Parametrisation of the wave-zonal flow interactions taking into account the full Coriolis acceleration. The necessity of going beyond the traditional approximation in the sub-inertial regime and in weakly stratified regions

TL;DR

This paper develops a non-traditional parametrisation of wave-zonal flow interactions that accounts for the full Coriolis acceleration, improving the accuracy of modeling inertia-gravity waves in sub-inertial and weakly stratified regimes.

Contribution

It introduces a non-traditional model including the full Coriolis acceleration, surpassing the traditional approximation, and provides a new parametrisation for wave-mean flow interactions.

Findings

TAR underestimates GIWs damping in sub-inertial regimes.

Full Coriolis acceleration predicts momentum deposition closer to wave excitation.

Non-traditional modelling shows stronger inhibition of convective and shear-induced overturnings.

Abstract

From the Earth's atmosphere and oceans to stellar radiation zones, inertia-gravity waves, which are called gravito-inertial waves (hereafter GIWs) in Astrophysics, are transporting momentum and mixing matter when they are damped through heat and viscous diffusions and when they break. Their short-time scale dynamics is governed by the buoyancy force and the Coriolis acceleration. Because of the transport they trigger, they modify the long-term evolution of the large-scale planetary atmospheric (oceanic) circulation and of the structure and rotation of stars. In many state-of-the-art models, the so-called Traditional Approximation of Rotation (hereafter denoted TAR), where the local projection of the rotation vector along the horizontal direction is neglected, is assumed. We aim to identify the applicability regime of this approximation and to propose a non-traditional parametrisation of wave - zonal flow interactions, in which the full Coriolis acceleration is taken into account. We build a prototype local non-traditional Cartesian model in which we take into account the full Coriolis acceleration, buoyancy, and heat and viscous diffusions. On the one hand, the TAR is strongly underestimating GIWs damping in the sub-inertial regime. In this regime a non-traditional modelling must be adopted to predict the correct altitude where momentum is deposited, which is closer to the excitation region of waves than the one predicted using the TAR. On the other hand, non-traditional modellings of GIWs convective and shear-induced breakings are proposed. Taking into account the full Coriolis acceleration leads to a stronger inhibition of the efficiency of the convective and shear-induced overturnings and to a weaker transport than those predicted when assuming the TAR. Finally, a fully non-traditional parametrisation of GIWs - mean zonal flows interaction is derived.