Diminishing inverse transfer and non-cascading dynamics in surface quasi-geostrophic turbulence
Abstract
Description
The inverse transfer in two-dimensional turbulence governed by the surface quasi-geostrophic (SQG) equation is studied. The nonlinear transfer of this system conserves the two quadratic quantities $Ψ_1=<|(-Δ)^{1/4}ψ|^2>/2$ and $Ψ_2=<|(-Δ)^{1/2}ψ|^2>/2$ (kinetic energy), where $ψ$ is the streamfunction and $<\cdot>$ denotes a spatial average. In the limit of infinite domain, the kinetic energy density $Ψ_2$ remains bounded. For power-law inverse-transfer region, the inverse flux of $Ψ_1$ diminishes as it proceeds toward sufficiently low wavenumbers, implying that no persistent inverse cascade of $Ψ_1$ is sustainable. The unrealizability of an inverse cascade of $Ψ_1$ implies that there is no direct cascade of $Ψ_2$. Hence, the dual-cascade picture which is widely believed to be realizable in two-dimensional Navier--Stokes turbulence does not apply to SQG turbulence. Numerical results supporting the theoretical predictions are presented.
17 pages, 2 figures, submitted to Physica D
17 pages, 2 figures, submitted to Physica D