Secondary Instabilities in Incompressible Axisymmetric Boundary Layers: Effect of Transverse Curvature

The secondary instability of the incompressible boundary layer in the axial flow past a cylinder is studied. The laminar flow is shown to be always stable at high transverse curvatures to secondary disturbances. Because the primary mode is stable as well, (Tutty , 2002, “Boundary Layer Flow on a Long Thin Cylinder,”. Phys. Fluids, 14 (2), pp. 628–637), this implies that the boundary layer on a thin long cylinder may undergo transition to turbulence by means very different from that on a flat plate. The azimuthal wavenumber of the least stable secondary modes (m±) are related to that of the primary (n) by m+ = 2n and m− = −n. The base flow is shown to be inviscidly stable at any curvature.
by Vinod Narayanan and Rama Govindarajan