A Linear Theory for Periodic Convectively Forced Gravity Waves near a Coastline

This study presents a simple 2D linear analytical model aimed at investigating gravity waves forced by temporally periodic convection near a coastline. This investigation encompasses two distinct convective heating scenarios: deep convective heating and stratiform heating/cooling. Our model explores the intricate behavior of gravity waves in proximity to a time-dependent convective source and examines their propagation characteristics across diverse atmospheric conditions. Close to the convective source, gravity waves demonstrate nearly horizontal propagation with vertically aligned phase lines. The velocity of their propagation primarily depends on the vertical scale of the convective heating. The presence of a tropopause further extends their horizontal reach through partial wave ducting between the surface and the tropopause. However, the horizontal scale of the convective heating also plays a crucial role in determining the horizontal wavelength and, consequently, affecting the horizontal propagation speed of the gravity waves. If the heating horizontal scale is small compared to the horizontal scale of free waves at the forcing frequency, the heating vertical scale determines the vertical wavelength and thus the horizontal wavelength. However, if the heating horizontal scale is large, the horizontal wavelength determined by the heating vertical scale has little energy, so that the horizontal wavelength is mainly determined by the heating horizontal scale. Moreover, longer periods of convective heating and stronger background winds contribute to an increased downstream propagation distance of the gravity waves away from the source. Additionally, inertia–gravity waves generated by diurnal convection can propagate horizontally over greater distances at a higher latitude but become confined or trapped at latitudes exceeding 30°.