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Abstract This article critically reviews research on tornado theory and observations over the last decade. From the theoretical standpoint, the major advances have come through improved numerical-simulation models of supercell convective storms, which contain the tornado’s parent circulation. These simulations are carried out on a large domain (to capture the supercell’s circulation system), but with high grid resolution and improved representations of sub-grid physics (to capture the tornado). These simulations offer new insights into how and why tornadoes form in some supercells, but not others. Observational advances have come through technological improvements of mobile Doppler radars capable of rapid scanning and dual-polarization measurements, which offer a much more accurate view of tornado formation, tornado structure, and the tornado’s place within its parent supercell. 

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 coexist 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.