Phase Shift of Rossby and Kelvin Waves and Wave-Jet Resonance on Tidally Locked Planets

Abstract:

Observations, theories, and numerical simulations have confirmed that atmospheric circulation on 1:1 tidally locked planets is characterized by equatorial superrotation, i.e., west-to-east winds over the equator. Recent studies shown that the superrotation can modify the phase of the waves through Doppler shift. But, a clear relationship between the superrotation and the phase shift was not examined. In this study, we re-investigate this problem using a two-dimensional (2D) linear shallow water model with a uniform zonal flow included. We find that the degree of the phase shift is a monotonous but nonlinear function of the strength of the mean flow with an upper limit of 180^o. The existence of the upper limit can be explained using the energy budget of the system. Under a given magnitude of the superrotation, the degree of the phase shift depends on radiation relaxation and friction drag timescales. When the relaxation timescale or the drag timescale is short (long), the phase shift is smaller (larger). We further show that a resonance between the Rossby wave and the supperrotation jet occurs when the speed of the eastward jet approaches to the westward phase speed of the Rossby wave, or a resonance between the Kelvin wave and a westward mean flow occurs when the speed of the westward jet approaches to the eastward phase speed of the Kelvin wave. Under the resonance, the amplitude of the wave reaches a peak and the wave is trapped in the source--the substellar region. The underlying mechanism is the same as that found in previous studies of Earth and hot Jupiters forced by longitudinally dependent diabatic heating or topography. Moreover, in the spin-up period of a more complex 3D global atmospheric general circulation simulation for a tidally locked terrestrial planet, we also find these two phenomenas--phase shift and wave-jet resonance. These results improve the understanding of wave-mean flow interactions on tidally locked planets.