On the spiking stages in deep transition and unsteady separation

Numerical simulations of a large-amplitude nonlinear two-dimensional train of Tollmien-Schlichting waves are performed first and show the development of short-scaled structures or spikes. A careful description of the spiking process and its subsequent development is given describing the generation of localized maxima in the streamwise pressure distribution and associated vortices, spikes in a perturbation velocity trace and the emergence of strong wall-normal pressure gradients. A high-Reynolds-number asymptotic theory has previously been developed by two of the authors which aims to describe this spiking process. The current work is the first to give a comparison between this theory and planar Navier-Stokes computations. We give a brief description of the theory showing how normal pressure gradients become active and their role in the generation of the streamwise pressure distribution and its subsequent effects such as vortex generation and wall-layer vorticity eruptions. The presentation is given with close qualitative reference to the simulations, so giving credence to the relevance of the theoretical account and an interpretation of that account in physical terms. The comparison, although primarily qualitative, is successful in that it is possible to identify the physical processes highlighted by the theory in the computations, so clarifying the complex fluid motions and suggesting directions for further research. The paper concludes with firstly a discussion of how the results of the simulations and the theory could be used to give an understanding of similar processes seen in unsteady planar separation and secondly their relevance to the strongly three-dimensional processes at work in deep transition experiments.