Steady streaming in a channel with permeable walls

TL;DR

This paper investigates steady streaming flows in a channel with permeable walls caused by oscillating blowing and suction, revealing that permeable boundaries significantly enhance streaming magnitude compared to impermeable cases.

Contribution

The study provides an asymptotic analysis of Navier-Stokes solutions for permeable walls, showing increased streaming effects due to boundary permeability.

Findings

Steady streaming magnitude is significantly larger with permeable walls.

Asymptotic expansion derived for small amplitude oscillations.

Permeability enhances flow effects compared to impermeable boundary cases.

Abstract

We study steady streaming in a channel between two parallel permeable walls induced by oscillating (in time) blowing/suction at the walls. We obtain an asymptotic expansion of the solution of the Navier-Stokes equations in the limit when the amplitude of the normal displacements of fluid particles near the walls is much smaller that both the width of the channel and the thickness of the Stokes layer. It is demonstrated that the magnitude of the steady streaming is much bigger than the corresponding quantity in the case of the steady streaming produced by vibrations of impermeable boundaries.