Transient growth in a flat plate boundary layer under a stream with uniform shear

TL;DR

This paper investigates how uniform shear in a flat plate boundary layer influences transient energy growth, revealing that shear amplifies disturbances exponentially and differs from classical Blasius flow in optimal disturbance characteristics.

Contribution

It provides new insights into transient growth in shear boundary layers, including scaling laws for energy amplification related to freestream shear.

Findings

Optimal disturbances are streamwise vortices.

Maximum energy amplification increases exponentially with shear gradient.

Differences observed compared to Blasius boundary layer.

Abstract

One of the simplest problems involving external vorticity in boundary layer flows is the flow over a semi-infinite plate under a stream of uniform shear. We study the transient growth phenomenon in this flow to investigate the role of freestream shear on energy amplification, and analyse the differences with the Blasius flow. The initial optimal disturbance which triggers the maximum growth is found to be streamwise vortices, as in other shear flows. Compared to the Blasius boundary layer, higher optimum energy and larger spanwise wavelength of streamwise vortices have been observed. We provide scaling laws for the maximum optimal amplification, which is found to increase exponentially with the freestream shear gradient.