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 et al., 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.

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