Large-scale structures in a developed flow over a wavy wall

Abstract

We address – motivated in part by the findings of Gong et al. (1996) and Miller (1995) – the role of streamwise-oriented large-scale structures in a developed flow between a sinusoidal bottom wall and a flat top wall. Particle image velocimetry (PIV) is used to examine the spatial variation of the velocity in different planes of the flow through a water channel with an aspect ratio of 12:1. The wave amplitude is equal to one tenth of the wall wavelength, Λ, and Reynolds numbers between 500 and 7300, defined with the bulk velocity and the half-height of the channel, are considered. To examine streamwise-oriented structures, the spanwise variation of the velocity field is studied in a plane parallel to the top wall, and in one that intersects the wavy surface at an uphill location. From a proper orthogonal decomposition (POD) of the streamwise velocity fluctuations, we obtain the dominant eigenfunctions with a characteristic spanwise scale of O(1.5Λ), which agrees with the scale of perturbations for the streamwise velocity at laminar conditions. A decomposition of the turbulent velocity field close to the uphill section of the wavy surface reveals smaller structures at a location that coincides with the Reynolds shear stress maximum.