| Abstract: | A family of exact solutions of the Navier-Stokes equations is used to describe local flows of incompressible stratified and compressible fluids. For some of the flows, the coefficient of viscosity can depend on the temperature. An example of an incompressible stratified flow for which the analysis is applicable is the sheared swirling flow that is produced between two parallel plates that translate with different velocities and rotate with different angular velocities about different, but parallel, axes. The fluid may be stratified in the direction normal to the plates. These generalized von Karman flows are relevant to the study of strong local atmospheric disturbances, such as might be produced by the passage of a tornado. Also, when the coefficient of viscosity depends on the temperature, they can be used to analyze the flow of molten metals between surfaces that are in relative motion. An example of a compressible flow for which the analysis is applicable is that produced by a plane shock wave as it traverses a layer where the fluid is sheared in a direction normal to the shock. |
