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Acoustic Filtering in Nonhydrostatic Pressure Coordinate Dynamics: A Variational Approach

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  • 1 Tartu Observatory, Toravere, Estonia
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Abstract

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 independent 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 and buoyancy waves. A Lagrangian function, corresponding to the wave equations, is derived. The acoustic filtering is carried out in the Lagrangian. The approximated Lagrangian generates filtered wave equations and the linear filtered 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 by nonlinear generalization of the Hamiltonian principle for the wave system. Thus, variational principles are employed for both the acoustical filtration and nonlinear extension of the filtered approximation, which guarantees the maintenance of conservational qualities of initial model in the final filtered version. The deduced dynamical model has no previous analogs.

Corresponding author address: Dr. R. Rõõm, Tartu Observatory, EE2444 Tõ→vere, Tartumaa, Estonia.

Email: room@aai.ee

Abstract

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 independent 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 and buoyancy waves. A Lagrangian function, corresponding to the wave equations, is derived. The acoustic filtering is carried out in the Lagrangian. The approximated Lagrangian generates filtered wave equations and the linear filtered 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 by nonlinear generalization of the Hamiltonian principle for the wave system. Thus, variational principles are employed for both the acoustical filtration and nonlinear extension of the filtered approximation, which guarantees the maintenance of conservational qualities of initial model in the final filtered version. The deduced dynamical model has no previous analogs.

Corresponding author address: Dr. R. Rõõm, Tartu Observatory, EE2444 Tõ→vere, Tartumaa, Estonia.

Email: room@aai.ee

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