Stability of boundary layer flow based on energy gradient theory

TL;DR

This paper investigates boundary layer flow stability on a flat plate using energy gradient theory and Navier-Stokes simulations, identifying key energy gradient features that lead to flow instability and turbulence.

Contribution

It applies energy gradient theory to analyze flow instability mechanisms at the boundary layer's edge and near the wall, providing new insights into turbulence generation.

Findings

Velocity profile overshoot at boundary layer edge causes instability.

Large energy gradient function at the edge induces flow entrainment.

Maximum energy gradient near the wall leads to turbulence generation.

Abstract

The flow of the laminar boundary layer on a flat plate is studied with simulation of Navier-Stokes equations. The mechanisms of flow instability at external edge of the boundary layer and near the wall are analyzed using the energy gradient theory. The simulation results show that there is an overshoot on the velocity profile at the external edge of the boundary layer. At this overshoot, the energy gradient function is very large which results in instability according to the energy gradient theory. It is found that the transverse gradient of the total mechanical energy is responsible for the instability at the external edge of the boundary layer, which induces the entrainment of external flow into the boundary layer. Within the boundary layer, there is a maximum of the energy gradient function near the wall, which leads to intensive flow instability near the wall and contributes to the generation of turbulence.