The growth mechanism of boundary layers for the 2D Navier-Stokes equations

TL;DR

This paper analyzes the formation of boundary layers in the 2D Navier-Stokes equations as viscosity approaches zero, showing how vorticity and layer width evolve over time.

Contribution

It provides a detailed description and proof of the boundary layer growth mechanism in the inviscid limit for 2D Navier-Stokes equations.

Findings

Vorticity near the boundary grows to size 1/√ν

Boundary layer width spreads proportionally to √ν

Growth time scale is approximately proportional to ν

Abstract

We give a detailed description of formation of the boundary layers in the inviscid limit problem. To be more specific, we prove that the magnitude of the vorticity near the boundary is growing to the size of $1/\sqrt{\nu}$ and the width of the layer is spreading out to be proportional the $\sqrt{\nu}$ in a finite time period. In fact, the growth time scaling is almost ${\nu}$