Critical levels in a vertically rotating compressible atmosphere
Abstract
The propagation properties of gravity waves in a vertically rotating compressible vertically sheared zonal flow are investigated. In slowlyvarying shear flows the local dispersion relation is used to study the wavenormal surfaces and the possible types of ray trajectory. It is found that the relaxation of the Boussinesq approximation modifies the two critical levels present in the Boussinesq fluid in such a way that waves approaching them can exhibit valvelike behaviour. However, in a full wave treatment the valve behaviour, already known to be effected by variations in the basic state, is here modified by the neglect of the Boussinesq approximation. The influence of compressibility is shown to increase the number of singularities by two. The wave invariant of the system (which represents conservation of the vertical total waveenergy flux) is used to examine the influence of the singularities on the vertical propagation of the waves, and to conclude that energy absorption can only occur at the singularities present in a slowly varying basic state in an incompressible Boussinesq fluid.
 Publication:

Quarterly Journal of Mechanics and Applied Mathematics
 Pub Date:
 August 1979
 Bibcode:
 1979QJMAM..32..313E
 Keywords:

 Atmospheric Stratification;
 Compressible Fluids;
 Gravity Waves;
 Rotating Fluids;
 Shear Flow;
 Wave Propagation;
 Boussinesq Approximation;
 Energy Absorption;
 Incompressible Fluids;
 Particle Trajectories;
 Singularity (Mathematics);
 Surface Waves;
 Vertical Distribution;
 Wave Equations;
 Zonal Flow (Meteorology);
 Geophysics