Spectrum correction in Ekman-Navier-Stokes turbulence

TL;DR

This paper investigates how linear friction modifies the energy spectrum in two-dimensional turbulence, using high-resolution GPU simulations to confirm a universal linear correction law related to the friction coefficient and enstrophy flux.

Contribution

It provides a numerical validation of the theoretical prediction that friction induces a universal linear correction to the energy spectrum in 2D turbulence.

Findings

Spectral correction exponent follows a universal linear law.

GPU simulations accurately measure spectral scaling exponents.

Friction coefficient scaled by enstrophy injection rate determines spectral correction.

Abstract

The presence of a linear friction drag affects significantly the dynamics of turbulent flows in two-dimensions. At small scales, it induces a correction to the slope of the energy spectrum in the range of wavenumbers corresponding to the direct enstrophy cascade. Simple arguments predict that this correction is proportional to the ratio of the friction coefficient to the characteristic deformation rate of the flow. In this work, we examine this phenomenon by means of a set of GPU-accelerated numerical simulations at high resolutions, varying both the Reynolds number and the friction coefficient. Exploiting the relation between the energy spectrum and the enstrophy flux, we obtain accurate measurements of the spectral scaling exponents. Our results show that the exponent of the spectral correction follows a universal linear law in which the friction coefficient is rescaled by the enstrophy injection rate.