Laminar-turbulent separatrix in a boundary layer flow

TL;DR

This paper investigates the laminar-turbulent transition in boundary layer flow by simulating the edge state on the separatrix, revealing key features of transitional dynamics and introducing a scale-separated modeling approach.

Contribution

It introduces a novel simulation of the edge state on the laminar-turbulent separatrix and presents a scale-separated model validated against turbulent boundary layer data.

Findings

Edge state resembles a low speed streak with vortices

Model reproduces outer boundary layer characteristics

Edge state provides insight into transition mechanisms

Abstract

The transitional boundary layer flow over a flat plate is investigated. The boundary layer flow is known to develop unstable Tollmien-Schlichting waves above a critical value of the Reynolds number. However, it is also known that this transition can be observed for sub-critical Reynolds numbers. In that case, the basin of attraction of the laminar state coexists with the sustained turbulence. In this article, the trajectory on the separatrix between these two states is simulated. The state on the separatrix is independent from the initial condition and is dynamically connected to both the laminar flow and the turbulence. Such an edge state provides information regarding the basic features of the transitional flow. The solution takes the form of a low speed streak, flanked by two quasi-streamwise sinuous vortices. The shape of the streaks is close to that simulated with the linear optimal perturbation method. This solution is compared to existing results concerning streak breakdown. The simulations are realized in a temporal framework for a local boundary layer, with periodic boundary conditions in the streamwise direction. A dedicated model, based on a scale separation, is presented. The mean flow is a solution of the Prandtl boundary layer equations while the superposed small-scale fluctuations are a solution of the periodic Navier-Stokes equations. The model is validated with turbulent flow simulations and satisfactorily reproduces the physical characteristics of a boundary layer flow, especially in the outer region, where external fluid is entrained toward the boundary layer.