Estimating w(k) in an unsteady, wind-generated surface wave field from the 2D complex wavelet transform of the surface slope

The initial formation and growth of capillary-gravity waves under wind-induced surface stress is studied by measurement of the instantaneous, 2D distribution of the along- wind slope at a fixed fetch. A new technique, using information from the complex 2D wavelet transform, is described for the calculation of the local, instantaneous dispersion relation. The technique is validated on simple test fields. The dispersion relation measured from the wave tank data is consistent with predictions from linear stability theory at early times, but departures can be noted later on. Some physical interpretations are offered, and possible nonlinear mechanisms are discussed.