Flow Instability: Transition and Non Linearity

The viscous boundary layer flow near an oscillating wall (Stokes problem) is known to exhibit extreme linear subcritical transient growth (Biau 2016), with energy amplification factors reaching up to 10^8 for Re =1200. While linear optimals are now well understood, the form of the finite-amplitude "minimal seed" capable of triggering transition to turbulence is unknown. In this talk, we address the nonlinear optimization problem of identifying the smallest finite-energy perturbations that produce the largest transient growth over a finite time T and ultimately the minimal seed. Using a direct-adjoint looping (DAL) method combined with steepest ascent in a fully nonlinear two-dimensional Navier–Stokes framework, we aim to uncover localized perturbation structures that surpass their linear counterparts in terms of intracyclic energy amplification. These results should offer new insight into nonlinear transition mechanisms in oscillatory shear flows.

Funding acknowledgement

ESPRC