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.
Highlights
Solitary waves are long waves of permanent form, which induce approximately constant velocity in the water column (Munk 1949)
We further observe in figure 19(c,d) that the primary and inner instabilities are more sensitive to E0 compared with outer instabilities. These results show that transition to turbulence in the solitary-wave boundary layer (SWBL) depends on the amplitude of environment perturbations even in the case of orderly transition with two-dimensional instability modes
We have investigated the transition to turbulence in the bottom boundary layer beneath a solitary wave by means of a simple parallel model taking into account finite-amplitude perturbations
Summary
Solitary waves are long waves of permanent form, which induce approximately constant velocity in the water column (Munk 1949). Finite amplitude external perturbations such as breaking-wave turbulence, sound or small-scale bedforms can lead to significant growth in finite times and yield secondary base states that can be unstable Such subcritical transition can take place in the FPG region before the arrival of the wave, and is analogous to bypass transition in zero-pressure gradient (ZPG) boundary layers (Morkovin 1969), as the modal instability is bypassed by another noise-induced mechanism. The cases with 5 % or more noise and Reδ 1500, where the Reynolds number is defined using Stokes length and the maximum free stream velocity (cf § 2 for details), showed an initial energy amplification inside the boundary layer lasting until another more rapidly growing amplification mechanism takes over in the APG stage after flow reversal They speculated that this early perturbation growth should be due to a nonlinear viscous instability, as it takes place in the FPG stage where velocity profiles do not contain any inflection point, a necessary condition for inviscid instability.
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