Minimal seeds for transition to turbulence in the Stokes boundary layer

The Stokes boundary layer is the oscillatory flow above a plate, with oscillations driven either by (1) transverse sinusoidal motion of the plate or (2) a sinusoidal applied pressure gradient. Beyond a critical Reynolds number of 2511, the laminar solution of the Stokes boundary layer is susceptible to linear instability (the eigenvalues of the linear problems in cases 1 and 2 are identical, Blennerhassett & Basson, 2002). However, this instability is subcritical given that turbulence is observed for Reynolds numbers above approximately 700 (Ozdemir et al., 2014) despite the flow being linearly stable in this subcritical range of Reynolds numbers. In order to examine potential mechanisms which may cause transition to turbulence from the laminar flow in this subcritical range, Biau (2016) computed linear optimal perturbations in the Stokes boundary layer using linear transient nonmodal analysis, noting the importance of the Orr mechanism. However, it is well-established (see Kerswell, 2018, for a review) that linear transient growth results offer limited insight into the inherently finite-amplitude disturbances which are most likely to trigger transition to turbulence. Instead, the `minimal seed' for turbulence, the smallest amplitude perturbation that causes transition, provides such a nonlinear description. This talk will describe minimal seeds and their dynamics in the Stokes boundary layer, how they differ between cases (1) and (2), and their dependence on Reynolds number.