On the calculation of wavenumber from measured time traces

Abstract

When characterising local geometry for unsteady water waves, the accurate determination of spatial quantities such as the wavenumber from measured time traces is non-trivial. The present study investigates different methods in order to highlight the discrepancies that arise when estimating the wavenumber from fully nonlinear numerical time traces of the free surface profile. To this extent, the open research topic relating to the accuracy of the Hilbert transform in analysing broad-banded signals is addressed. The accuracy of local wavenumber estimates from the Hilbert transform are shown to have a strong dependency on the bandwidth of the underlying spectrum. For broad-banded sea-states there is a significant departure of the Hilbert transform predictions from actual wavenumber values. In contrast, the Double Fourier numerical model of Baldock and Swan (1994) [1] is shown to obtain accurate estimates of local wave geometry from just a single measured time trace, regardless of spectral characteristics; it is thus the recommended method. In addition, an empirical correction factor is proposed that can be applied to the linear dispersion equation in order to obtain an improved wavenumber estimate. The correction is tested for unidirectional deep water, nonlinear random sea-states and shown to offer considerable improvements in the local wavenumber estimates.