Energy fluxes in quasi-equilibrium flows

We examine the relation between the absolute equilibrium state of the spectrally truncated Euler equations (TEE) predicted by Kraichnan (J. Fluid Mech., vol. 59 (4), 1973, pp. 745–752) to the forced and dissipated flows of the spectrally truncated Navier–Stokes (TNS) equations. In both of these idealized systems, a finite number of Fourier modes is kept contained inside a sphere of radius . In both cases, a finite forward or inverse flux is present even for the cases where the flow is close to the equilibrium state solutions. However, unlike the classical turbulence, where an energy cascade develops with a mean energy flux that is large compared to its fluctuations, the quasi-equilibrium state has a mean flux of energy that is subdominant to the large flux fluctuations observed.