Wave Steepness Parameter Research Articles

Joint Distribution of Successive Wave Steepness Parameters

A joint distribution of wave steepness parameters associated with two successive waves is presented. The wave steepness parameters considered herein are the crest front steepness and the total wave steepness. This joint distribution is represented by a two-dimensional Weibull distribution with the parameters α = 0.84 and β = 1.40. The application of the results is illustrated by an example.

Capillary rollers and bores

At any free surface at which the tangential stress τns vanishes there must be a surface vorticity ω = −2κq, where κ is the curvature and q the tangential velocity. In a surface wave on water, this condition produces a (Stokes) boundary layer with thickness of order δ = (2ν/σ)½, where ν is the kinemetic viscosity and σ the radian frequency of the wave. To first order in the wave steepness parameter ak, the vorticity remains within the boundary layer, but at second order some escapes through the Stokes layer. The mean vorticity at the outer edge of the Stokes layer is of order 2(ak)2σ, twice the mean vorticity generated at the free surface.These results are applied to steep capillary waves, particularly the parasitic capillaries often seen on the forward face of short gravity waves. Because of the high value of σ for the capillaries, the vorticity they generate is much larger than that generated by the gravity wave itself. Hence the capillaries contribute significantly to the vortex (roller) often found at the crest of short gravity waves, when capillaries are present. It is argued that the crest roller and the capillaries form a cooperative system, a ‘capillary roller’ in which each supports the other, with the aid of surface tension and viscosity. Energy is supplied by the gravity wave.A capillary roller is one instance of a more general phenomenon: a ‘capillary bore’, which is a noticeable feature of many disturbed water surfaces.

Comparison of wave steepness based on spatial and temporal distributions

It is common practice to estimate wave steepness parameters from zero crossing analysis of wave elevation records in the time domain. Numerical and experimental investigations were carried out to compare steepness parameters based on spatial-domain and time-domain wave profiles. It was found that significant biases may occur in steepness parameters based on time-domain analysis of irregular wave trains. A new hybrid zero crossing analysis method is described that can provide more accurate information on wave steepness.

Lagrangian moments and mass transport in Stokes waves

The orbital motions in surface gravity waves are of interest for analysing wave records made by accelerometer buoys. In this paper we derive some exact expressions for the first, second and third cumulants of the vertical orbital displacements in a regular Stokes wave of finite amplitude in terms of previously known integral quantities of the wave: the kinetic and potential energies, the phase speed c and the mass-transport velocity U at the free surface. These results generalize a remarkably simple relation found previously between the Lagrangian-mean surface level and the product Uc.Expansions are given in powers of the wave steepness parameter ak which show that the third Lagrangian cumulant is very small – of order (ak)6, indicating a high degree of vertical symmetry in the orbit. This contrasts with the situation in random waves, where the third cumulant is of order (ak)4 only. It is shown that the increased skewness in random waves is due mainly to an O(ak)2 shift in the Lagrangian mean level of individual waves. Such shifts in mean level may be too gradual to be fully detected by some accelerometer buoys. In that case the apparent skewness will be reduced.

Discus Buoy Stability and the Spectrum of Steep Waves

Thick discus buoys are used in the ocean as platforms from which oceanographic and meteorological measurements are made and reported to shore. The stability of these buoys is sensitive to steep breaking waves, and a few have capsized in the ocean from large breaking waves. This occurrence can be simulated in laboratory scale-model studies. Generally, in the laboratory, the buoys will not capsize for a breaking wave that is small relative to buoy diameter. The problem is predicting the probability of capsizing for engineering planning purposes. This paper describes how first approximations can be made from a combination of laboratory scale-model testing of buoy capsizings in random waves, a few reported occurrences of buoy capsizings in the open ocean, and the statistics of ocean waves. An estimate of the joint probability density distribution function of a wave steepness parameter and a wave height parameter is made from buoy motion measurements. It is found that in the northeastern Pacific Ocean the wave climate is quite severe and includes a large percentage of relatively large breaking waves. Under such circumstances, buoy diameters of 10 m have a relatively low reliability. The reliability increases rapidly as buoy diameter increases.