Thermally Forced Gravity Waves in an Atmosphere at Rest

Abstract

The transient linear response of a quiescent, two-dimensional, nonrotating atmosphere to prescribed heat sources and sinks is investigated. Analytical solutions of the hydrostatic Boussinesq equations are obtained for a rigid lid and for a semi-infinite region. For the rigid lid solution, vertically trapped gravity waves propagate away from the source with a speed that depends on the Brunt?Väisälä frequency and the vertical wavenumber of the heating. The amplitude of the disturbance field in the region of the forcing approaches a constant value. Two modes are of particular interest: 1) a deep fast-moving mode which is responsible for subsidence warming through the depth of the troposphere; 2) a slower moving mode which corresponds to midlevel inflow and lower- and upper-level outflows. A solution is also obtained for a semi-infinite region. Although gravity wave energy can now propagate upward, the structure of the low-level fields still shows many similarities with the rigid lid solution. An analytical solution is also obtained for the rigid lid case for a pulse forcing function. This solution shows that when the heating is turned off the disturbance separates into two parts moving in opposite directions. The structure of these propagating disturbances is similar to gravity waves produced in two-dimensional numerical simulations of Florida convection. A term analysis is presented that confirms the predominantly linear character of the numerically simulated gravity waves.