Spectrum correction in Ekman-Navier-Stokes turbulence

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.