Non-equilibrium 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 {α}-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.