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SUMMARY:Energy cascade in turbulent flows: quantifying effects of Reynolds
  number and local and nonlocal interactions - Domaradzki\, JA (Southern Ca
 lifornia)
DTSTART:20080930T150000Z
DTEND:20080930T153000Z
UID:TALK13845@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:The classical Kolmogorov theory of three-dimensional turbulenc
 e is based on the concept of the energy transfer from larger to progressiv
 ely smaller scales of motion. The theory postulates that bulk of the energ
 y transfer in the inertial range of turbulence occurs between scales of si
 milar size\, a process known as the local energy cascade. The locality all
 ows to postulate that after multiple cascade steps the small scale dynamic
 s become universal\, i.e.\, independent of particulars of large scales tha
 t are determined by geometry\, boundary conditions\, and forces causing a 
 flow. Yet despite its central role in the Kolmogorov theory the locality a
 ssumption cannot be easily verified\, neither analytically nor experimenta
 lly. This is because the energy transfer is a result of interactions among
  different scales of motion originating from the nonlinear term in the Nav
 ier-Stokes equation that couples all scales. Relevant questions have been 
 productively addressed for the first time using databases generated in lar
 ge scale numerical simulations. We revisit and extend previous work and us
 e such databases to compute detailed energy exchanges between scales of mo
 tion obtained by decomposing numerical velocity fields using banded filter
 s\, and investigate how the detailed transfers contribute to the global qu
 antities such as the classical energy transfer\, the energy flux\, and the
  subgrid-scale transfer. We address two questions in detail. First\, for t
 he purposes of quantitative analyzes\, various definitions of scales of mo
 tion can be used. This non-uniqueness leads to the possibility\, raised in
  the literature on the subject\, that properties of the energy transfer de
 duced from such analyzes can be qualitatively affected by the employed sca
 le definitions. We address this question by computing detailed energy exch
 anges between different scales of motion defined by decomposing velocity f
 ields using three specific filters: sharp spectral\, Gaussian\, and tangen
 t hyperbolic. Second\, we quantify the locality of the energy transfer and
  address a persistent controversy concerning the role of nonlocal interact
 ions in the energy transfer process\, i.e.\, the role of much larger scale
 s than those transferring energy. The analysis of detailed interactions re
 veals that the individual nonlocal contributions are always large but sign
 ificant cancellations lead to the global quantities asymptotically dominat
 ed by the local interactions. The detailed locality functions are computed
  and their behavior compared with the asymptotic scaling laws valid for in
 finite Reynolds numbers turbulence. Apart from an intellectual challenge o
 f clarifying these issues\, obtained results have bearing on practical que
 stions of turbulence modeling that will also be addressed in the talk.
LOCATION:Seminar Room 1\, Newton Institute
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