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

TL;DR

This paper investigates the stability of the boundary layer under solitary waves, revealing how finite amplitude disturbances and streaks influence transition to turbulence through linear and nonlinear analyses.

Contribution

It introduces a combined linear and nonlinear approach to analyze boundary layer stability under solitary waves, highlighting the dual role of streaks in transition mechanisms.

Findings

Moderate streaks stabilize the boundary layer until adverse pressure stages.

High-amplitude streaks (>15% of free-stream velocity) induce secondary instabilities.

Subcritical transition to turbulence can occur ahead of the wave crest due to streak instability.

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 rollers. One of these roller configurations is then selected and deployed to nonlinear equations, and streaks of various amplitudes are generated via 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 15% of 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., bypass transition, can be already initiated in the favourable-pressure-gradient region ahead of the wave crest.