Minimal seeds in the Stokes boundary layer

TL;DR

This paper investigates the smallest perturbations that can cause turbulence in the Stokes boundary layer, highlighting the roles of linear transient growth and nonlinear interactions in transition.

Contribution

It identifies the characteristics of minimal seeds in the Stokes boundary layer and explains their dynamics involving linear growth and nonlinear energy transfer.

Findings

Minimal seeds are dominated by linear transient growth initially.

Only 73% of initial energy comes from the linearly optimal mode.

Nonlinear interactions transfer energy to spanwise- and streamwise-independent structures.

Abstract

Minimal seeds, the smallest amplitude perturbations that trigger transition to turbulence, are presented in the Stokes boundary layer, the oscillating flow of a viscous fluid above a flat plate. The minimal seed trajectories are dominated by the Stokes boundary layer's large linear transient growth at early times, but only 73% of the initial energy is formed from the linearly optimal growing mode; the remainder ensures that nonlinear interaction transfers energy from spanwise- to streamwise- independent structures, and makes up for a timing mismatch between the end of linear transient growth and the production phase of the edge state (the saddle point separating laminar and turbulent basins of attraction).