Non-equilibrium fluctuations of the direct cascade in Surface Quasi Geostrophic turbulence

TL;DR

This paper investigates the temporal fluctuations of surface potential energy flux in SQG turbulence through simulations and theory, revealing non-equilibrium effects and developing a method to distinguish equilibrium from non-equilibrium contributions.

Contribution

It introduces a theoretical prediction for non-equilibrium spectral corrections and a novel method to separate equilibrium and non-equilibrium effects in turbulent spectra.

Findings

Identified subleading spectral corrections due to energy imbalance.

Derived power-law behavior for non-equilibrium spectral corrections.

Developed a method to disentangle equilibrium and non-equilibrium spectral contributions.

Abstract

We study the temporal fluctuations of the flux of surface potential energy in Surface Quasi-Geostrophic (SQG) turbulence. By means of high-resolution, direct numerical simulations of the SQG model in the regime of forced and dissipated cascade of temperature variance, we show that the instantaneous imbalance in the energy budget originates a subleading correction to the spectrum of the turbulent cascade. Using a multiple-scale approach combined with a dimensional closure we derive a theoretical prediction for the power-law behavior of the corrections, which holds for a class of turbulent transport equations known as {\alpha}-turbulence. Further, we develop and apply a method to disentangle the equilibrium and non-equilibrium contribution in the instantaneous spectra, which can be generalized to other turbulent systems.