imaging field observed with JWST. We make use of the ancillary Hubble optical images (5 filters
spanning 0.4−0.9µm) and novel JWST images with 14 filters spanning 0.8−5µm, including 7 mediumband filters, and reaching total exposure times of up to 46 hours per filter. We combine all our data
at > 2.3µm to construct an ultradeep image, reaching as deep as ≈ 31.4 AB mag in the stack and
30.3-31.0 AB mag (5σ, r = 0.1” circular aperture) in individual filters. We measure photometric
redshifts and use robust selection criteria to identify a sample of eight galaxy candidates at redshifts
z = 11.5 − 15. These objects show compact half-light radii of R1/2 ∼ 50 − 200pc, stellar masses of
M⋆ ∼ 107−108M⊙, and star-formation rates of SFR ∼ 0.1−1 M⊙ yr−1
. Our search finds no candidates
at 15 < z < 20, placing upper limits at these redshifts. We develop a forward modeling approach to
infer the properties of the evolving luminosity function without binning in redshift or luminosity that
marginalizes over the photometric redshift uncertainty of our candidate galaxies and incorporates the
impact of non-detections. We find a z = 12 luminosity function in good agreement with prior results,
and that the luminosity function normalization and UV luminosity density decline by a factor of ∼ 2.5
from z = 12 to z = 14. We discuss the possible implications of our results in the context of theoretical
models for evolution of the dark matter halo mass function.
Slide 1: Title Slide
Extrachromosomal Inheritance
Slide 2: Introduction to Extrachromosomal Inheritance
Definition: Extrachromosomal inheritance refers to the transmission of genetic material that is not found within the nucleus.
Key Components: Involves genes located in mitochondria, chloroplasts, and plasmids.
Slide 3: Mitochondrial Inheritance
Mitochondria: Organelles responsible for energy production.
Mitochondrial DNA (mtDNA): Circular DNA molecule found in mitochondria.
Inheritance Pattern: Maternally inherited, meaning it is passed from mothers to all their offspring.
Diseases: Examples include Leber’s hereditary optic neuropathy (LHON) and mitochondrial myopathy.
Slide 4: Chloroplast Inheritance
Chloroplasts: Organelles responsible for photosynthesis in plants.
Chloroplast DNA (cpDNA): Circular DNA molecule found in chloroplasts.
Inheritance Pattern: Often maternally inherited in most plants, but can vary in some species.
Examples: Variegation in plants, where leaf color patterns are determined by chloroplast DNA.
Slide 5: Plasmid Inheritance
Plasmids: Small, circular DNA molecules found in bacteria and some eukaryotes.
Features: Can carry antibiotic resistance genes and can be transferred between cells through processes like conjugation.
Significance: Important in biotechnology for gene cloning and genetic engineering.
Slide 6: Mechanisms of Extrachromosomal Inheritance
Non-Mendelian Patterns: Do not follow Mendel’s laws of inheritance.
Cytoplasmic Segregation: During cell division, organelles like mitochondria and chloroplasts are randomly distributed to daughter cells.
Heteroplasmy: Presence of more than one type of organellar genome within a cell, leading to variation in expression.
Slide 7: Examples of Extrachromosomal Inheritance
Four O’clock Plant (Mirabilis jalapa): Shows variegated leaves due to different cpDNA in leaf cells.
Petite Mutants in Yeast: Result from mutations in mitochondrial DNA affecting respiration.
Slide 8: Importance of Extrachromosomal Inheritance
Evolution: Provides insight into the evolution of eukaryotic cells.
Medicine: Understanding mitochondrial inheritance helps in diagnosing and treating mitochondrial diseases.
Agriculture: Chloroplast inheritance can be used in plant breeding and genetic modification.
Slide 9: Recent Research and Advances
Gene Editing: Techniques like CRISPR-Cas9 are being used to edit mitochondrial and chloroplast DNA.
Therapies: Development of mitochondrial replacement therapy (MRT) for preventing mitochondrial diseases.
Slide 10: Conclusion
Summary: Extrachromosomal inheritance involves the transmission of genetic material outside the nucleus and plays a crucial role in genetics, medicine, and biotechnology.
Future Directions: Continued research and technological advancements hold promise for new treatments and applications.
Slide 11: Questions and Discussion
Invite Audience: Open the floor for any questions or further discussion on the topic.
Toxic effects of heavy metals : Lead and Arsenicsanjana502982
Heavy metals are naturally occuring metallic chemical elements that have relatively high density, and are toxic at even low concentrations. All toxic metals are termed as heavy metals irrespective of their atomic mass and density, eg. arsenic, lead, mercury, cadmium, thallium, chromium, etc.
The ability to recreate computational results with minimal effort and actionable metrics provides a solid foundation for scientific research and software development. When people can replicate an analysis at the touch of a button using open-source software, open data, and methods to assess and compare proposals, it significantly eases verification of results, engagement with a diverse range of contributors, and progress. However, we have yet to fully achieve this; there are still many sociotechnical frictions.
Inspired by David Donoho's vision, this talk aims to revisit the three crucial pillars of frictionless reproducibility (data sharing, code sharing, and competitive challenges) with the perspective of deep software variability.
Our observation is that multiple layers — hardware, operating systems, third-party libraries, software versions, input data, compile-time options, and parameters — are subject to variability that exacerbates frictions but is also essential for achieving robust, generalizable results and fostering innovation. I will first review the literature, providing evidence of how the complex variability interactions across these layers affect qualitative and quantitative software properties, thereby complicating the reproduction and replication of scientific studies in various fields.
I will then present some software engineering and AI techniques that can support the strategic exploration of variability spaces. These include the use of abstractions and models (e.g., feature models), sampling strategies (e.g., uniform, random), cost-effective measurements (e.g., incremental build of software configurations), and dimensionality reduction methods (e.g., transfer learning, feature selection, software debloating).
I will finally argue that deep variability is both the problem and solution of frictionless reproducibility, calling the software science community to develop new methods and tools to manage variability and foster reproducibility in software systems.
Exposé invité Journées Nationales du GDR GPL 2024
Deep Software Variability and Frictionless Reproducibility
Dynamics and global stability of three-dimensional flows
1. Introduction Global stability theory Roughness-induced transition Conclusion
Dynamics and global stability analysis of
three-dimensional flows
Jean-Christophe Loiseau1,2
supervisor: Jean-Christophe Robinet1
co-supervisor: Emmanuel Leriche2
(1): DynFluid Laboratory - Arts & M´etiers-ParisTech - 75013 Paris, France
(2): LML - University of Lille 1 - 59655 Villeneuve d’Ascq, France
PhD Defence, May 26th 2014
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2. Introduction Global stability theory Roughness-induced transition Conclusion
What are hydrodynamic instabilities?
• Let us consider the flow of water (ν = 15.10−6 m2.s−1) past a
two-dimensional cylinder of diameter D = 1.5 cm.
• If water flows from left to right at U = 4.5 cm.s−1 (Re = 45),
nothing really fancy takes place: the flow is steady and stable.
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3. Introduction Global stability theory Roughness-induced transition Conclusion
What are hydrodynamic instabilities?
• If you increase the velocity to U = 5 cm.s−1 (Re = 50), the flow
looks very different.
• The steady flow became (globally) unstable and has experienced a
(supercritical) bifurcation.
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4. Introduction Global stability theory Roughness-induced transition Conclusion
How do we study these instabilities?
• Let us consider a non-linear dynamical system
B
∂Q
∂t
= F(Q) (1)
1. Compute a fixed point (or base flow): F(Qb) = 0
2. Linearise the dynamics of an infinitesimal perturbation q in the vicinity
of this solution:
B
∂q
∂t
= Jq with J =
∂F
∂q
(2)
3. Investigate the stability properties of this linear dynamical system.
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5. Introduction Global stability theory Roughness-induced transition Conclusion
How do we study these instabilities?
• In the context of fluid dynamics, this includes several different
approaches depending on the nature of the base flow:
• Local stability analysis for parallel flows:
֒→ Temporal stability, Spatial stability, Absolute/Convective stability,
Response to harmoning forcing, Transient growth
• Global stability analysis for two-dimensional and three-dimensional
flows:
֒→ Temporal stability, Response to harmoning forcing (Resolvent),
Transient growth
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6. Introduction Global stability theory Roughness-induced transition Conclusion
Local stability analysis
• The base flow depends on a single space coordinate:
Ub = (Ub(y), 0, 0)T
• Linear dynamical system (2) is now autonomous in time and in the x
and z coordinates of space.
֒→ The perturbation q can be decomposed into normal modes:
q(x, y, z, t) = ˆq(y) exp(iαx + iβz + λt) + c.c with λ = σ + iω
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7. Introduction Global stability theory Roughness-induced transition Conclusion
Local stability analysis
• Introducing such decomposition into the system (2) yields to a
generalised eigenvalue problem:
λBˆq = J(y, α, β)ˆq (3)
• The stability of the base flow Ub is governed by the growth rate σ:
֒→ If σ < 0, the base flow is said to be locally stable.
֒→ If σ > 0, the base flow is said to be locally unstable.
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8. Introduction Global stability theory Roughness-induced transition Conclusion
Local stability analysis
Theoretical point of view
• Relies on the parallel flow assumption.
• Provides insights into the local stability properties of the flow.
֒→ Requires a good theoretical and mathematical background.
Practical point of view
• The generalised eigenproblem involves small matrices (∼ 100 × 100)
• Can be solved using direct eigenvalue solvers in a matter of seconds
even on a 10 years old laptop.
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9. Introduction Global stability theory Roughness-induced transition Conclusion
Global stability theory
• The base flow has two components both depending on the x and y
space coordinates:
Ub = (Ub(x, y), Vb(x, y), 0)T
• Linear dynamical system (2) is now only autonomous in time and in
z.
֒→ The perturbation q can be decomposed into normal modes:
q(x, y, z, t) = ˆq(x, y) exp(iβz + λt) + c.c with λ = σ + iω
Base flow of the 2D separated boundary layer at Re = 600 as in Ehrenstein & Gallaire (2008).
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10. Introduction Global stability theory Roughness-induced transition Conclusion
Global stability theory
• Introducing such decomposition into the system (2) yields to a
generalised eigenvalue problem once again:
λBˆq = J(x, y, β)ˆq (4)
• The stability of the base flow Ub is governed by the growth rate σ:
֒→ If σ < 0, the base flow is said to be globally stable.
֒→ If σ > 0, the base flow is said to be globally unstable.
Streamwise velocity component of the leading unstable global mode for the 2D separated boundary layer.
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11. Introduction Global stability theory Roughness-induced transition Conclusion
Global stability analysis
Theoretical point of view
• Got rid of the parallel flow assumption.
• Allows to investigate more realistic configurations as separated flows
very common in Nature and industries.
Practical point of view
• The generalised eigenproblem involves relatively large matrices
(∼ 105 × 105)
• Mostly solved using iterative eigenvalue solvers on large workstations.
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12. Introduction Global stability theory Roughness-induced transition Conclusion
Objectives
• Bagheri et al. (2008) and Ilak et al. (2012) performed the first global
stability analysis ever on a 3D flow (jet in crossflow).
• Extension of the global stability tools to a fully three-dimensional
framework.
֒→ Mostly a numerical problem due to the (extremely) large matrices
involved.
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13. Introduction Global stability theory Roughness-induced transition Conclusion
Objectives
λ2 visualisation of the hairpin vortices shed behind a hemispherical roughness element. Courtesy of P. Fischer.
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14. Introduction Global stability theory Roughness-induced transition Conclusion
Context
• PhD thesis part of a larger project: Simulation and Control of
Geometrically Induced Flows (SICOGIF)
֒→ Funded by the French National Agency for Research (ANR)
֒→ Involves several different parties (IRPHE, EPFL, Arts et M´etiers
ParisTech and Universit´e Lille-1)
֒→ Aims at improving our understanding of instability and transition in
complex 2D and 3D separated flows both from an experimental and
numerical point of view.
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15. Introduction Global stability theory Roughness-induced transition Conclusion
Context
• Three flow configurations have been investigated:
֒→ The lid-driven cavity flow
֒→ The asymmetric stenotic pipe flow
֒→ The roughness-induced boundary layer flow
Vertical velocity component of the leading global mode for a LDC having a spanwise extent Λ = 6 at Re = 900.
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16. Introduction Global stability theory Roughness-induced transition Conclusion
Context
• Three flow configurations have been investigated:
֒→ The lid-driven cavity flow
֒→ The asymmetric stenotic pipe flow
֒→ The roughness-induced boundary layer flow
Streamwise velocity component for the two existing steady states of an asymmetric stenotic pipe flow at Re = 400.
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17. Introduction Global stability theory Roughness-induced transition Conclusion
Context
• Three flow configurations have been investigated:
֒→ The lid-driven cavity flow
֒→ The asymmetric stenotic pipe flow
֒→ The roughness-induced boundary layer flow
Identification of the vortical structures by the λ2 criterion (Jeong & Hussain 1995).
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18. Introduction Global stability theory Roughness-induced transition Conclusion
Introduction
Global stability theory and algorithm
Base flows
Global stability theory
How to solve the eigenvalue problem?
Roughness-induced transition
Motivations
Fransson 2005 experiment
Parametric investigation
Physical analysis
Non-linear evolution
Conclusions & Perspectives
Conclusions
LDC & Stenosis
Perspectives
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19. Introduction Global stability theory Roughness-induced transition Conclusion
Global stability analysis of
three-dimensional flows
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20. Introduction Global stability theory Roughness-induced transition Conclusion
How to compute base flows?
• Base flow are given by:
F(Qb) = 0 (5)
• Various techniques can be employed to compute these peculiar
solutions:
֒→ Analytical solutions, impose appropriate symmetries, Newton and
quasi-Newton methods, ...
• In the present work, we use the Selective frequency damping
approach (see Akervik et al. 2006).
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21. Introduction Global stability theory Roughness-induced transition Conclusion
Selective frequency damping
• Enables the stabilisation of the solution by applying a low-pass filter
to the Navier-Stokes equations.
֒→ A forcing term is added to the r.h.s of the equations.
֒→ The system is extended with an equation for the filtered state.
∂Q
∂t
= F(Q) + χ(Q − ¯Q)
∂ ¯Q
∂t
= ωc(Q − ¯Q)
(6)
• The cutoff frequency ωc is connected to the frequency of the most
dominant instabilities and should be smaller than this frequency
(ωc < ω).
• The gain χ needs to be large enough to stabilise the system (χ > σ).
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22. Introduction Global stability theory Roughness-induced transition Conclusion
Selective frequency damping
Pros
→ Really easy to implement within
an existing DNS code.
→ Memory footprint similar to that
of a simple direct numerical
simulation.
→ Easy to use/tune the low-pass
filter.
Cons
→ As time-consuming as a direct
numerical simulation.
→ Requires a priori information
regarding the instability of the
flow.
→ Unable to stabilise the system if
the instability is non-oscillating.
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23. Introduction Global stability theory Roughness-induced transition Conclusion
Global stability theory
• Dynamics of a three-dimensional infinitesimal perturbation
q = (u, p)T evolving onto the base flow Qb = (Ub, Pb)T are
governed by:
∂u
∂t
= −(u · ∇)Ub − (Ub · ∇)u − ∇p +
1
Re
∆u
∇ · u = 0
(7)
• If projected onto a divergence-free vector space, this set of equations
can be recast into:
∂u
∂t
= Au (8)
with A the (projected) Jacobian matrix of the Navier-Stokes
equations.
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24. Introduction Global stability theory Roughness-induced transition Conclusion
Global stability theory
• Using a normal mode decomposition
u(x, y, z, t) = ˆu(x, y, z)e(σ+iω)t
+ c.c
• System (8) can be formulated as an eigenvalue problem
(σ + iω)ˆu = Aˆu (9)
• The sign of σ determines the stability of the base flow Ub:
֒→ If σ < 0, the base flow is said to be asymptoticaly linearly stable.
֒→ If σ > 0, the base flow is said to be asymptoticaly linearly unstable.
• ω determines whether the instability is oscillatory (ω = 0) or not
(ω = 0).
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25. Introduction Global stability theory Roughness-induced transition Conclusion
How to solve the eigenvalue problem?
• Depends on the dimension of the discretised problem.
Base Flow Inhomogeneous Dimension Storage
direction(s) of ˆu of A
Poiseuille U(y) 1D 102 ∼ 1 Mb
2D bump U(x, y) 2D 105 ∼ 1-50 Gb
3D bump U(x, y, z) 3D 107 ∼ 1-100 Tb
• For 3D global stability problem, A is so large that it cannot be
explicitely constructed.
Matrix-free approach is mandatory!
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26. Introduction Global stability theory Roughness-induced transition Conclusion
Time-stepping approach
• Time-stepping approach (Edwards et al. 1994, Bagheri et al. 2008) is
based on the formal solution to system (8):
u(∆t) = eA∆t
u0
• The operator M(∆t) = eA∆t is nothing but a matrix. Its application
on u0 can be computed by time-marching the linearised Navier-Stokes
equations.
֒→ Its stability properties can be investigated by eigenvalue analysis.
MˆU = ˆUΣ (10)
with ˆU the matrix of eigenvectors and Σ the eigenvalue matrix of
M = eA∆t.
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27. Introduction Global stability theory Roughness-induced transition Conclusion
Arnoldi algorithm
• The eigenvalue problem (10) is solved using an Arnoldi algorithm.
1. Given M and u0, construct a small Krylov subspace (compared to the
size of the initial problem),
Km(M, u0) = span u0, Mu0, M2
u0, · · · , M(m−1)
u0
2. Orthonormalize: U = [U1, · · · , Um]
3. Project operator M ≈ UHUT
−→ MUk = Uk Hk + rk eT
k
with Hk : upper Hessenberg matrix.
4. Solve small eigenvalue problem (ΣH , X): HX = XΣH, (m × m),
m < 1000
5. Link with the initial eigenproblem (ΛA, ˆu):
ΛA =
log(ΣH)
∆t
, ˆu = UX
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29. Introduction Global stability theory Roughness-induced transition Conclusion
Summary
• All calculations have been performed with the code Nek 5000
֒→ Legendre spectral elements code developed by P. Fischer at Argonne
National Laboratory.
֒→ Semi-implicit temporal scheme.
֒→ Massively parallel code based on an MPI strategy.
• Base flow computation
֒→ Selective frequency damping approach : application of a low-pass filter
to the fully non-linear Navier-Stokes equations (Akervik et al. 2006).
• Global stability analysis
֒→ Arnoldi algorithm similar to the one published by Barkley et al. (2008).
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31. Introduction Global stability theory Roughness-induced transition Conclusion
Motivations
• Roughness elements have numerous applications in aerospace
engineering:
֒→ Stabilisation of the Tollmien-Schlichting waves,
֒→ Shift and/or control of the transition location, ...
• Their influence on the flow has been extensively investigated since the
early 1950’s.
Experimental visualisation of the flow induced by a roughness element. Gregory & Walker, 1956.
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32. Introduction Global stability theory Roughness-induced transition Conclusion
Delay of the natural transition
• Cossu & Brandt (2004): Theoretical prediction of the stabilisation of
TS waves by streamwise streaks.
• Fransson et al. (2004-2006): Experimental demonstration using a
periodic array of roughness elements.
Schematic setup
Experimental observations
Figures from Fransson et al. (2006).
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33. Introduction Global stability theory Roughness-induced transition Conclusion
Roughness-induced transition
• Problem: If the Reynolds number is too high, transition occurs right
downstream the roughness elements!
Illustration of the early roughness-induced transition. λ2 visualisation of the vortical structures.
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34. Introduction Global stability theory Roughness-induced transition Conclusion
Roughness-induced transition
• Since the early 1950’s: Numerous experimental investigations.
֒→ Transition diagram by von Doenhoff & Braslow (1961).
• Despite the large body of literature, the underlying mechanisms are
not yet fully understood.
Transition diagram from von Doenhoff & Braslow (1961).
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35. Introduction Global stability theory Roughness-induced transition Conclusion
Motivations
• Methods used until now rely on a parallel flow assumption:
֒→ Local stability theory (Brandt 2006, Denissen & White 2013, ...),
֒→ Local transient growth theory (Vermeersch 2010, ...)
• Objective:
֒→ Might a 3D global instability of the flow explain the roughness-induced
transition?
֒→ If so, what are the underlying physical mechanisms?
• Methods:
֒→ Fully three-dimensional global stability analyses,
֒→ Direct numerical simulations,
֒→ Comparison with available experimental data.
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36. Introduction Global stability theory Roughness-induced transition Conclusion
Problem formulation
z X
y
d h
Lz
l
Lx
Ly
δ
0
Sketch of the computational arrangement and various scales used for DNS and stability analysis.
- (Lx , Ly , Lz ) = (105, 50, 8η)
- η = d/h = 1, 2, 3
- Re = Ueh/ν
- Reδ∗
= Ueδ∗/ν
- Inflow: Blasius profile,
- Outflow: ∇U · x = 0,
- Top: U = 1, ∂y V = ∂y W = 0,
- Wall: no-slip B.C.
- Lateral: periodic B.C.
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37. Introduction Global stability theory Roughness-induced transition Conclusion
Numerical informations
η Number of SEM Gridpoints (N = 6-12) Number of cores used
1 10 000 2-17.106 256
2 17 500 3.5-30.106 512
3 20 000 4.5-35.106 512
Typical size of the numerical problem investigated. N is the order of the Legendre polynomials used in the three directions
within each element.
Typical SEM distribution in a given horizontal plane. Full mesh with Legendre polynomials of order N = 8.
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38. Introduction Global stability theory Roughness-induced transition Conclusion
Roughness-induced transition
The Fransson 2005 experiment
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39. Introduction Global stability theory Roughness-induced transition Conclusion
Experimental setup
• Experimental demonstration of the ability for finite amplitude streaks
to stabilise TS waves.
• Unfortunately, transition takes place right downstream the array of
roughness elements if the Reynolds number is too high.
h D η Lz/h xk/h Rec
δ∗
1.4mm 4.2mm 3 10 57.14 ≃ 290
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40. Introduction Global stability theory Roughness-induced transition Conclusion
Base flow
(a)
(b)
• Upstream and downstream
reversed flow regions:
֒→ Induces a central low-speed
region.
• Vortical system stemming:
֒→ Investigated by Baker (1978)
֒→ Horseshoe vortices whose legs
are streamwise oriented
counter-rotating vortices.
֒→ Creation of streamwise
velocity streaks (lift-up effect)
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41. Introduction Global stability theory Roughness-induced transition Conclusion
Base flow
(a) X=20 (b) X=40 (c) X=60 (d) X=80
Visualisation of the base flow deviation from the Blasius boundary layer flow in various streamwise planes for Re = 466. High
speed streaks are in red while low-speed ones are in blue.
• Low-speed region generated by the roughness element’s blockage.
֒→ Fades away quite rapidly in the streamwise direction.
• High- and low-speed streaks on each side of the roughness element
due to the horshoe vortex.
֒→ Sustains over quite a long streamwise distance.
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42. Introduction Global stability theory Roughness-induced transition Conclusion
Global stability
Eigenspectrum of the linearised Navier-Stokes operator.
• Hopf bifurcation taking place in-between 550 < Rec < 575.
֒→ Linear interpolation: Rec = 564, i.e. Rec
δ∗
= 309.
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43. Introduction Global stability theory Roughness-induced transition Conclusion
Global stability
(a) Top view of u = ±10% iso-surfaces
(b) X = 23 (c) X = 40
Visualisation of streamwise velocity component of the leading unstable mode for Re = 575.
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44. Introduction Global stability theory Roughness-induced transition Conclusion
Global stability
• Leading unstable mode exhibits a varicose symmetry:
֒→ Streamwise alternated patches of positive and negative velocity mostly
localised along the central low-speed region.
֒→ Non-linear DNS have revealed that it gives birth to hairpin vortices.
• Rec predicted by global stability analysis only 6% larger than the
experimental one from Fransson et al. (2005):
֒→ Global instability of the flow appears as one of the possible
explanations to roughness-induced transition.
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45. Introduction Global stability theory Roughness-induced transition Conclusion
Roughness-induced transition
Parametric investigation
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46. Introduction Global stability theory Roughness-induced transition Conclusion
Parametric investigation
• Aims of the parametric investigation:
֒→ How do the Reynolds number and the aspect ratio of the roughness
elements impact the base flow and its stability properties?
֒→ Does the leading unstable mode always exhibit a varicose symmetry?
• To do so:
֒→ The spanwise extent of the domain is taken large enough so that the
roughness element behaves as being isolated.
֒→ δ99/h is set to 2 to isolate the influence of the Reynolds number only.
֒→ The roughness element’s aspect ratio varies from η = 1 up to η = 3.
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47. Introduction Global stability theory Roughness-induced transition Conclusion
Base flows
(a) (Re, η) = (600, 1) (b) (Re, η) = (1250, 1)
Influence of the Reynolds number on the flow within the z = 0 plane. Streamwise velocity iso-contours ranging from U = 0.1
up to U = 0.99.
• Influence of the Reynolds number:
֒→ Does not qualitatively change the shape of the downstream reversed
flow region.
֒→ Strengthen the gradients and reduces the thickness of the shear layer.
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48. Introduction Global stability theory Roughness-induced transition Conclusion
Base flows
(a) (Re, η) = (600, 1)
(b) (Re, η) = (1250, 1)
Top view of the low-speed (white) and high-speed (black) streaks induced by the roughness element. Streak have been
identified using the deviation of the base flow streamwise velocity from the Blasius boundary layer flow.
• Influence of the Reynolds number:
֒→ Strongly increases the amplitude and the streamwise extent of the
central low-speed region.
֒→ Slightly increases the amplitude of the outer velocity streaks.
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49. Introduction Global stability theory Roughness-induced transition Conclusion
Base flows
(a) (Re, η) = (600, 2) (b) (Re, η) = (600, 3)
Influence of the aspect ratio on the flow within the z = 0 plane. Streamwise velocity iso-contours ranging from U = 0.1 up to
U = 0.99.
• Influence of the aspect ratio:
֒→ Strengthen the gradients and reduces the thickness of the shear layer.
֒→ Strongly increases the amplitude and the streamwise extent of the
central low-speed region.
֒→ Strongly increases the amplitude of the outer velocity streaks.
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50. Introduction Global stability theory Roughness-induced transition Conclusion
Base flows
(a) (Re, η) = (600, 2)
(b) (Re, η) = (600, 3)
Top view of the low-speed (white) and high-speed (black) streaks induced by the roughness element. Streak have been
identified using the deviation of the base flow streamwise velocity from the Blasius boundary layer flow.
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52. Introduction Global stability theory Roughness-induced transition Conclusion
Global stability
(a) (Re, η) = (1200, 1)
(b) (Re, η) = (900, 2)
Evolution of the leading unstable mode when the roughness element’s aspect ratio is changed from η = 1 to η = 2. Isosurfaces
u = ± 10% of the modes streamwise velocity component.
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53. Introduction Global stability theory Roughness-induced transition Conclusion
Global stability
(a) (Re, η) = (1200, 1) (b) (Re, η) = (900, 2)
Evolution of the leading unstable mode when the roughness element’s aspect ratio is changed from η = 1 to η = 2 in the
X = 25 plane.
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54. Introduction Global stability theory Roughness-induced transition Conclusion
Global stability
• Increasing the roughness element’s aspect ratio decreases the critical
Reynolds number.
η 1 2 3 Fransson (η = 3)
Rec 1040 850 656 564
Rec
h 813 630 513 519
Symmetry S V V V
Summary of the global stability analyses. V: varicose, S: sinuous. Reh is the roughness Reynolds number.
• Exchange of symmetry in qualitative agreements with Sakamoto &
Arie (1983) and Beaudoin (2004).
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55. Introduction Global stability theory Roughness-induced transition Conclusion
Roughness-induced transition
Physical analysis
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56. Introduction Global stability theory Roughness-induced transition Conclusion
Physical analysis
• Aims of the analysis:
֒→ Unravel the underlying physical mechanisms for each mode.
֒→ How and where do they extract their energy?
֒→ Where do they originate?
• Type of analysis:
֒→ Kinetic energy transfer between the base flow and the perturbation
(Brandt 2006).
֒→ Computation of the wavemaker region (Giannetti & Luchini 2007).
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57. Introduction Global stability theory Roughness-induced transition Conclusion
Kinetic energy budget
• The evolution of the perturbation’s kinetic energy is governed by the
Reynolds-Orr equation:
∂E
∂t
= −D +
9
i=1 V
Ii dV (11)
• with the total kinetic energy E and dissipation D given by:
E =
1
2 V
u · u dV , and D =
1
Re V
∇u : ∇u dV (12)
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58. Introduction Global stability theory Roughness-induced transition Conclusion
Kinetic energy budget
• The integrands Ii representing the different production terms are
given by:
I1 = −u2 ∂Ub
∂x
, I2 = −uv
∂Ub
∂y
, I3 = −uw
∂Ub
∂z
I4 = −uv
∂Vb
∂x
, I5 = −v2 ∂Vb
∂y
, I6 = −vw
∂Vb
∂z
I7 = −wu
∂Wb
∂x
, I8 = −wv
∂Wb
∂y
, I9 = −w2 ∂Wb
∂z
(13)
• Their sign indicates whether the associated local transfer of kinetic
energy acts as stabilising (negative) or destabilising (positive).
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59. Introduction Global stability theory Roughness-induced transition Conclusion
Kinetic energy budget: Sinuous mode
0
0.5
1
I1 I2 I3 I4 I5 I6 I7 I8 I9 D
(a) (Re, η) = (1125, 1)
0
0.5
1
I1 I2 I3 I4 I5 I6 I7 I8 I9 D
(b) (Re, η) = (1250, 1)
X0 30 60 90
2.0x10
-03
4.0x10
-03
6.0x10
-03
∫I2dydz
∫I3dydz
(c) (Re, η) = (1125, 1)
X0 30 60 90
2.0x10
-03
4.0x10
-03
6.0x10
-03
∫I2dydz
∫I3dydz
(d) (Re, η) = (1250, 1)
Top: Sinuous unstable mode’s kinetic energy budget integrated over the whole domain. Bottom: Streamwise evolution of the
production terms y,z I2 dydz (red dashed line) and y,z I3 dydz (blue solid line).
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60. Introduction Global stability theory Roughness-induced transition Conclusion
Kinetic energy budget: Sinuous mode
(a) I2 = −uv∂U/∂y (b) I3 = −uw∂U/∂z
Spatial distribution of the I2 = −uv∂Ub/∂y (a) and I3 = −uw∂Ub/∂z (b) production terms in the plane x = 25 for
(Re, η) = (1125, 1). Solid lines depict the base flows streamwise velocity isocontours from Ub = 0.1 to 0.99, whereas the red
dashed lines stand for the location of the shear layer.
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61. Introduction Global stability theory Roughness-induced transition Conclusion
Kinetic energy budget: Sinuous mode
(a) I2 = −uv∂U/∂y
(b) I3 = −uw∂U/∂z
Spatial distribution of I2 (c) and I3 (d) in the y = 0.75 horizontal plan.
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62. Introduction Global stability theory Roughness-induced transition Conclusion
Kinetic energy budget: Varicose mode
0
1
2
I1 I2 I3 I4 I5 I6 I7 I8 I9 D
(a) (Re, η) = (850, 2)
0
1
2
I1 I2 I3 I4 I5 I6 I7 I8 I9 D
(b) (Re, η) = (1000, 2)
X0 30 60 90
.0x10
+00
4.0x10
-03
8.0x10
-03
∫I2dydz
∫I3dydz
(c) (Re, η) = (850, 2)
X0 30 60 90
.0x10
+00
4.0x10
-03
8.0x10
-03
∫I2dydz
∫I3dydz
(d) (Re, η) = (1000, 2)
Top: Varicose unstable mode’s kinetic energy budget integrated over the whole domain. Bottom: Streamwise evolution of the
production terms y,z I2 dydz (red dashed line) and y,z I3 dydz (blue solid line).
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63. Introduction Global stability theory Roughness-induced transition Conclusion
Kinetic energy budget: Varicose mode
(a) I2 = −uv∂U/∂y (b) I3 = −uw∂U/∂z
Spatial distribution of the I2 = −uv∂Ub/∂y (a) and I3 = −uw∂Ub/∂z (b) production terms in the plane x = 25 for
(Re, η) = (850, 2). Solid lines depict the base flows streamwise velocity isocontours from Ub = 0.1 to 0.99, whereas the red
dashed lines stand for the location of the shear layer.
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64. Introduction Global stability theory Roughness-induced transition Conclusion
Kinetic energy budget: Varicose mode
Spatial distribution of the I3 = −uw∂Ub/∂z production term in the plane y = 0.5 for (Re, η) = (850, 2).
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65. Introduction Global stability theory Roughness-induced transition Conclusion
Wavemaker
• Kinetic energy budgets provide valuable insights into the mode’s
dynamics but very limited about its core region, i.e. the wavemaker.
• Defined by Giannetti & Luchini (2007) as the overlap of the direct
global mode u and its adjoint u†:
ζ(x, y, z) =
u† u
u†, u
(14)
• Allows the identification of the most likely region for the inception of
the global instability under consideration.
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66. Introduction Global stability theory Roughness-induced transition Conclusion
Wavemaker
Figure: Sinuous wavemaker in the y = 0.75 plane.
Figure: Varicose wavemaker in the z = 0 plane.
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67. Introduction Global stability theory Roughness-induced transition Conclusion
Wavemaker
Figure: Sinuous wavemaker in the y = 0.75 plane.
Figure: Varicose wavemaker in the z = 0 plane.
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68. Introduction Global stability theory Roughness-induced transition Conclusion
Wavemaker
• Sinuous wavemaker:
֒→ Exclusively localised within the spatial extent of the downstream
reversed flow region.
֒→ Shares close connections with the von K´arm´an global instability in the
2D cylinder flow (Giannetti & Luchini 2007, Marquet et al. 2008).
• Varicose wavemaker:
֒→ Localised on the top of the central low-speed region shear layer.
֒→ Quite extended in the streamwise direction.
֒→ Yet, its amplitude in the reversed flow region is almost ten times larger
than its amplitude in the wake.
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69. Introduction Global stability theory Roughness-induced transition Conclusion
Sinuous instability mechanism
What we know from local stability
approaches?
• Central low-speed region can
sustain local convective
instabilities (Brandt 2006).
• Related to the work of the
Reynolds stresses against the
wall-normal and spanwise
gradients of Ub.
• Not the dominant local
instability though.
What global stability analyses
revealed?
• Existence of a global sinuous
instability.
• Related to the downstream
reversed flow region.
• Similar to the von K´arm´an
instability in the 2D cylinder
flow.
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70. Introduction Global stability theory Roughness-induced transition Conclusion
Varicose instability mechanism
What we know from local stability
approaches?
• Central low-speed region can
sustain local convective
instabilities (Brandt 2006,
Denissen & White 2013).
• Related to the work of the
Reynolds stresses against the
wall-normal gradient of Ub.
• Dominant local instability and
possible large transient growth
(Vermeersch 2010)
What global stability analyses
revealed?
• Existence of a global varicose
instability.
• Find its roots in the reversed
flow region.
• Mechanism might be similar to
the one proposed by Acarlar &
Smith (1987).
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71. Introduction Global stability theory Roughness-induced transition Conclusion
Roughness-induced transition
Non-linear evolution
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72. Introduction Global stability theory Roughness-induced transition Conclusion
Non-linear evolution
• Varicose instability
֒→ Induces a varicose modulation of the central low-speed region and
surrounding streaks.
֒→ Numerous hairpin vortices are shed right downstream the roughness
element and trigger very rapid transition to turbulence.
֒→ Dominant frequency and wavelength of this vortex shedding is well
captured by global stability analyses.
Streamwise velocity distribution in the y = 0.5 plane for (Re, η) = (575, 3).
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73. Introduction Global stability theory Roughness-induced transition Conclusion
Non-linear evolution
• Varicose instability
֒→ Induces a varicose modulation of the central low-speed region and
surrounding streaks.
֒→ Numerous hairpin vortices are shed right downstream the roughness
element and trigger very rapid transition to turbulence.
֒→ Dominant frequency and wavelength of this vortex shedding is well
captured by global stability analyses.
Identification of the vortical structures by the λ2 criterion (Jeong & Hussain 1995).
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74. Introduction Global stability theory Roughness-induced transition Conclusion
Non-linear evolution
• Sinuous instability
֒→ Induces a sinuous wiggling of the central low-speed region (Beaudoin
2004, Duriez et al. 2009).
֒→ Frequency of this sinuous wiggling well captured by global stability
analysis.
֒→ Hairpin vortices are nonetheless observed to be shed downstream the
roughness element..
Streamwise velocity distribution in the y = 0.5 plane for (Re, η) = (1125, 1).
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75. Introduction Global stability theory Roughness-induced transition Conclusion
Non-linear evolution
• Sinuous instability
֒→ Induces a sinuous wiggling of the central low-speed region (Beaudoin
2004, Duriez et al. 2009).
֒→ Frequency of this sinuous wiggling well captured by global stability
analysis
֒→ Hairpin vortices are nonetheless observed to be shed downstream the
roughness element..
Identification of the vortical structures by the λ2 criterion (Jeong & Hussain 1995).
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76. Introduction Global stability theory Roughness-induced transition Conclusion
Non-linear evolution
• Sinuous instability
֒→ Monitoring the amplitude of the spanwise velocity in the central
mid-plane revealed the bifurcation is supercritical.
−20 0 20 40 60 80 100
−0.1
−0.05
0
0.05
0.1
ε=Re−Rec
Amplitude
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78. Introduction Global stability theory Roughness-induced transition Conclusion
Conclusion
• Sinuous instability
֒→ Dominant instability for low aspect ratio roughness elements.
֒→ von K´arm´an-like global instability of the reversed flow region.
֒→ Vortices shed from this region then experiences weak spatial transient
growth.
֒→ The creation of hairpin vortices by sinuous global instability is not yet
understood.
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79. Introduction Global stability theory Roughness-induced transition Conclusion
Conclusion
• Varicose instability
֒→ Dominant instability for large aspect ratio roughness elements.
֒→ Mechanism similar to the one proposed by Acarlar & Smith (1987).
֒→ Triggers rapid transition to a turbulent-like state by promoting the
creation of hairpin vortices.
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80. Introduction Global stability theory Roughness-induced transition Conclusion
Conclusion
• Critical roughness Reynolds numbers and observations from DNS in
qualitatively good agreements with the transition diagram by von
Doenhoff & Braslow (1961).
֒→ Three-dimensional global instability of the flow appears as one of
the possible explanations to roughness-induced transition.
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81. Introduction Global stability theory Roughness-induced transition Conclusion
Lid-driven cavity flow
• Same instability mechanism as
before:
֒→ Centrifugal instability of the
primary vortex core.
• For large LDC, Rec in good
agreements with predictions
from 2.5D stability analysis.
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82. Introduction Global stability theory Roughness-induced transition Conclusion
Lid-driven cavity flow
• DNS revealed bursts of kinetic energy related to intermittent chaotic
dynamics.
֒→ Koopman modes decomposition suggests it would type-2 intermittent
chaos (Pomeau & Manneville 1980).
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83. Introduction Global stability theory Roughness-induced transition Conclusion
Stenotic pipe flow
• Asymmetry of the stenosis triggers the wall-reattachment at lower Re
compared to the axisymmetric case.
• Existence of a hysteresis cycle related to a subcritical pitchfork
bifurcation.
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84. Introduction Global stability theory Roughness-induced transition Conclusion
Stenotic pipe flow
• Nonetheless, predictions from global stability analyses are
uncorelatted to the experimental observations (Passaggia et al.)
֒→ Transition is dominated by transient growth.
• Preliminary optimal perturbation analysis appears to be more
conclusive.
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85. Introduction Global stability theory Roughness-induced transition Conclusion
Perspectives
• Several questions are still unanswered and require further in-depth
investigations:
֒→ What is the mechanism responsible for the creation of hairpin vortices
in the sinuous case?
֒→ Is the varicose bifurcation super- or subcritical?
֒→ How does global optimal perturbation influence these transition
scenarii? Can they trigger subcritical transition to turbulence?
֒→ How does the shape of the roughness element impact the stability
properties of the flow?
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86. Introduction Global stability theory Roughness-induced transition Conclusion
Perspectives
• How to answer these questions?
֒→ More direct numerical simulations!
֒→ Non-linear analyses of these DNS (Koopman modes decomposition,
POD, statistical analysis, ...).
֒→ Linear and non-linear transient growth analysis.
֒→ Conduct similar investigations for smooth bumps and hemispherical
roughness elements to assess the robustness of these results.
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