Wave Motion in a Rotating Couette Flow of a Viscous Fluid

Abstract

With the assumption of non-divergence horizontal flow, a certain class of solutions of the nonlinear hydrodynamic equations are obtained for a viscous Couette flow on an earth whose variation of Coriolis parameter with latitude is constant. These solutions yield waves of transient type, of which the amplitude, wave velocity, and the inclination of the trough and ridge lines vary with time. For Couette flow with both lateral and vertical velocity-shears, the vertical profile of the amplitude of the waves can either be exponential in z or independent of z, whereas for Couette flow with lateral velocity-shear only it permits to be independent of z, a sinusoidal function, or a hyperbolic sine or cosine of z. These waves will eventually disappear in a Couette flow regardless the fluid is viscous or not, although under certain conditions waves may be amplified within a certain time interval. Pressure field, geostrophic deviation, meridional transports of energy and westerly momentum are obtained for such a flow system. For reasonable values of the constants for atmospheric systems, geostrophic deviation can be as high as one order magnitude smaller than the actual wind speed. DOI: 10.1111/j.2153-3490.1955.tb01174.x