The form of the asymptotic depth-limited wind-wave spectrum: Part II — The wavenumber spectrum

Data from a spatial array of wave gauges is analysed using the Wavelet Directional Method (WDM) to directly determine the wavenumber spectrum. The data shows that the asymptotic depth-limited wavenumber spectrum can be represented as a two-parameter form, which is far simpler than the corresponding frequency spectrum. The WDM analysis shows that there are significant nonlinear processes active in the finite depth water, which results in energy being “smeared” across a range of wavenumbers and frequencies around the standard dispersion shell. As a result, the wavenumber spectrum has much less peak enhancement than seen in the frequency spectrum obtained with standard Fourier analysis. In addition, the wavenumber spectrum does not have the clear harmonic previously observed in the finite depth frequency spectrum. This result demonstrates that the harmonic is nonlinearly phase-locked to the spectral peak.