A brief study over the performance of a water wave maker under its steady state condition
using linear small-amplitude wave theory.
The goal is to determine a free surface wave profile \(\eta(x,t)\), using the depth of the wave
container,
which is a driving value in the study of small amplitude waves, and the angular frequency of the
wavemaker.
The ratio of the wave height to flap stroke \(\frac{H}{S}\) is of interest as it characterizes
the performance of the system at a specific tank depth and angular frequency.
The greatest challenge with this analysis is determining an infinite series of roots for the
intersection of a periodic function and hyperbolic function. Each root describes a coefficient for a
series of standing waves that, when superimposed on the progressive wave, produce the unique wave
profile at the wavemaker flap.
Wave Profile function in time and space
The MATLAB program used to generate this information is linked below, as well as some useful resources
and sources.
project.m
findStandingDispersion.m
Wikiwaves.org
Water Wave Mechanics for Engineers and Scientists, Robert G. Dean, Robert A. Dalrymple