An idealized ray model of gravity wave‐tidal interactions

Abstract

The interaction of a gravity wave with a solar tide is analyzed using ray theory in order to assess whether the temporal oscillation of the tide has any significant effects on the interaction. We consider two types of solution: a “full ray solution,” in which tidal accelerations are included in the gravity wave ray‐tracing equations, and a second “Lindzen solution,” in which they are neglected; the latter is so named because it yields similar results to the parameterization of Lindzen [1981]. Initially, we consider an idealized tide of constant velocity amplitude in a steady isothermal atmosphere, as this allows analytical solutions to be derived. A numerical ray‐tracing code is employed to determine ray solutions within more complex tidal backgrounds. Full ray solutions often differ markedly in amplitude, wavenumber, and trajectory from Lindzen solutions for the same wave, highlighting the importance of tidal accelerations. Tidal accelerations have a stabilizing influence on gravity wave amplitudes by refracting waves to larger intrinsic phase speeds, thus reducing both the occurrence and intensity of tidally modulated gravity wave breaking. Even in the absence of dissipation, time‐varying refraction gives rise to time‐oscillating gravity wave action densities, ∂A/∂t, which in turn lead to wave momentum‐flux densities which are anticorrelated with tidal winds in agreement with mesospheric observations. Although ∂A/∂t averages to zero over one cycle of a constant‐amplitude tide, its phase locking to the tide implies transient flow accelerations which temporarily amplify tidal wind oscillations and might permanently change tidal amplitudes in a nonlinear interactive model. Numerical simulations through more complex tidal backgrounds show instances where permanent ∂A/∂t values are induced in a gravity wave through its interaction with the tide. Our results point to weaknesses in a Lindzen parameterization of gravity wave‐tidal interactions. A simple extension of the parameterization is suggested which incorporates some of these time‐varying influences.