Turbulent boundary layer over 2D and 3D large-scale wavy walls

Abstract

An experimental investigation of the flow over two- and three-dimensional large-scale wavy walls was performed using high-resolution planar particle image velocimetry in a refractive-index-matching (RIM) channel. The 2D wall is described by a sinusoidal wave in the streamwise direction with amplitude to wavelength ratio a/λx = 0.05. The 3D wall is defined with an additional wave superimposed on the 2D wall in the spanwise direction with a/λy = 0.1. The flow over these walls was characterized at Reynolds numbers of 4000 and 40 000, based on the bulk velocity and the channel half height. Flow measurements were performed in a wall-normal plane for the two cases and in wall-parallel planes at three heights for the 3D wavy wall. Instantaneous velocity fields and time-averaged turbulence quantities reveal strong coupling between large-scale topography and the turbulence dynamics near the wall. Turbulence statistics show the presence of a well-structured shear layer that enhances the turbulence for the 2D wavy wall, whereas the 3D wall exhibits different flow dynamics and significantly lower turbulence levels. It is shown that the 3D surface limits the dynamics of the spanwise turbulent vortical structures, leading to reduced turbulence production and turbulent stresses and, consequently, lower average drag (wall shear stress). The likelihood of recirculation bubbles, levels and spatial distribution of turbulence, and rate of the turbulent kinetic energy production are shown to be severely affected when a single spanwise mode is superimposed on the 2D sinusoidal wall. Differences of one and two order of magnitudes are found in the turbulence levels and Reynolds shear stress at the low Reynolds number for the 2D and 3D cases. These results highlight the sensitivity of the flow to large-scale topographic modulations; in particular the levels and production of turbulent kinetic energy as well as the wall shear stress.