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On the equilibrium states predicted by second moment models in rotating, stably stratified homogeneous shear flow
Physics of Fluids (2004)
  • Minsuk Ji, Stanford University
  • Paul A. Durbin, Stanford University

The structural equilibrium behavior of the general linear second-moment closure model in a stably stratified, spanwise rotating homogeneous shear flow is considered with the aid of bifurcation analysis. A closed form equilibrium solution for the anisotropy tensor aij, dispersion tensor Kij, dimensionless scalar variance q2/k (S/Sθ)2, and the ratio of mean to turbulent time scale ε/Sk is found. The variable of particular interest to bifurcation analysis, ε/Sk is shown as a function of the parameters characterizing the body forces: Ω/S (the ratio of the rotation rate to the mean shear rate) for rotation and Rig (the gradient Richardson number) for buoyancy; it determines the bifurcation surface in the ε/Sk-Ω/S-Ri g space. It is shown, with the use of the closed form solution, that the Isotropization of Production model does not have a real and stable equilibrium solution when rotational and buoyant forces of certain magnitudes are simultaneously imposed on the flow. When this occurs, time integration of the turbulence model results in a diverging solution. A new set of scalar model coefficients that is consistent with experimental data, predicts turbulence decay past the critical gradient Richardson number Ricrg=0.25, and ensures the existence of stable, real solutions for all combinations of rotation and buoyancy is proposed.

  • anisotropy,
  • bifurcation (mathematics,
  • buoyancy,
  • mathematical models,
  • parameter estimation,
  • tensors,
  • bifurcation analyses,
  • closure models,
  • spanwise rotation,
  • shear flow,
  • equilibrium,
  • fluid dynamics,
  • rotating flow,
  • stratified flow
Publication Date
October, 2004
Publisher Statement
Copyright 2004 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.
Citation Information
Minsuk Ji and Paul A. Durbin. "On the equilibrium states predicted by second moment models in rotating, stably stratified homogeneous shear flow" Physics of Fluids Vol. 16 Iss. 10 (2004)
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