Implicit Turbulence Modeling for High Reynolds Number Flows

We continue our investigation of the implicit turbulence modeling property of the nonoscillatory finite volume scheme MPDATA. We start by comparing MPDATA simulations of decaying turbulence in a triply periodic cube with analogous pseudospectral studies. In the regime of direct numerical simulation, MPDATA is shown to agree closely with the pseudospectral model. As viscosity is reduced, the two model results diverge. We study the MPDATA results in the inviscid limit, using a combination of mathematical analysis and computational experiment. We validate the inviscid MPDATA results as representing the turbulent flow in the limit of very high Reynolds number.

[1]  L. Margolin,et al.  MPDATA: A Finite-Difference Solver for Geophysical Flows , 1998 .

[2]  L. Margolin,et al.  A Class of Nonhydrostatic Global Models. , 2001 .

[3]  Paul Linden,et al.  Molecular mixing in Rayleigh–Taylor instability , 1994, Journal of Fluid Mechanics.

[4]  L. Margolin,et al.  Large-eddy simulations of convective boundary layers using nonoscillatory differencing , 1999 .

[5]  A. Clarke.  Profiles of the Future , 1962 .

[6]  L. Margolin,et al.  A rationale for implicit turbulence modelling , 2001 .

[7]  Jackson R. Herring,et al.  Development of enstrophy and spectra in numerical turbulence , 1993 .

[8]  B. Geurts.  Inverse modeling for large-eddy simulation , 1997 .

[9]  N. Adams,et al.  An approximate deconvolution procedure for large-eddy simulation , 1999 .

[10]  A. Kolmogorov.  The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers , 1991, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[11]  P. Smolarkiewicz,et al.  On Forward-in-Time Differencing for Fluids: Extension to a Curvilinear Framework , 1993 .

[12]  Lohse,et al.  Bottleneck effects in turbulence: Scaling phenomena in r versus p space. , 1994, Physical review letters.

[13]  Piotr K. Smolarkiewicz,et al.  On Forward-in-Time Differencing for Fluids , 1991 .

[14]  U. Frisch.  Turbulence: The Legacy of A. N. Kolmogorov , 1996 .

[15]  F. Grinstein,et al.  Monotonically integrated large eddy simulation of free shear flows , 1999 .

[16]  Len G. Margolin,et al.  On Forward-in-Time Differencing for Fluids: an Eulerian/Semi-Lagrangian Non-Hydrostatic Model for Stratified Flows , 1997 .

[17]  Jay P. Boris,et al.  Computing Turbulent Shear Flows — A Convenient Conspiracy , 1993 .

[18]  Paul R. Woodward,et al.  Kolmogorov‐like spectra in decaying three‐dimensional supersonic flows , 1994 .

[19]  J. Domaradzki,et al.  The subgrid-scale estimation model in the physical space representation , 1999 .