On the Effect of the Coriolis Force on the Enstrophy Cascade

Abstract.

We study the direct enstrophy cascade at small spatial scales in statistically stationary forced-dissipated two-dimensional Navier–Stokes equations subject to the Coriolis force in the [Formula: see text]-plane approximation. We provide sufficient conditions inspired by Bedrossian et al. [ Arch. Ration. Mech. Anal., 237 (2020), pp. 103–145] and Xie and Bühler [ J. Fluid Mech., 851 (2018), pp. 672–686] to prove that at small scales, in the presence of the Coriolis force, the so-called third-order structure function’s asymptotics follows the third-order universal law of two-dimensional turbulence without the Coriolis force. Our result indicates that at small scales, the enstrophy flux from larger to smaller scales is not affected by the Coriolis force, confirming experimental and numerical observations. To the best of our knowledge, this is the first mathematically rigorous study of the above equations.