STABILITY OF A FLUID FLOW IN A FLAT CHANNEL WITH WAVY WALLS

This paper presents the study of a viscous fluid flow between two wavy horizontal surfaces unbounded longitudinally and transversely. Full Navier–Stokes equations are applied to describe the linear stability of such a flow with respect to various three-dimensional perturbations. Two types of wall waviness are studied: longitudinal and transverse periodic corrugation. The first stage is comprised of obtaining the main solution and linearizing initial equations in the vicinity of this solution. The second stage is comprised of solving the generalized problem of determining eigenvalues and analysing the entire possible spectrum of perturbations. The varied parameters are the Reynolds number, as well as corrugation amplitude, period, and shape. Velocity and pressure field perturbations are generally characterized by two wave numbers, which are additional parameters. The influence of the parameters and shape of the wall waviness on the region where the laminar-turbulent transition begins is investigated.