APPLICATIONS OF EXACT-SOLUTIONS TO THE NAVIER-STOKES EQUATIONS - FREE SHEAR LAYERS

A family of exact solutions to the Navier-Stokes equations is used to analyse unsteady three-dimensional viscometric flows that occur in the vicinity of a plane boundary that translates and rotates with time-varying velocities. Such flows are important in the study of flows that are produced by rotating machinery. They are also useful in describing local behaviour in more complex global flows, such as that produced in a shear layer by the passage of a disturbance in the mainstream. An example is the flow produced in a turbulent shear layer by the passage of the core of a Rankine vortex. When the effect of viscosity is unimportant, the use of Lagrangian coordinates reduces the mathematical problem to that of solving a set of linear ordinary differential equations.