Pump flow solutions of the Navier-Stokes equations

Exact solutions of the Navier-Stokes equations are used to describe pump fl ows that involve the interaction of several different components. As an ill ustration of the general representations obtained, a detailed description i s given of flows that involve both a swirl and a shear component. Such flow s are common in the atmosphere. For example, they are produced in the core of a vortex as it moves over a horizontal surface into a region where the f low is sheared in a direction normal to the surface. Far from the surface, the vortex core translates in a direction parallel to the surface, and the flow asymptotes to that in an Ekman spiral. When the core rotates and trans lates with speeds that vary in time, the flow develops both updraft and dow ndraft regions.