On separation of variables in the linearized nonhydrostatic atmospheric model

Abstract

The equations of the vertical and time-horizontal structures of the linearized nonhydrostatic atmospheric model are derived based only on a supposition of separation of variables. The obtained results are compared with those of the traditional approach of searching for solutions in the wave form with respect to time and/or horizontal coordinates. It is shown that all formulas of the vertical structure follow from the supposition of separation of the vertical coordinate alone. The time-horizontal structure equations are derived in a general form, which is reduced to the wave-type formulas under additional assumptions.

Keywords

• nonhydrostatic equations
• small perturbations
• separation of variables
• vertical structure equation