ACOUSTIC FILTERING IN NONHYDROSTATIC PRESSURE COORDINATE DYNAMICS - AVARIATIONAL APPROACH

A nonhydrostatic, acoustically filtered model of atmospheric dynamics in pressure coordinates is derived using a special filtering technique . The initial complete nonhydrostatic equations in pressure space are linearized. The linearized system is divided into two subsystems-an in dependent equation for potential vorticity, which determines the quasi -solenoidal horizontal flow and is a local invariant in the absence of heat sources, and a fourth-order wave system describing acoustical an d buoyancy waves. A Lagrangian function, corresponding to the wave equ ations, is derived. The acoustic filtering is carried out in the Lagra ngian. The approximated Lagrangian generates filtered wave equations a nd the linear Altered equations of motion. As a final step, the linear model is extended to a nonlinear nonhydrostatic acoustically filtered model by inclusion of advection terms in the vorticity equation and b y nonlinear generalization of the Hamiltonian principle for the wave s ystem. Thus, variational principles are employed for both the acoustic al filtration and nonlinear extension of the filtered approximation, w hich guarantees the maintenance of conservational qualities of initial model in the final filtered version. The deduced dynamical model has no previous analogs.