Thermalization and free decay in Surface Quasi-Geostrophic flows

TL;DR

This paper derives and verifies statistical equilibrium solutions for truncated inviscid surface quasi-geostrophic flows, revealing enstrophy thermalization, energy condensation, and spectral scaling laws, with insights into free-decay behavior at high Reynolds numbers.

Contribution

It introduces new statistical equilibrium solutions for truncated SQG equations and compares viscous and inviscid decay laws, advancing understanding of SQG turbulence.

Findings

Enstrophy thermalizes in truncated SQG flows.

Energy condenses at the largest scales.

Spectral scaling laws are identified for early times.

Abstract

We derive statistical equilibrium solutions of the truncated inviscid surface quasi-geostrophic (SQG) equations, and verify the validity of these solutions at late times in numerical simulations of the truncated SQG equations. The results indicate enstrophy thermalizes while energy can condense at the gravest modes, in agreement with previous indications of a direct cascade of enstrophy and an inverse cascade of energy in forced-dissipative SQG systems. At early times, the truncated inviscid SQG simulations show a behavior reminiscent of forced-dissipative SQG turbulence, and we identify spectral scaling laws for the energy and enstrophy spectra. Finally, a comparison between viscous and inviscid simulations allows us to identify free-decay similarity laws for the enstrophy in SQG turbulence at very large Reynolds number.