The Turbulent Boundary Layer on a Horizontally Moving, Partially Submerged, Surface-Piercing Vertical Wall

TL;DR

This study investigates turbulence and air entrainment at a vertical, surface-piercing wall using a laboratory setup with a moving belt, revealing how surface fluctuations relate to flow speed and turbulence, and comparing observations to theoretical predictions.

Contribution

It introduces a novel experimental setup to study turbulence and air entrainment on a moving, partially submerged vertical wall, providing new insights into surface fluctuations and entrainment mechanisms.

Findings

Surface height fluctuations increase linearly with belt speed.

A dominant spectral peak at a specific frequency in Couette flow.

Air entrainment mechanisms are observed and compared to theoretical models.

Abstract

The complex interactions between turbulence and the free surface, including air entrainment processes, in boundary layer shear flows created by vertical surface-piercing plates are considered. A laboratory-scale device was built that utilizes a surface-piercing stainless steel belt that travels in a loop around two vertical rollers, with one length of the belt between the rollers acting as a horizontally-moving flat wall. The belt is operated both as a suddenly-started plate to reproduce boundary layer flow or at steady state in the presence of a stationary flat plate positioned parallel to the belt to create a Couette flow with a free surface. Surface profiles are measured with a cinematic laser-induced fluorescence system in both experiments and air entrainment events and bubble motions are observed with stereo underwater white-light movies in the suddenly started belt experiment. It is found that the RMS surface height fluctuations, $\eta$, peak near the boundaries of the flows and increase approximately linearly with belt speed. In the Couette flow experiments, a dominant peak in the spectrum of $\partial\eta/\partial t$ is found at the dimensionless frequency $fH/U\approx 0.7$. In the suddenly started belt experiment, surface fluctuations appear to be strongly influenced by sub-surface turbulence within the boundary layer, while ripples propagate freely when farther from the belt. Additionally, some mechanisms for air entrainment are observed and comparisons are made to predictions of incipient entrainment conditions in Brocchini and Pregrine (J. Fluid Mech., 499, 225-254, 2001).