2004/01/30 by Chuong V. Tran · 2 citations
Engineering · Mathematics · Physics and Astronomy · #Fluid Dynamics and Turbulent Flows #Nanofluid Flow and Heat Transfer #Navier-Stokes equation solutions #nlin.CD
paper · pdf · doi:10.1016/j.physd.2003.11.005
5 figures, 28 pages
openalex publication_date 2004/01/30 · arxiv created 2004/03/03 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.