1) Removing eddy-eddy interactions in a dry GCM causes the eddy momentum flux maximum to shift downward away from the upper troposphere, indicating these interactions are important for concentrating flux in the upper troposphere.
2) Restoring only barotropic triad interactions in the reduced model is enough to recover the upper troposphere flux maximum.
3) Baroclinic wave lifecycle experiments show the importance of eddy-eddy interactions, particularly near critical layers, for vorticity rearrangement and mixing that enhances the upper troposphere flux.
Atmospheric flows are governed by the equations of fluid dynamics. These equations are nonlinear. But because atmospheric flows are inhomogeneous and anisotropic, the nonlinearity may manifest itself only weakly through interactions of non-trivial mean flows with disturbances or eddies. In such situations, the quasi-linear (QL) approximation, that retains eddy-mean flow interactions but neglect eddy-eddy interactions, hold promise in resolving large-scale atmospheric dynamics. The statistics of the QL system corresponds to closing the hierarchy of statistical moments at the second order.
Hence, exploring QL dynamics paves the way for the development of direct statistical simulations of geophysical flows.
Using a hierarchy of idealized general circulation models, we identify when the QL approximation captures large-scale dynamics. We show that the QL dynamics fails to capture the flow when the dissipation of large-scale eddies occurs through strongly nonlinear eddy-eddy interactions in upper tropospheric surf zones, as it is often the case on Earth. But we demonstrate that the QL approximation captures eddy absorption when it arises from the shearing by the mean flow, for example when the eddy amplitude is small enough or the planetary rotation rate is large enough.
These results illustrate different classes of nonlinear processes that can control wave dissipation in the upper troposphere and show that in some parameter regimes the QL approximation is accurate to resolve large-scale dynamics.
ALMA will deliver exciting opportunities to advance our understanding of solar prominences and filaments, and constrain models of prominence fine structures.
WaReS is a code developed by Marine Analytica to calculate loads and responses of floating structures. This memo presents an extract of the verification report.
Atmospheric flows are governed by the equations of fluid dynamics. These equations are nonlinear. But because atmospheric flows are inhomogeneous and anisotropic, the nonlinearity may manifest itself only weakly through interactions of non-trivial mean flows with disturbances or eddies. In such situations, the quasi-linear (QL) approximation, that retains eddy-mean flow interactions but neglect eddy-eddy interactions, hold promise in resolving large-scale atmospheric dynamics. The statistics of the QL system corresponds to closing the hierarchy of statistical moments at the second order.
Hence, exploring QL dynamics paves the way for the development of direct statistical simulations of geophysical flows.
Using a hierarchy of idealized general circulation models, we identify when the QL approximation captures large-scale dynamics. We show that the QL dynamics fails to capture the flow when the dissipation of large-scale eddies occurs through strongly nonlinear eddy-eddy interactions in upper tropospheric surf zones, as it is often the case on Earth. But we demonstrate that the QL approximation captures eddy absorption when it arises from the shearing by the mean flow, for example when the eddy amplitude is small enough or the planetary rotation rate is large enough.
These results illustrate different classes of nonlinear processes that can control wave dissipation in the upper troposphere and show that in some parameter regimes the QL approximation is accurate to resolve large-scale dynamics.
ALMA will deliver exciting opportunities to advance our understanding of solar prominences and filaments, and constrain models of prominence fine structures.
WaReS is a code developed by Marine Analytica to calculate loads and responses of floating structures. This memo presents an extract of the verification report.
Simulation of Dispersion in a Heterogeneous Aquifer: Discussion of Steady ver...Amro Elfeki
). Simulation of Dispersion in a Heterogeneous Aquifer: Discussion of Steady versus Unsteady Groundwater Flow and Uncertainty analysis. International Symposium on Stochastic Hydraulics, Eds. Vrijling, J.K., Rurijgh, E., Stalenberg, B. Van Gelder, P.H.A.I.M., Verlaan, M., Zijderveld, A., and Waarts, papers on CD-ROM., 23-24, May, 2005. Nijmegen, The Netherlands. ISBN: 90-805649-9-0.
IOSR Journal of Applied Physics (IOSR-JAP) is an open access international journal that provides rapid publication (within a month) of articles in all areas of physics and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in applied physics. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Simulation of Dispersion in a Heterogeneous Aquifer: Discussion of Steady ver...Amro Elfeki
). Simulation of Dispersion in a Heterogeneous Aquifer: Discussion of Steady versus Unsteady Groundwater Flow and Uncertainty analysis. International Symposium on Stochastic Hydraulics, Eds. Vrijling, J.K., Rurijgh, E., Stalenberg, B. Van Gelder, P.H.A.I.M., Verlaan, M., Zijderveld, A., and Waarts, papers on CD-ROM., 23-24, May, 2005. Nijmegen, The Netherlands. ISBN: 90-805649-9-0.
IOSR Journal of Applied Physics (IOSR-JAP) is an open access international journal that provides rapid publication (within a month) of articles in all areas of physics and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in applied physics. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
The stable atmospheric boundary layer a challenge for wind turbine operatio...ndkelley
An overview presentation of the impact and challenge of the stable atmospheric boundary layer on wind turbine dynamics presented to AGU Fall Meeting 2008
Nwtc seminar overview of the impact of turbulence on turbine dynamics, sept...ndkelley
Overview presentation on the impact of atmospheric turbulence on the dynamic response of wind turbines derived from 20 years of research at the National Renewable Energy Laboratory.
These slides come to highlight the work of Jost von Hardenberg, Elisa Palazzi, Silvia Terzago and others in downscaling the projection of GCM in order to obtain very local statistics of climate suitable to be applied, for instance, at the scale of river Adige or its main tributaries.
RINA - AOG 2017 - Numerical Modelling of Marine Structure Behaviours in Steep...Nick Bentley
The interaction of steep waves with structures is still not fully
understood, and is of great importance for the design and operation of these structures. A particular difficulty with modelling such interaction lies in necessity of modelling the waves field in a large scale of about 20 kilometers during a seat state (about 3 hours) and nonlinear behaviours of the structures. This presentation will describe how we tackle the difficulty to obtain the results of large scale nonlinear wave fields, to
numerically calculate the wave loading on fixed structures, to simulate the responses of single and two floating bodies to steep waves, and to investigate the effects of sloshing on the motion of floating structures.
The presentation will also discuss the difference between nonlinear wave loadings on a structures moving with a forward speed and on the structure which is fixed but subjected to a current with a speed same as the forward speed when they are all in steep waves. The difference is an issue because the forward speed of a moving structure should not affect the incoming wave field but the current may alter the incoming waves if nonlinearity must be taken into account. This will lead to the difference in wave loadings even though the encountering frequency is the same. This issue has not been well understood so far but would be important for the problems involving steeps waves.
Directional Spreading Effect on a Wave Energy ConverterElliot Song
The results demonstrate the importance of tuning the WEC system for specific wave environments to harvest most energy and to avoid potential capsize due to hurricanes etc.
Energy Budget in Tunnel Fires – FFFS ConsiderationsWSP
Presentation delivered by Matthew Bilson and Katie McQuade from WSP | Parsons Brinckerhoff in the USA, on March 16, 2016 at the 7th International Symposium on Tunnel Safety and Security (ISTSS) held in Montreal, Canada.
Interannual and decadal variations of Antarctic ice shelves using multi-mission satellite radar altimetry, and links with oceanic and atmospheric forcings
1. On the vertical structure of the
tropospheric eddy momentum flux
Farid Ait Chaalal(1,3) and Tapio Schneider(2,3)
(1)Brown University, Providence, USA (2)ETH, Zurich, Switzerland
(3)Caltech, Pasadena, USA
19th Conference on Atmospheric and Oceanic Fluid Dynamics
17–21 June 2013, Newport, Rhode Island
2. Eddy momentum flux maximum in the upper troposphere
Held, 2000: upper level zonal mean flow favors linear wave
meridional propagation
Upper level enhancement not captured without nonlinear
saturation (Simmons and Hoskins, 1978; Merlis and Schneider,
2009)
10 6
m s 2
Motivation
Eddy momentum flux
convergence in the
atmosphere (colors), zonal
wind (contours, m/s) and
tropopause (grey line).
ERA 40 1980-2001
Latitude
Sigma
10
10
3030
−10
−60 −30 0 30 60
0.2
0.8
−50
0
50
10
20
20
0
0
3. Surface friction?
Large scale eddy-eddy interactions?
Outline
Why is eddy momentum flux concentrated in
the upper troposphere?
4. An idealized dry GCM
GFDL pseudospectral dynamical core
Radiation: Newtonian relaxation toward temperature
profile
Convection: relaxation of vertical lapse rate toward
0.7 ⨉ (dry adiabatic)
Uniform surface, no seasonal cycle
Run at T85 with 30 vertical sigma-levels
600 days average after 1400 days spin-up
(Schneider andWalker, 2006)
5. The role of surface friction
Colors: eddy momentum flux divergence
Contours and dashed lines: zonal mean flow (m/s)
Dotted line: potential temperature (K)
Grey line: tropopause (2K/km lapse rate)
Simulation with positive 90 K
pole-to-equator temperature
contrast ∆h.
Simulation with
negative ∆h = -90 K.
Poles heated, tropics cooled.
10 6
m s 2
LatitudeSigma
−10
−20
−30
−40 −40
300
320
350
−60 −30 0 30 60
0.2
0.8
−10
−5
0
5
10
Latitude
Sigma
30 30
10
10
20 20
300
320
350
−60 −30 0 30 60
0.2
0.8
−50
0
50
10 6
m s 2
6. Removal of eddy-eddy interactions
Quasi-linear (QL) model
(O’Gorman and Schneider, 2007)
Retained:
Wave-mean flow interaction (mean flow = zonal average)
Interaction of waves of opposite zonal wavenumber
(Reynolds stress)
Neglected:
All other eddy-eddy interactions
(Statistics equivalent to 2nd order cumulant expansion,
see Brad Marston’s talk)
8. Eddy Momentum Flux Divergence
Latitude
Sigma
30 30
10
10
20 20
300
320
350
−60 −30 0 30 60
0.2
0.8
−50
0
50
Colors:
eddy momentum
flux convergence
Contours:
zonal mean flow
(m/s)
Dotted lines:
potential
temperature (K)
Grey line:
tropopause
Eddy momentum flux convergence
Full
No
eddy-eddy
10 6
m s 2
9. Restoring barotropic triads
Latitude
Sigma
10
10
1010
40 40
300
320
350
−60 −30 0 30 60
0.2
0.8
−50
0
50
Latitude
Sigma
30 30
10
10
20 20
300
320
350
−60 −30 0 30 60
0.2
0.8
−50
0
50
10 6
m s 2
Colors:
eddy momentum
flux convergence
Contours:
zonal mean flow
(m/s)
Dotted lines:
potential
temperature (K)
Grey line:
tropopause
Full
With
barotropic
triads
10. Baroclinic wave lifecycle experiments
Initialize a zonal wavenumber 6 perturbation in the
zonally averaged circulation (fully non-linear model)
Experiments run with full model, no eddy-eddy model,
and model with only barotropic triads
Why eddy momentum flux not maximum in the
upper troposphere in the QL model ?
Why enhancement captured when barotropic triads
are restored?
Also: eddy kinetic energy larger in the QL model
usually, larger momentum flux expected
Removal of eddy-eddy interactions
11. 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75
−5
0
5
10
x 10
−5 full model
Days
W/kg
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75
−5
0
5
10
x 10
−5
Days
W/kg
only barotropic eddy−eddy
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75
−5
0
5
10
x 10
−5
Days
W/kg
no eddy−eddy
Baroclinic conversion.
Eddy available potential energy
to eddy kinetic energy
Barotropic conversion.
Zonal kinetic energy to
eddy kinetic energy
Full
No eddy-eddy Only barotropic eddy-eddy
Energy conversion
12. 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75
−5
0
5
10
x 10
−5
Days
W/kg
only barotropic eddy−eddy
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75
−5
0
5
10
x 10
−5
DaysW/kg
no eddy−eddy
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75
−5
0
5
10
x 10
−5 full model
Days
W/kg
Colors: QG potential vorticity flux
Contours: zonal mean flow (m/s)
Arrows: QG Eliassen-Palm vector
Full No eddy-eddy Only barotropic eddy-eddy
10 5
m s 2
Latitude Latitude Latitude
Sigma
Maximum
of barotropic conversion
13. 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75
−5
0
5
10
x 10
−5
Days
W/kg
only barotropic eddy−eddy
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75
−5
0
5
10
x 10
−5
DaysW/kg
no eddy−eddy
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75
−5
0
5
10
x 10
−5 full model
Days
W/kg
Sigma
Latitude Latitude Latitude
Minimum
of baroclinic conversion
Colors: QG potential vorticity flux
Contours: zonal mean flow (m/s)
Arrows: QG Elliassen-Palm vector
Full No eddy-eddy Only barotropic eddy-eddy
10 5
m s 2
14. Potential vorticity rearrangement and mixing
Days
W/kg
15 20 25 30 35
−5
0
5
10
x 10
Days
W/kg
15 20 25 30 35
−5
0
5
10
x 10
For a theoretical study of critical layers (SWW solution) in the QL approximation:
Haynes and McIntyre, 1987
Full
(350 K
isentrope)
No
eddy-eddy
(320 K
isentrope)
Day 26 Day 30 Day 35
Day 17 Day 22 Day 30
PV fields on isentropes
210
PVU
15. Potential vorticity rearrangement and mixing
Days
W/kg
15 20 25 30 35
−5
0
5
10
x 10
15 20 25 30 35
−5
0
5
10
x 10
−5
Days
W/kg
only barotropic eddy−eddy
No
eddy-eddy
(320 K
isentrope)
Only
barotropic
eddy-eddy
(320 K
isentrope)
Day 17 Day 22 Day 30
Day 25 Day 28 Day 32
PV fields on isentropes
210
PVU
16. Conclusions
Surface friction not an important factor
Wave packets generated in LT propagate upward until
they reach UT and tropopause, where horizontal
propagation is favored
Vorticity rearragement and mixing through eddy-eddy
interaction near critical layers essential
Keeping only barotropic triads captures the enhancement
Understanding nonlinear barotropic critical layer
dynamics might suffice
Why is eddy momentum flux concentrated in
the upper troposphere?
17. Conclusions
What still favors meridional propagation of waves in the upper-
troposphere? (tropopause as a wave guide? ...)
Index of refraction
for zonal wavenumber 6 baroclinic waves.
Latitude
Sigma
30
30
1010
−60 −30 0 30 60
0.2
0.8
0
5
10
15
20
Why is eddy momentum flux concentrated in the upper
troposphere?
Full
No
eddy-eddy
18. Dry GCM without eddy-eddy interactions
Removal of the eddy-eddy interactions (O’Gorman and Schneider,
2007).
Advection of a quantity a = a + a0 by the meridional flow v = v + v0
(zonal mean/eddy decomposition):
@a
@t
= v
@a
@y
= v
@a
@y
v
@a0
@y
v0 @a
@y
v0 @a0
@y
transformed into
@a
@t
= v
@a
@y
v
@a0
@y
v0 @a
@y
v0
@a0
@y
Statistics of such a model are equivalent to a second order cumulant
expansion (third order cumulants set to 0 in the second order
equations).
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 4 / 19
@a
@t
= v
@a
@y
= v
@a
@y
v
@a0
@y
v0 @a
@y
v0
@a0
@y
@a
@t
= v
@a
@y
= v
@a
@y
v
@a0
@y
v0 @a
@y
v0 @a0
@y
Removal of the eddy-eddy interactions
19. Latitude
Sigma
0
0
−5
−10
−30
−40
−40
300
320
350
−60 −30 0 30 60
0.2
0.8
−10
−5
0
5
10
The role of surface friction
Latitude
Sigma
0
0
−5
−10
−30
−40
−40
300
320
350
−60 −30 0 30 60
0.2
0.8
−10
−5
0
5
10
Simulation with ∆h = -90 K
Latitude
Sigma
10
5
10
5
−50
−50
−40
−30
−10
300
320
350
−60 −30 0 30 60
0.2
0.8
−10
−5
0
5
10
Colors: Eddy momentum fluxes ()
Dashed lines: winds in m/s
Dotted line: potential temperature in K
Grey line: tropopause
Friction/10 Friction Friction * 10
20. The role of surface friction
Colors: Eddy momentum fluxes divergence
Dashed lines: winds in m/s
Dotted line: potential temperature in K
Grey line: tropopause
Simulation with positive ∆h = 90 K Surface friction balances upper level
momentum fluxes divergence (EMFD)
Long been recognized effect on
midlatitudes eddies amplitude, jet streams
strength and location, energy conversions
(James, 1987; Robinson 1997; Chen et al.,
2007; etc...)
Can it explain upper level EMDF
e n h a n c e m e n t ? S o m e t i m e
suggested in text books (e.g.
Vallis, 2006)Latitude
Sigma
30
10
−5
−5
−10
300
320
350
−60 −30 0 30 60
0.2
0.8
−10
−5
0
5
10
5.10 6
m s 2