Nonlinear transfer and spectral distribution of energy in α turbulence

✍ Scribed by Chuong V. Tran

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 200 KB
• Volume: 191
• Category: Article
• ISSN: 0167-2789
• DOI: 10.1016/j.physd.2003.11.005

✦ Synopsis

Two-dimensional turbulence governed by the so-called α turbulence equations, which include the surface quasi-geostrophic equation (α = 1), the Navier-Stokes system (α = 2), and the governing equation for a shallow flow on a rotating domain driven by a uniform internal heating (α = 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.