Stability of the solitary wave boundary layer subject to finite-amplitude disturbances

Abstract

The stability and transition in the bottom boundary layer under a solitary wave are analysed in the presence of finite-amplitude disturbances. First, the receptivity of the boundary layer is investigated using a linear input-output analysis, in which the environment noise is modelled as distributed body forces. The most 'dangerous' perturbations in a time frame until flow reversal are found to be arranged as counter-rotating streamwise-constant vortices. One of these vortex configurations is then selected and deployed to nonlinear equations, and streaks of various amplitudes are generated via the lift-up mechanism. By means of secondary stability analysis and direct numerical simulations, the dual role of streaks in the boundary-layer transition is shown. When the amplitude of streaks remains moderate, these elongated features remain stable until the adverse-pressure-gradient stage and have a dampening effect on the instabilities developing thereafter. In contrast, when the low-speed streaks reach high amplitudes exceeding 15A % of the free stream velocity at the respective phase, they become highly unstable to secondary sinuous modes in the outer shear layers. Consequently, a subcritical transition to turbulence, i.e.A bypass transition, can be initiated already in the favourable-pressure-gradient region ahead of the wave crest.