On the non-linear evolution of Goertler vortices in non-parallel boundary layers

Perturbation methods based on the smallness of the nondimensional wavelength of vortices are employed to calculate the nonlinear development of finite amplitude Goertler vortices in a nonparallel boundary layer on a curved wall. A critical growth or decay stage of the vortices is found to take place in a viscous layer. The downstream velocity component of the perturbation features a mean flow correction of the same order of magnitude as the fundamental driving it. The disturbance at a particular location is determined to either expand into a full vortex or decay to zero, depending on downstream conditions being steady or unsteady. A sufficiently large curvature is necessary for a concave wall to trip the vortices in the case of a Blasius boundary layer. The disturbance at first grows linearly, then is stabilized by nonlinear effects.