The boundary layer flow induced above the torsional motion of a disk

Abstract

The boundary layer flow above a disk in torsional motion with azimuthal velocity proportional to rm is investigated for all values of m ≥ 1; here, r is the radial coordinate measured from the center of the disk. The resulting flow is a fully three-dimensional exact solution to the steady, axisymmetric boundary layer equations in the form of similarity solutions. We compute wall shear stresses in the radial and azimuthal directions as a function of the torsional exponent m, as well as the flow induced in the far field. The large m asymptotics of the problem are computed and compared with numerical solutions. The induced radial velocity profiles have a "wall-jet" structure, and it is found that both the radial and azimuthal velocity components become confined close to the surface of the disk as m increases.