Numerical modelling of internal gravity waves generated by a thermal forcing in an anelastic atmospheric flow with vertical shear

A numerical model is presented for internal gravity waves generated by deep or shallow latent heating in the lower atmosphere. The configuration comprises a background fluid flow with vertical shear and vertical stratification in a two-dimensional computational domain. A thermal forcing term is included in the energy conservation equation for the fluid flow. This term is sinusoidal in the horizontal direction and localized in the vertical direction and it generates a perturbation in the form of an upward-propagating internal gravity wave with a horizontal wavelength corresponding to that of the thermal forcing oscillation. If there is no critical level where the background flow speed is equal to the wave phase speed, then the wave propagates to the upper boundary of the domain where a non-reflecting boundary condition or radiation condition is imposed numerically. With a vertically-sheared background flow, where a critical level is present, nonlinear wave-mean-flow interactions occur. Vertical fluxes of momentum and energy lead to the development of higher horizontal wavenumber and zero wavenumber components. There is a transfer of momentum and energy to the background flow which reduces the wave amplitude in the upper levels of the domain and results in changes in the background velocity and temperature and the development of regions of convective instability near the critical level. • A numerical model is presented for internal gravity waves generated by latent heating in the atmosphere. • The background fluid flow has vertical shear and vertical stratification. • Nonlinear wave-mean-flow interactions are investigated. • It is found that convective instabilities develop as a result of the nonlinear interactions.