The linear hydrostatic, geostrophic adjustment problem for an inviscid, compressible, diatomic, isothermal base-state atmosphere in a rotating reference frame is analytically investigated. A hydrostatic, geostrophic imbalance is produced by the application of an instantaneous, localized heat source. The final state is determined through consideration of potential vorticity conservation. Adjustment back to a hydrostatic, geostrophic state is achieved through the action of acoustic and gravity waves. Some of the energy associated with the heating is lost from the initial state to acoustic gravity waves. The fraction of total energy lost to the waves depends on the geometry of the heating function. For example, less energy is lost to the waves when the width of the heating is increased and the amplitude and net heating are held constant. The initial boundary-value problem can be expressed as a Sturm - Liouville type problem in space. Solving the Sturm - Liouville problem can be achieved by finding the orthonormal eigensolutions that are implied through boundary conditions. The eigensolutions comprise a complete set onto which any particular solution specified by initial conditions must project. Such a solution method is tested for a horizontally homogenous fluid bounded above and below by rigid boundaries. The fluid is heated rapidly by a delta function in time and a top hat vertical spatial structure. Acoustic waves are generated and are explicitly described by the eigensolutions. Work in progress involves extending the solution of the 1D, finite-volume problem to the 3D, semi-infinite problem. Finding the eigensolutions to the 3D, semi-infinite problem should explicitly reveal the difference between the roles of acoustic waves and gravity waves in achieving hydrostatic, geostrophic balance.
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12th Conference on Atmospheric and Oceanic Fluid Dynamics