Variable enstrophy flux and energy spectrum in two-dimensional turbulence with Ekman friction

TL;DR

This paper presents an analytical model explaining deviations from the classical $k^{-3}$ energy spectrum in 2D turbulence with Ekman friction, highlighting the role of variable enstrophy flux and its impact on the energy spectrum.

Contribution

The paper introduces a novel analytical model that accounts for variable enstrophy flux due to Ekman friction, explaining observed spectral deviations in 2D turbulence.

Findings

Energy spectrum deviates from $k^{-3}$ in Ekman friction flows.

Enstrophy flux exhibits logarithmic dependence in the inertial range.

Energy spectrum transitions from power law to exponential with increasing Ekman friction.

Abstract

Experiments and numerical simulations reveal that in the forward cascade regime, the energy spectrum of two-dimensional turbulence with Ekman friction deviates from Kraichnan's prediction of $k^{-3}$ power spectrum. In this letter we explain this observation using an analytic model based on variable enstrophy flux arising due to Ekman friction. We derive an expression for the enstrophy flux which exhibits a logarithmic dependence in the inertial range for the Ekman-friction dominated flows. The energy spectrum obtained using this enstrophy flux shows a power law scaling for large Reynolds number and small Ekman friction, but has an exponential behaviour for large Ekman friction and relatively small Reynolds number.