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SUMMARY:Modelling two-time velocity correlations for prediction of both La
 grangian and Eulerian statistics - Cambon\, C (Ecole Centrale de Lyon)
DTSTART:20081001T161000Z
DTEND:20081001T164000Z
UID:TALK13857@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:More information on two-point two-time velocity correlations a
 re needed for a better prediction of turbulent dispersion as well as radia
 ted noise using an acoustic analogy. Conceptual aspects will be emphasized
  and not applications. Only isotropic turbulence will be considered\, alth
 ough many applications are developped in our team towards strongly anisotr
 opic turbulence\, mainly in rotating\, stably stratified and/or MHD flows.
 \n\nA simple synthetic model of isotropic turbulence is firstly considered
 \, using a random superposition of Fourier modes : This is the KS (Kinemat
 ic simulation) following Kraichnan and Fung et al. Unsteadiness of velocit
 y field realizations is mimicked using temporal frequencies\, which are ex
 pressed in term of a prescribed energy spectrum and the wavenumber. Even i
 f the orientation of the wavevector is randomly chosen\, the link of the t
 emporal frequency to the wavenumber is deterministic in the simpler versio
 n of the KS model. Although such a model was relevant for several applicat
 ions\, it is dramatically questioned for the evaluation of two-time veloci
 ty correlations. It is shown that spurious oscillations are generated\, an
 d that it is needed to model the temporal frequencies as random Gaussian v
 ariables with a standard deviation of the same order of magnitude as their
  mean value. Further applications to noise radiation are touched upon\, in
  order to illustrate dominant (Lagrangian) `straining' or dominant (Euleri
 an) `sweeping' effects\, according to the scale under consideration.\n\nTh
 e role of a typical time-scale for the decorrelation of triple velocity co
 rrelations is then recalled and discussed in the classical `triadic closur
 es' from the Orszag and Kraichnan's legacy\, such as EDQNM\, DIA and semi-
 Lagrangian more sophisticated variants.\n\nFinally\, these different conce
 pts (diffusive and/or dispersive eddy dampings\, straining or sweeping pro
 cesses) are applied to a recent closure theory of weakly compressible isot
 ropic turbulence. A Gaussian kernel for the decorrelation of triple veloci
 ty correlations was shown to give much better results than the classical e
 xponential kernel inherited from EDQNM in the incompressible case. A new e
 xplanation is given in accordance with the renormalization of the acoustic
  wave frequency by a pure random term with zero mean but with a standard d
 eviation of the same order of the eddy damping term formerly used in EDQNM
 . This analysis can be related to the concept of Kraichnan's random oscill
 ator\, recently revisited by Kaneda (2007)\, with a connection to the much
  simpler KS problem firstly presented (see also the monograph `homogeneous
  turbulence dynamics' by Pierre Sagaut and Claude Cambon\, just published 
 in Cambridge University Press.)
LOCATION:Seminar Room 1\, Newton Institute
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