Abstract
Abstract We examine, for the case of stationary turbulence, the correlation between fully resolved turbulence (in the sense of Fourier modes) and a system composed of the same equations on a reduced wavenumber span. This ‘reduced system’ is subjected to a wavenumber-dependent eddy viscosity contrived so that the full and reduced systems have the same energy spectrum, on the reduced span. The particular numerical problem studied is isotropic turbulence, and the model of turbulence is a Langevin representation of the test-field model (Kraichnan (1971, J. Fluid Mech., 47: 513–524). The correlation between the full and reduced systems is surprisingly small, a fact we attribute to be related to the unpredictability of the underlying Navier-Stokes equations. The (qualitative) form of the eddy viscosity introduced by such modeling is also discussed, and it is noted that at large Reynolds numbers, there exists an optimal cut-off wavenumber which permits an elimination of explicit empiricism from this form of large eddy simulation (LES). Our computations permit a spectral estimate of the magnitude of the backscatter term in LES, along the lines recently proposed by Schumann (1995, Proc. R. Soc. London, Ser. A, 451: 293–318).
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call