Accuracy of solitary wave generation by a piston wave maker.

Guizien Katell,Barthélemy Eric

doi:10.1080/00221680209499946

Guizien Katell, Barthélemy Eric

Open Access

https://doi.org/10.1080/00221680209499946

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Abstract

A new experimental procedure to generate solitary waves in a flume using a piston type wave maker is derived from Rayleigh's (1876, [18]) solitary wave solution. Resulting solitary waves fordimensionless amplitudes £ ranging from 0.05 to 0.5 are as pure as the ones generated using Goring's (1978, [7]) procedure which is based on Boussinesq (1871a, [1]) solitary wave, with trailing waves of amplitude lower than 3 % of the main pulse amplitude. In contrast with Goring's procedure, the new procedure results in very little loss of amplitude in the initial stage of the propagation of the solitary waves. We show that solitary waves generated using this new procedure are more rapidly established. This is attributed to the better description of the outskirts decay coefficient in a solitary wave given by Rayleigh's solution rather than by a Boussinesq expression. Two other generation procedures based on first-order (KdV) and second order shallow water theories are also tested. Solitary waves generated by the latter are of much lower quality than those generated with Rayleigh or Boussinesq-based procedures.

Highlights

The aim of this study is to assess solitary wave generation proce dures
A new experimental procedure to generate solitary waves in a flume using a piston type wave maker is derived from Rayleigh's (1 876, [1 8])solitary wave solution
During the second set of experiments, we studied the changes occurring in the first moments of propagation of the solitary wave emerging from the Korteweg-De Vries (KdV) and Rayleigh solutions, between x = 1 7h0 andx = 83h0 for h0 = 0.3 m

Summary

Introduction

The aim of this study is to assess solitary wave generation proce dures. Hammack and Segur ( 1 974, [ 1 0]) showed experimentally and theoretically that from any net positive volume of water above the sti l l water level, at least one solitary wave wil l emerge followed by a train of (dispersive) waves. And Stephan (1952, [6]) displaced a given mass of water by the vet1ical motion of a piston rising from the bottom of a tank. Our concern in this study is to generate solitary wave as 'pure' as possible This means we have focussed our efforts in generating waves with minimised trailing waves and of stable amplitude during propagation. As the dimensionless amplitude of a solitary wave increases up to£= 0.796 (E = A!h0 where A is the solitary wave amplitude and h0 is the mean water depth), its phase speed in creases Above this value, the phase speed tends to de crease (Longuet-Higgins and Fenton, 1 974 [ 1 5], Byatt-Smith and Longuet-Higgins, 1 976 [4]). In most applications, generating the largest solitary wave is not so impor tant

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