1. Personal experiences
at the boundary of
physics and mathematics
E. Jurjen Kranenborg,
ABB Corporate Research,
Västerås, Sweden

2. Career Path
 Childhood Hobbies
 Education at Twente University:
o Start of Computer Science, Start of Applied Mathematics
o M.Sc. In Applied Maths., Fluid Dynamics, Grid generation
 Ph.D at Utrecht University, Physics & Astronomy
o Density driven Convection (“Double-Diffusive Convection”)
 PostDoc, Free University of Amsterdam (Earth Sciences)
 Research/Consultancy at Delft Hydraulics
 Research at Philips Research (Software Architectures)
 Currently: ABB Corp. Research (Thermal modeling of Power
Transformers using CFD), Västerås, Sweden

3. Childhood Hobbies
Astronomy …
… Analog Electronics
16/32-bit Processor
Architecture …

4. M.Sc. In Applied Mathematics
 Topic: “Control Functions for Numerical Orthogonal Grid
generation in Curved Geometries”
Final grid in
physical domain
Computational grid

5. Main Part
Ph.D. Research
(1991-1996)
Utrecht University,
Physics & Astronomy
Promotores:
Prof. W.P.M. de Ruijter,
Prof. H.A. Dijkstra

6. Oceanic layered structures near polar ice

7. Melting Icebergs ...
… Lateral mixing
of meltwater
Influence of layers
on iceberg melting ...

8. Layer Development
Heating up of left sidewall at t > 0.
Shown: Perturbation of initial stable salt gradient.
Layer thickness h scales with a.DT / b.fS

10. Layer properties, Problem parameters
Ra (Rayleigh) = measure of thermal & saline forcing intensity
R (Buoyancy Ratio) = b.DS / a.DT

11. Ph.D. Research Issues
 Flow dynamics & pattern selection
o Video suggests: transitions between steady states!
o Continuation and stability analysis to map out
solution behaviour in parameter space
 Physical mechanisms?
o Layer merging
o Layer self-propagation
 Scaling up towards oceanographic conditions:
o determination of effective diffusivities

12. Patterns & Pattern selection: “Attractor Analysis”
 Flow Model as a Dynamical System
o Main steady states?
o Stability of steady states?
o Transitions between steady states?
 Result: Qualitative picture of dynamics as a
function of combined thermal/saline forcing
(Ra) and buoyancy ratio (R)
 Model: Sidewall heating of a stable salinity
gradient, using Ra as bifurcation parameter, R
fixed at R = 3
T=0
S=0
T=1
S=1
AGU Geophysical Monograph 94, 89–96, 1995,
Phys. Fluids 7(3), 680–682, 1995,
Int. J. Heat Mass Transfer 39, 2699–2710, 1996
R=3

13. S.S. patterns, function of buoy. forcing
A: weak forcing regime

14. S.S. patterns, function of buoy. forcing
B: strong forcing regime

15. Heat, salt transport
Heat
(Nu)
Salt
(Sh)

16. Transitions between flow patterns
Interface migration
Perturbation
causing this ...
Unstable states may be physically relevant!

17. Layer merging
Int. J. Heat Mass Transfer 41, 2743–2756, 1998

18. Self-propagation of layers
Int. J. Heat Mass Transfer 41, 2113–2124, 1998
Propagation after forcing stopped …
Kinetic energy increase ...
... does not happen if
initial vertical temperature
gradient is absent

19. Convection near an ice plate geometry
Int. J. Heat Mass Transfer 41, 1873–1884, 1998.

20. Global transport: effective diffusivities
 Vertical salt fluxes determined for several simulations:
o Ra = [5*104 - 1*106]
o R = [2.5 - 10]
 Results satisfy a published Flux law for vertical salt
transport validated by laboratory experiments
 After analysis of our case: vertical salt diffusivity takes
extremely simple form:
o KS = cS * Ra1/3 (dim. less, cS = 1.15*10-3 from simulations)
o independent of diffusive interface stability
 KS in fair agreement with oceanographic measurements
o Ra is much larger ( O(109), i.e. 104 times)
o Fails only for diffusive interfaces with very low stability
Time-Dependent Nonlinear Convection (Advances in Fluid Mechanics), 1998

21. Final Part
Recent employment activities

22. PostDoc at Free University of Amsterdam
 Domain: Sedimentary Geology
 Context: Climate reconstruction from sediment
analysis of calcium carbonate
 Project: Model Implementation of CaCO3
Dissolution due to Organic Carbon Degradation
Tectonophysics, 320, 347–374, 2000

23. Research/Consultancy at Delft Hydraulics
 Project leader: drill slib deposition in the Scheldt
Estuary;
o numerical modeling and visualisation of hydrodynamics + slib
transport,
 Hong Kong power plant water inlet: water quality
scenario study,
 Project leader: software module for nutrient
regeneration due to organic carbon degradation in
North Sea sediments,
 Feasibility study for fresh water retrieval, Indonesia;
o data retrieval & checking
o analytical modeling of lake desalination.

24. Research at Philips Research the Netherlands
 2000 - 2002: Cluster Domain Modelling,
 2003 - 2004: Cluster Internet Connected
Consumer Systems,
o Gatewayed Services Architecture for internet-
enabled consumer electronics devices (project
2003),
o Home Networking Security (project 2004).

25. … [ Experiment ] make your own private
layered structure [ Experiment ] …
 Ocean Model: Cup of HOT coffee
 Ice-edge model: Use a Transparent, Glass Cup
 Add Salt Stratification: GENTLY pour some coffee milk
 Wait for a few minutes and …
 Your private oceanic staircase is ready for consumption !

26. The End
WEB publications:
 Ph.D. work: www.kranenborg.org/jurjen
 (Analog) electronics: www.kranenborg.org/ee