Steven R. Long

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 an appropriate spectral analysis of such a wave field must retain this local phase information. To this end, the 2-D, complex wavelet functions ‘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 result is complex, and the phase, φ, is defined over all b. Arc can be used to measure the energy of the wave field over b as a function of z.sfnc;k|, and the direction-specific wavelet, Morlet2D, can be used for the spatial energy distribution of k. n nSurface waves generated by unsteady wind have dislocations in phase that are widespread and persist until the initial wave field becomes disordered in appearance. While the energy at fundamental wavelengths (the wavelength of the initial instability) appears to saturate, the energy of the subharmonic component continues to increase with time. There appears to be significant energy in both modes, from early on in the life history of these organised wave fields. The energy of wavevectors aligned at a small angle off the mean wind direction vector (the including angle, α ≈ 20°) increases to become a substantial fraction of the total energy. The possible role of the pattern defects in local nonlinear mechanisms of energy transfer is discussed, and analogies are drawn with recent results in plane mixing layers. Techniques for the measurement of the complex dispersion relation, ω(k), and group velocity, Ug(k), utilising the local space-scale decomposition of the 2D wavelet transform, are proposed.

The local properties of ocean surface waves by the phase-time method

Traditionally, investigation of statistical properties of ocean waves has been limited largely to global quantities related to elevation and amplitude such as the power spectral and various probability density functions. Although these properties give valuable information about the wave field, the results cannot be related directly to any portion of the time data from which it was derived. We present a new approach using phase information to view and study the properties of frequency modulation, wave group structures, and wave breaking. We apply the method here to ocean wave time series data and identify a new type of wave group (containing the large “rogue” waves), but the method also has the capability of broad applications in the analysis of time series data in general.

Blocking and trapping of waves in an inhomogeneous flow

Abstract The blocking and trapping of waves and wave packets by inhomogeneous flow fields were studied in a laboratory setting. Evidence for multiple reflections and thus trapping within the current gradient zone near the blocking point are the main results obtained, and lead to the following conclusions: (1) a strong current gradient zone near the blocking point can trap wave energy, which will shift the wavenumbers into the capillary region, to match the microwave wavelength of many remote sensing instruments; (2) this mechanism provides a direct link between strong current gradient zones (bathymetric features in tidal flows, eddies, current boundaries, etc.) and the surface wave structure, which in turn allows instruments such as the Synthetic Aperture Radar (SAR) to form images of bottom features based solely on the small wave conditions; (3) an indication of direct energy transfer from the carrier waves to low-frequency waves was also observed, and resolved by wavelet analsysis. The instantaneous spectra from wavelet analysis reveal that a large portion of wave energy transfers directly into the low-frequency band from the carrier waves at the trapping zone. Subharmonics may play a critical role in the energy transfer process, but details are still to be established.

MEASUREMENTS OF THE INTERACTION OF WAVE GROUPS WITH SHORTER WIND-GENERATED WAVES

Fields of statistically steady wind-generated waves produced in the NASA-Wallops wind wave facility, were perturbed by the injection of groups of longer waves with various slopes, mechanically generated at the upwind end of the tank. The time histories of the surface displacements were measured at four fetches in ensembles consisting of 100 realizations of each set of experimental conditions, the data being stored and analysed digitally. The overall interaction was found to have four distinct phases. (i) When the longer waves overtake the pre-existing wind-generated waves, during the first half of the group where successive crests are increasing in amplitude, vigorous wave breaking near the crests reduces the energy density and

Light Reflection from Water Waves: Suitable Setup for a Polarimetric Investigation under Controlled Laboratory Conditions

overline{zeta^2}

Time-resolved polarimetry over water waves: relating glints and surface statistics

in the wind waves while straining by the orbital velocities of the group reduces their wavelengths near the crests; the ‘significant slope’

Directional wind wave development

2pi(overline{zeta^2})^{frac{1}{2}}/lambda

Method of surface topography retrieval by direct solution of sparse weighted seminormal equations

at the crests is found to be very nearly constant and equal to the initial, undisturbed value. After the maximum wave of the group has passed, breaking appears to virtually cease but the earlier energy loss results in suppression of the short waves. The overall suppression by a group of waves is significantly less than that measured by Mitsuyasu (1966) and Phillips & Banner (1974) in a continuous train of waves whose slope is equal to the maximum in the group. A simple description of this phase of the interaction, involving constant significant slope of the breaking waves over the leading half of the group and conservation of action thereafter, gives suppression ratios close to those measured. (ii) Once the group has passed, the surface is much smoother and the waves begin to regenerate under the continued influence of the wind but at rates considerably slower than those suggested by Plants formula, using the averaged value of u * . This is qualitatively consistent with a locally reduced surface stress as the wind blows from rougher water well behind the group to the smoother surface immediately behind it. (iii) The regeneration is interrupted by the arrival of a wave energy front moving down the tank, across which the energy density rises abruptly to values up to six times greater than in the undisturbed field. At the same time, the dominant frequencies just behind the wave energy front are lower than in the initial field, and the significant slope

A Laboratory Study of the Velocity Field Below Surface Gravity Waves

(overline{zeta^2})^{frac{1}{2}} sigma^2/g

An Experimental Study of the Statistical Properties of Wind-Generated Gravity Waves

is, within experimental uncertainty, again identical to that in the initial field. The front was found to propagate notably faster than the appropriate group velocity ( g /2σ) and it is suggested that this is the combined result of dispersion, nonlinearity and wind amplification, together with wind-induced drift in the tank. Finally, (iv) the energy density gradually subsides and the dominant wave frequency increases as the wind waves relax towards their undisturbed state, the relaxation seeming to be essentially complete when energy packets arriving at a point have originated at the upwind end of the tank, rather than at the wave energy front.