Boundary Layers due to the Combined Effects of Rotation and Translation

Exact solutions of the Navier-Stokes equations are given for certain flows in which an infinite plane and the adjacent fluid have relative rotation and translation. Equations for the boundary-layer profiles are given in a general form that includes the possibility of time-dependent solutions. Numerical results are restricted to two cases of steady flow, in which either the fluid is translating and the plate is rotating, or the plate is in pure translation adjacent to a rotating fluid. Analytical solutions are discussed, including time-dependent cases, for vanishing and for small differences between the angular velocities of the plate and the fluid.