Acoustic-gravity wave dispersion relations in a baroclinic atmosphere

Transforming the linearized inviscid Navier-Stokes equations to a symmetric hyperbolic system of partial differential equations leads to a unique dispersion relation for the propagation of acoustic-gravity waves in a baroclinic atmosphere. The dispersion relation differs from the usual one because of the presence of a baroclinic term. In addition, C(y-l) -1/2V Zn 0q replaces the Brunt-Vaisala frequency, where C is sound speed, Y is the usual ratio of specific heats, and 0q is potential temperature, and C^((y-l)(V £n + (1/Y - 0.5) ^ in p^ 4- 0.5 V Zn C)^) replaces the square of the acoustic cut-off frequency where p^ is atmospheric pressure. It is argued that this dispersion relation be accepted as the standard for acoustic-gravity waves in either a baroclinic or a barotropic atmosphere.