Nonlinear transfer and spectral distribution of energy in alpha turbulence

Chuong Van Tran

Research output: Contribution to journalArticlepeer-review

29 Citations (Scopus)

Abstract

Two-dimensional turbulence governed by the so-called alpha turbulence equations, which include the surface quasi-geostrophic equation (alpha = 1), the Navier-Stokes system (alpha = 2), and the governing equation for a shallow flow on a rotating domain driven by a uniform internal heating (alpha = 3), is studied here in both the unbounded and doubly periodic domains. This family of equations conserves two inviscid invariants (energy and enstrophy in the Navier-Stokes case), the dynamics of which are believed to undergo a dual cascade. It is shown that an inverse cascade can exist in the absence of a direct cascade and that the latter is possible only when the inverse transfer rate of the inverse-cascading quantity approaches its own injection rate. Constraints on the spectral exponents in the wavenumber ranges lower and higher than the injection range are derived. For Navier-Stokes turbulence with moderate Reynolds numbers, the realization of an inverse energy cascade in the complete absence of a direct enstrophy cascade is confirmed by numerical simulations. (C) 2003 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)137-155
Number of pages19
JournalPhysica D: Nonlinear Phenomena
Volume191
Issue number1-2
DOIs
Publication statusPublished - 15 Apr 2004

Keywords

  • alpha turbulence
  • dual cascade
  • energy spectra
  • TWO-DIMENSIONAL TURBULENCE
  • QUASI-GEOSTROPHIC FLOW
  • 2-DIMENSIONAL TURBULENCE
  • INVERSE CASCADE
  • ROSSBY WAVES
  • DIFFUSION
  • BEHAVIOR

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