Theoretical Studies of Convectively Forced Mesoscale Flows in Three Dimensions. Part I: Uniform Basic-State Flow

Convectively forced mesoscale flows in three dimensions are theoretically investigated by examining the transient response of a stably stratified atmosphere to convective heating. Solutions for the equations governing small-amplitude perturbations in a uniform basic-state wind with specified convective heating are analytically obtained using the Green function method. In the surface pulse heating case, it is explicitly shown that the vertical displacement at the center of the 3D steady heating decreases as fast as t−1 for large t. Hence, unlike in two dimensions, the steady state is approached in three dimensions. In the finite-depth steady heating case, the perturbation vertical velocity field in the stationary mode shows a main updraft region extending over the heating layer and V-shaped upward and downward motions above and below the heating layer. Including the third dimension results in a stronger updraft at an early stage, a weaker compensating downward motion, and a weaker stationary gravity wave field in a quasi-steady state than in the case of two dimensions. An examination of flow response fields for various vertical structures of convective heating indicates that stationary gravity waves above the main updraft region become strong in intensity as the height of the maximum convective heating increases. In response to the transient heating, a main updraft region extending over the heating layer no longer appears at a dissipation stage of deep convection. Instead, alternating regions of upward and downward motion with an upstream phase tilt appear.