An investigation of the mesoscale waves of small amplitude in the westerlies

Abstract

The complete set of hydrodynamic equations for a stratified, compressible, inviscid fluid undergoing zonal motion on a rotating earth is transformed into a linearized symmetric form, assuming simple harmonic behavior in zonal direction and time. These perturbation equations are then combined into a second order, partial differential equation involving the pressure perturbation as the dependent variable and assuming the parameters to be a function of the coordinates transverse to the flow. This equation is of standard type and can be reduced to an Orr-Sommerfeld equation of which the mountain wave equation is a special case. Special approximate solutions are investigated in order to determine the basic characteristics of the perturbation flow. The associated characteristic or frequency equation is of ninth degree in the frequency. From an analysis of this frequency equation it is postulated that there exists a potentially unstable band of wavelengths in the mesoscale regime whose characteristics are determined primarily by the stable stratification and wind shear of the basic flow. Wind and temperature data from Project Jet Stream support this hypothesis. Although the phase relationships between the variables could not be confirmed quantitatively, the ratio of the amplitudes were of the order of magnitude consistent with the theory which predicts simple periodic relationships.