Dynamic covariance equations for hinged wavemakers

Abstract

The squared modulus of the theoretical dimensionless frequency response functions for the wavemaker stroke spectrum, | H s ( ω)| 2, and for the wavemaker hydrodynamic pressure moment spectrum, | H M ( ω)| 2, were verified experimentally for hinged wavemakers of variable-draft in the Oregon State Wave Research Facility (OSU-WRF). The random motions of the hinged wavemaker that were employed in the experimental studies were synthesized on a mini-computer from two types of two-parameter theoretical design wave spectra by a unique inverse stacked finite Fourier transform algorithm. The dimensionless frequency response function for the hydrodynamic pressure moment about the wavemaker hinge was not measured directly; but was instead estimated from the dynamic covariance equations for a hinged wavemaker of variable-draft through a linear combination of related dimensionless frequency response functions and cross-spectral estimates. The measured estimates for these two theoretical dimensionless frequency response functions are shown to compare favourably with the analytical values. The use of the theoretical dimensionless frequency response functions for the stoachastic design of hinged wavemakers of variable-draft now appears to be experimentally justified by these unique measurements of hydrodynamic pressure moment spectra on hinged wavemakers.