| A mechanism that generates waves on the lower atmosphere is convection due to heat irradiated from the ground. As these waves propagate upward, they deform and break, hence transferring momentum and mixing the air.; Mixing is a fundamental process in the dynamics of the atmosphere, it is very poorly understood on theoretical grounds. In this thesis we shall not attempt to model vertical mixing, but focus instead on the transfer of momentum through the breaking upward propagating waves.; Our main goal is to build a simple mathematical model that permits us to analyze the behavior of the upward propagating waves generated by a moving heat source—with deterministic and stochastic components—in a two-dimensional atmosphere described by the equations of conservation of mass and conservation of momentum, with no vertical mixing.; In order to work in the simplest possible setting, we introduce the hydrostatic balance approximation in the vertical momentum equation and a change to isentropic coordinates.; The nonlinearity of the equations plays a fundamental role in the description of the system, since their linearized version diverges at the “top” of the atmosphere: the small perturbations around mean values, considered for the approximation, amplify explosively as they approach the upper atmosphere. One may therefore conjecture that nonlinearity induces the formation of shocks, which dissipate energy and transfer momentum.; An additional difficulty posed by these equations is the presence of local and global variables simultaneously: pressure has to be computed by integration using the boundary condition at the “top”, and the vertical coordinate, z, needs the boundary condition at the ground to be computed.; The way we devised to treat these problems makes use of the Galilean invariance of the system of equations and the conservative character of the Jacobian in the horizontal momentum equation. The computational code implemented using these ideas is validated by comparing the numerical results with exact particular linear solutions.; We use the numerical results to analyze the effects of the upward propagating waves on the mean state of the atmosphere, using the energy profile of the system to monitor the dissipation due to breaking waves. |
