Abstract

A framework, which combines mathematical analysis, closure theory, and phenomenological treatment, is developed to study the spectral transfer process in turbulent flows that are subject to rotation. First, we outline a mathematical procedure that is particularly appropriate for problems with two disparate time scales. The approach that is based on the Green's method leads to the Poincaré velocity variables and the Poincare transformation when applied to rotating turbulence. The effects of the rotation are now conveniently included in the momentum equation as the modifications to the convolution of nonlinear term. The Poincaré transformed equations are used to obtain a time-dependent Taylor-Proudman theorem valid in the asymptotic limit when the nondimensional parameter μ≡Ωt→∞ (Ω is the rotation rate and t is the time). The "split" of the energy transfer in both direct and inverse directions is established. Second, we apply the Eddy-Damped-Quasinormal-Markovian (EDQNM) closure to the Poincaré transformed Euler/ Navier-Stokes equations. This closure leads to expressions for the spectral energy transfer. In particular, a unique triple velocity decorrelation time is derived with an explicit dependence on the rotation rate. This provides an important input for applying the phenomenological treatment of Zhou [Phys. Fluids 7, 2092 (1995)]. In order to characterize the relative strength of rotation, another nondimensional number, a spectral Rossby number, which is defined as the ratio of rotation, and turbulence time scales, is introduced. Finally, the energy spectrum and the spectral eddy viscosity are deduced.

Original languageEnglish (US)
Pages (from-to)2138-2152
Number of pages15
JournalPhysics of Fluids
Volume8
Issue number8
DOIs
StatePublished - Aug 1996

ASJC Scopus subject areas

  • Computational Mechanics
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Fluid Flow and Transfer Processes

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