Turbulent Boundary-layer Flow Beneath A Vortex. Part 1. Turbulent Bodewadt Flow

The equations governing the mean fluid motions within a turbulent boundary layer adjoining a stationary plane beneath an axisymmetric circumferential flow , where is cylindrical radius, are solved by assuming the eddy diffusivity is proportional to times a diffusivity function , where is axial distance from the plane. The boundary-layer shape and structure depend on the dimensionless vorticity , but are independent of the strength of the circumferential flow. This problem has been solved using a spectral method in the case of rigid-body motion ( and ) for two models of : constant (model A) and constant within a rough layer of thickness adjoining the boundary and increasing linearly with outside that layer (model B). The influence of the rough layer is quantified by the dimensionless radial coordinate , where . The boundary-layer thickness varies parabolically with for model A and nearly linearly with for model B. Inertial stability of the outer flow causes the velocity components to decay with axial distance as exponentially damped oscillations, with the radial flow consisting of a sequence of jets. Axial flow is positive (flowing out of the boundary layer). Outflow from the layer, velocity gradients at the bounding plane, meridional-plane circulation and oscillations all increase as radius decreases.