Assessing the validity of regular wave theory in a short physical wave flume using particle image velocimetry

Abstract

The modelling of ocean waves is an integral part of coastal and offshore engineering. Both theoretical and experimental modelling methods are available and are commonly used in support of each other. In particular, due to the difficulty in measuring the velocity throughout the water column, the wave kinematics are often derived, by means of wave theory, from a measurement of the free surface elevation. However, wave theory is often based upon idealistic conditions, such as infinite spatial domains and time lengths. The question therefore arises, how well are the wave kinematics in an experimental wave tank described by wave theory? The present paper compares theoretical solutions against experimental data, for the free surface elevation and the velocity throughout the water column, to assess the ability of Stokes’ wave theory to describe the kinematics of regular waves in a short, physical, wave flume. Experimentally, the free surface elevation is measured with a set of resistive wave probes, while wave kinematic data is acquired with particle image velocimetry (PIV). For this study, ten different regular waves, of varying steepness, are generated in a 35 m long and 0.7 m deep wave flume. The theoretical solutions are computed based on Stokes 2nd order wave theory. The presented results show error values of the order of 10–20%, indicating validity of the employed wave theory as a function of the reflection coefficient achieved in the physical wave flume. These result highlight the potential inaccuracies incurred in any wave tank if the wave theory is used to derive the kinematics from the free surface elevation without having detailed knowledge of the reflection characteristics at the point of interest in the tank.