Centrifugal instability in a turbulent wall jet over a circular cylinder

The vortex instability mode is considered in a turbulent wall jet over a circular cylinder. The linear and nonlinear stability analyses are carried out within the scope of the parabolized stability equations. The results demonstrate that the neutral point may depend on the initial conditions because of the transient growth phenomenon but, farther downstream, the results collapse onto one curve. The marching method is compared with a quasi-parallel normal mode analysis. It is shown that the growth rate is overestimated in the normal mode approach. The results indicate that the zero harmonic (with respect to the spanwise direction) generated due to nonlinear effects may shift the maximum measured velocity profile farther from the surface than it is in a wall-jet over a flat wall.