WAVE SOLUTIONS OF THE VORTICITY EQUATION FOR THE 2½-DIMENSIONAL MODEL

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Abstract
Wave solutions of the non-linear quasi-geostrophic equations for the so-called “2½-dimensional model” without friction are derived. The solutions describe wave motions which propagate at different speeds in each layer. The amplitudes of the disturbances, are either changing periodically with time (stable waves) or increasing exponentially (unstable waves). The critical value of wavelength, at which waves maintain a constant amplitude, is expressed as a function of thermal stability and of vertical wind shear in the basic current. It is also found that, while the inclination of trough lines to the vertical increases monotonically with time in stable waves, it varies very slowly in the unstable waves and tends to approach a certain limiting value.

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