Impact of Vertical Wind Shear on Gravity Wave Propagation in the Land-sea Breeze Circulation at the Equator

The impact of vertical wind shear on the land-sea breeze circulation at the equator is explored using idealized 2D numerical simulations and a simple 2D linear analytical model. Both the idealized and linear analytical models indicate Doppler shifting and attenuation effects co-exist under the effect of vertical wind shear for the propagation of gravity waves that characterize the land-sea breeze circulation. Without a background wind, the idealized sea-breeze has two ray paths of gravity waves that extend outward and upward from the coast. A uniform background wind causes a tilting of the two ray paths due to Doppler shifting. With vertical shear in the background wind, the downstream ray path of wave propagation can be rapidly attenuated near a certain level, whereas the upstream ray path is not attenuated and the amplitudes even increase with height. The downstream attenuation level is found to descend with increasing linear wind shear. The present analytical model establishes that the attenuation level corresponds to the critical level where the background wind is equal to the horizontal gravity-wave phase speed. The upstream gravity-wave ray path can propagate upward without attenuation as there is no critical level there.