Download presentation

Presentation is loading. Please wait.

Published byKenna Shibley Modified over 3 years ago

1
Non-Fickian diffusion and Minimal Tau Approximation from numerical turbulence A.Brandenburg 1, P. Käpylä 2,3, A. Mohammed 4 1 Nordita, Copenhagen, Denmark 2 Kiepenheuer Institute, Freiburg, Germany 3 Dept Physical Sciences, Univ. Oulu, Finland 4 Physical Department, Oldenburg Univ., Germany …and why First Order Smoothing seemed always better than it deserved to be

2
2 MTA - the minimal tau approximation 1) replace triple correlation by quadradatic 2) keep triple correlation 3) instead of now: 4) instead of diffusion eqn: damped wave equation i) any support for this proposal?? ii) what is tau?? (remains to be justified!)

3
Brandenburg: non-Fickian diffusion3 Purpose and background Need for user-friendly closure model Applications (passive scalar just benchmark) –Reynolds stress (for mean flow) –Maxwell stress (liquid metals, astrophysics) –Electromotive force (astrophysics) Effects of stratification, Coriolis force, B-field First order smoothing is still in use –not applicable for Re >> 1 (although it seems to work!)

4
4 Testing MTA: passive scalar diffusion >>1 (!) primitive eqn fluctuations Flux equation triple moment MTA closure

5
Brandenburg: non-Fickian diffusion5 System of mean field equations >>1 (!) mean concentration flux equation Damped wave equation, wave speed (causality!)

6
Brandenburg: non-Fickian diffusion6 Wave equation: consequences >>1 (!) small tau i)late time behavior unaffected (ordinary diffusion) ii)early times: ballistic advection (superdiffusive) large tauintermediate tau Illustration of wave-like behavior:

7
Brandenburg: non-Fickian diffusion7 Comparison with DNS Finite difference –MPI, scales linearly –good on big Linux clusters 6 th order in space, 3 rd order in time forcing on narrow wavenumber band Consider k f /k 1 =1.5 and 5

8
Brandenburg: non-Fickian diffusion8 Test 1: initial top hat function Monitor width and kurtosis black: closure model red: turbulence sim. Fit results: k f /k 1 St= uk f 1.5 1.8 2.2 1.8 5.1 2.4

9
Brandenburg: non-Fickian diffusion9 Comparison with Fickian diffusion No agreement whatsoever

10
Brandenburg: non-Fickian diffusion10 Spreading of initial top-hat function

11
Test 2: finite initial flux experiment Initial state: but with black: closure model red: turbulence sim. direct evidence for oscillatory behavior! Dispersion Relation: Oscillatory for k 1 /k f <3

12
Brandenburg: non-Fickian diffusion12 Test 3: imposed mean C gradient >>1 (!) Convergence to St=3 for different Re

13
Brandenburg: non-Fickian diffusion13 kf=5

14
Brandenburg: non-Fickian diffusion14 kf=1.5

15
Brandenburg: non-Fickian diffusion15 Comment on the bottleneck effect Comment on the bottleneck effect Dobler et al (2003) PRE 68, 026304

16
Brandenburg: non-Fickian diffusion16 Bottleneck effect: 1D vs 3D spectra

17
Brandenburg: non-Fickian diffusion17 Relation to laboratory 1D spectra Parseval used:

18
Brandenburg: non-Fickian diffusion18 Conclusions MTA viable approach to mean field theory Strouhal number around 3 –FOSA not ok (requires St 0) Existence of extra time derivative confirmed –Passive scalar transport has wave-like properties –Causality In MHD, contribution arrives naturally Coriolis force & inhomogeneity straightforward

Similar presentations

OK

Direct numerical simulation study of a turbulent stably stratified air flow above the wavy water surface. O. A. Druzhinin, Y. I. Troitskaya Institute of.

Direct numerical simulation study of a turbulent stably stratified air flow above the wavy water surface. O. A. Druzhinin, Y. I. Troitskaya Institute of.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on quality education in india Ppt on uttar pradesh tourism Ppt on challenges of democracy in india Presentations ppt online viewer Ppt on density based traffic light control system Ppt on extinct species in india Agriculture templates free download ppt on pollution Ppt on nepali culture Ppt on latest technology in mechanical Ppt on waste management in india