Stability of an Axisymmetric Wake

Abstract

The stability of an axisymmetric wake is studied relative to infinitesimal axisymmetric disturbances. The Orr-Sommerfeld equation is solved by an expansion in powers of αR, where α is the non-dimensional wave number and R the Reynolds number with respect to the effective radius and the velocity defect in the center of the wake. The critical Reynolds number is found to be 5.19. The asymptotic behavior of the neutral curve as α→0 is such that R→1.08α⁻¹ and c→0.676.