Transition of free disturbances in inflectional flow over an isolated surface roughness

Three-dimensional nonlinear initial-value problems are derived on the onset of transition, in inflectional flow, over a surface roughness buried within a boundary layer and in related configurations. This start on the basic transition physics is for the free evolution of general disturbances rather than forced, fixed-frequency or fixed-wavelength evolutions. An integral criterion of earlier nonlinear work holds at leading order. The nonlinear amplitude-evolution equation then obtained at the next order is for fairly general initial conditions of the disturbance, not just wave packets. Three or four such initial-value problems are developed, along with analytical and computational solution properties which include nonlinear bounded behaviour leading to persistent vortex effects as time increases, or quasi-linear decay, or nonlinear finite-time blow-ups of the disturbance amplitude. The discussion includes the connections between the different cases present, and the Links with roughness-transition experiments.