The Principal Investigator will undertake a theoretical investigation of moist atmospheric adjustment processes. Moist atmospheric adjustment is defined as the response of a moist compressible atmosphere to a prescribed heating and/or moistening. Immediately after an instantaneous heating/moistening of arbitrary shape, the atmosphere will, in general, be in a state of geostrophic and hydrostatic imbalance. The study of moist atmospheric adjustment describes the subsequent tendency of the air to achieve a state of geostrophic and hydrostatic balance. It is an extension of the classic problem of geostrophic adjustment to include the effects of compressibility and to allow for nonhydrostatic and moist processes. The solutions will also shed light on the dynamics of clouds, gust fronts, and other nonhydrostatic circulations driven by moist convection. Although both heating and moistening correspond to an addition of buoyancy to the air mass, there is a fundamental difference. An addition of heat can be transformed to other forms of energy which can be propagated away; an addition of water must be conserved and can not be transformed (in the absence of phase changes) and propagated out of the system. A prototype model of the atmospheric response to the problem of evaporative cooling in a compressible atmosphere is presented in the proposal.
A suite of problems are proposed to examine the full effects of compressibility that include heating and moistening. Linear and nonlinear solutions of idealized one-dimensional problems will use Lagrangian techniques and the conservation of potential vorticity to obtain the final state of balance. Laplace and Fourier transform techniques will be used to solve for the linear time-dependent problems analytically and numerically. The energetics will be examined and the partitioning of the energy between the acoustic and gravity modes and the balanced final state will be assessed. These solutions provide a benchmark to test the dynamical cores of mesoscale, cloud, and forecasting models.
The proposed research will also seek to develop a set of moist anelastic equations that are energy conserving, that are consistent with the acoustic component of moist atmospheric adjustment, and that best capture the effect of moisture on the Brunt-Vaisala frequency.
Successful completion of this theoretical study will increase knowledge of the accuracy of various approximations that are often employed in atmospheric forecast systems.