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 work shows that the Traditional Approximation of Rotation (TAR) can significantly misrepresent gravito-inertial wave dynamics in sub-inertial and weakly stratified regimes, necessitating a non-traditional treatment of the full Coriolis acceleration. The authors develop a local non-traditional Cartesian model, derive the dissipative Poincaré equation, and analyze adiabatic propagation and linear damping, revealing that TAR underestimates damping and misplaces momentum deposition. They further quantify convective and shear-induced wave breaking under non-traditional dynamics, demonstrating reduced momentum transport and equatorial confinement of sub-inertial wave effects, especially in stellar radiative zones. A non-traditional parametrisation for GIW–mean flow interactions is derived, providing a path toward improved long-term evolution models for planetary atmospheres, oceans, and rotating stars, with planned extensions to global geometry and magnetic fields.

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.

Figures (7)

• Figure 1: The local studied Cartesian box in the "$f$-plane" reference frame.
• Figure 2: Ratios ${\widehat{\tau}}_{\rm T}/{\widehat{\tau}}_{\rm NT}$ and ${k^{2}_{V}}_{\rm T}/{k^{2}_{V}}_{\rm NT}$ as a function of the normalised frequency $\omega/2\Omega$ for different colatitudes $\theta\equiv\left\{0,\pi/8,\pi/4,3\pi/8,\pi/2\right\}$ in the weakly stratified ($N/2\Omega=5$; left panel) and in the strongly stratified ($N/2\Omega=50$; right panel) cases.
• Figure 3: Ratios ${k^{2}_{V}}_{\rm T}/{k^{2}_{V}}_{\rm NT}$ (left column) and ${\widehat{\tau}}_{\rm T}/{\widehat{\tau}}_{\rm NT}$ (right column) as a function of the ratio $N/2\Omega$ and of the colatitude $\theta$ in the sub-inertial ($\omega=1.5\Omega$; first line) and in the super-inertial ($\omega=2.5\Omega$; second line) regimes. We recover that in the sub-inertial regime, GIWs are trapped in an equatorial belt while they are propagating at all colatitudes in the super-inertial regime.
• Figure 4: Ratio of the vertical flux of momentum computed with taking into account the full Coriolis acceleration (left panel) and assuming the TAR (right panel) with its value computed in the non-rotating case (with $\Omega\equiv0$) as a function of the colatitude ($\theta$) for a fixed value of the wave's Froude number ($F_r=\omega/N=0.25$) and different values of the wave's Rossby number ($R_o=\left\{0.1,0.5,1,2,100\right\}$). In the non-traditional case, we have fixed $\alpha=\pi/4$.
• Figure 5: Ratio of the vertical flux of momentum computed with taking into account the full Coriolis acceleration with its value computed in the traditional case as a function of the colatitude ($\theta$) for a fixed value of the wave's Froude number ($F_r=\omega/N=0.25$) and different values of the wave's Rossby number ($R_o=\left\{0.1,0.5,1,2,100\right\}$). In the non-traditional case, we have fixed $\alpha=\pi/4$.