Oscillations of laminar flow velocity in a channel induced by harmonic perturbation of mass injection velocity through the permeable wall

TL;DR

This paper investigates how small harmonic perturbations in mass injection velocity through a permeable channel wall induce oscillations in laminar flow velocity, revealing amplitude growth and frequency effects along the channel.

Contribution

It derives a simplified equation for flow velocity profile and analyzes the impact of harmonic perturbations on oscillation behavior in permeable channels.

Findings

Oscillation amplitude peaks increase with distance along the channel.

Higher frequencies cause peaks to move closer to the walls.

Flow velocity oscillations are significantly affected by perturbation parameters.

Abstract

Transient Navies--Stokes equations for laminar flow of incompressible fluid in a channel with permeable wall are reduced to a single equation for the transversal profile of longitudinal flow velocity. Small--amplitude harmonic perturbation of injection velocity induces oscillations of longitudinal velocity with the peak at the walls. The oscillations amplitude in peaks dramatically increases with the distance along the channel; with the frequency growth peaks come closer to the walls.