A 2-D COMPLEX WAVELET ANALYSIS OF AN UNSTEADY WIND-GENERATED SURFACE-WAVE FIELD

Nonlinear wave-wave interactions can be quite localised in space and a n appropriate spectral analysis of such a wave field must retain this local phase information. To this end, the 2-D, complex wavelet functio ns 'Arc' and 'Morlet2D' can be used to decompose a wave field in space b and scale a. As both wavelets are Hardy functions, the transform re sult is complex, and the phase, phi, is defined over all b. Arc can be used to measure the energy of the wave field over b as a function of Absolute value of k, and the direction-specific wavelet, Morlet2D, can be used for the spatial energy distribution of k. Surface waves gener ated by unsteady wind have dislocations in phase that are widespread a nd persist until the initial wave field becomes disordered in appearan ce. While the energy at fundamental wavelengths (the wavelength of the initial instability) appears to saturate, the energy of the subharmon ic component continues to increase with time. There appears to be sign ificant energy in both modes, from early on in the life history of the se organised wave fields. The energy of wavevectors aligned at a small angle off the mean wind direction vector (the including angle, alpha almost-equal-to 20-degrees) increases to become a substantial fraction of the total energy. The possible role of the pattern defects in loca l nonlinear mechanisms of energy transfer is discussed. and analogies are drawn with recent results in plane mixing layers. Techniques for t he measurement of the complex dispersion relation, omega(k), and group velocity, U(g)(k), utilising the local space-scale decomposition of t he 2D wavelet transform, are proposed.