Physical Sciences and Mathematics Commons^™

Is The Subdominant Part Of The Energy Spectrum Due To Downscale Energy Cascade Hidden In Quasi-Geostrophic Turbulence?, Eleftherios Gkioulekas, Ka Kit Tung

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

In systems governing two-dimensional turbulence, surface quasi-geostrophic turbulence, (more generally $\alpha$-turbulence), two-layer quasi-geostrophic turbulence, etc., there often exist two conservative quadratic quantities, one "energy''-like and one "enstrophy''-like. In a finite inertial range there are in general two spectral fluxes, one associated with each conserved quantity. We derive here an inequality comparing the relative magnitudes of the "energy'' and "enstrophy'' fluxes for finite or infinitesimal dissipations, and for hyper or hypo viscosities. When this inequality is satisfied, as is the case of 2D turbulence,where the energy flux contribution to the energy spectrum is small, the subdominant part will be effectively hidden. …