ABSTRACT

A new experimental investigation is presented. A series of regular progressive gravity waves were observed within a laboratory wave flume and the underlying kinematics were measured using laser Doppler anemometry. Three different wave forms were considered, and the horizontal velocity component was determined throughout the crest to trough region. For the purpose of wave loading, the maximum horizontal velocity component occurring beneath the wave crest is deemed to be of particular importance. To assess this parameter the present measurements were concentrated within the crest region, and include measurements just beneath the maximum crest elevation. The observations are compared with a number of different wave theories. It is shown that the appropriate steady wave theory can provide a very good description of the flow field within the crest to trough region. However, to achieve this the solution must incorporate the ‘Eulerian back-flow’ which will develop within an experimental wave flume. Provided this is taken into account there is no evidence to suggest that the steady wave theories overestimate the positive velocities occurring beneath the wave crest and underestimate the negative velocities occurring beneath the wave trough. As a result, the present measurements cast considerable doubt on the use of the various "stretching techniques within the crest to trough region.

INTRODUCTION

It is widely accepted that the near surface kinematics associated with a series of progressive gravity waves produce a significant proportion of the total load experienced by a surface piercing structure. The application of Morison's equation suggests that both the drag force and the inertial force attain their maximum value within the near surface region. The drag force is proportional to the square of the wave induced horizontal velocity (u) and is therefore a maximum beneath the wave crest. The inertial force is dependant upon the magnitude of the horizontal acceleration (du/dt). This also attains its maximum value on the surface profile approximately midway between the wave crest and the wave trough. In this case it is interesting to note that as the wave steepness increases there is a corresponding increase in the horizontal acceleration, and the relative phase at which it occurs moves closer to the wave crest.

As a result of these effects the wave induced kinematics within the crest to trough region have been the subject of several investigations. For example. Le Mehaute et al (1968) produced a comparison between theory and experiment in shallow water conditions, and Nath and Koburn (1978) produced a similar comparison in deep water conditions. More recently, this experimental data has been used as the basis for several comparisons involving a variety of different wave theories (eg Gudmestad and Connor, 1986). Although this experimental data is rather limited, a number of researchers have concluded that the available wave theories are unable to satisfactorily explain the observed kinematics within the crest to trough region. Gudmestad and Connor (1986) suggested that a classical Stokes expansion overestimates the magnitude of the horizontal velocity beneath the wave crest, and underestimates the magnitude beneath a wave trough.

This content is only available via PDF.
You can access this article if you purchase or spend a download.