Nonequilibrium fluctuations of the direct cascade in surface quasi-geostrophic turbulence

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 apply a method to disentangle the equilibrium and nonequilibrium contribution in the instantaneous spectra, which can be generalized to other turbulent systems.