The dynamics of nonlinear water wave groups (original) (raw)

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Kinematics of extreme waves in deep water

Applied Ocean Research, 2003

The velocity profiles under crest of a total of 62 different steep wave events in deep water are measured in laboratory using particle image velocimetry. The waves take place in the leading unsteady part of a wave train, focusing wave fields and random wave series. Complementary fully nonlinear theoretical/numerical wave computations are performed. The experimental velocities have been put on a nondimensional form in the following way: from the wave record (at a fixed point) the (local) trough-to-trough period, T TT and the maximal elevation above mean water level, h m of an individual steep wave event are identified. The local wavenumber, k and an estimate of the wave slope, e are evaluated from v 2 =ðgkÞ ¼ 1 þ e 2 ; kh m ¼ e þ 1 2 e 2 þ 1 2 e 3 ; where v ¼ 2p=T TT and g denotes the acceleration of gravity. A reference fluid velocity, e ffiffiffiffi g=k p is then defined. Deep water waves with a fluid velocity up to 75% of the estimated wave speed are measured. The corresponding kh m is 0.62. A strong collapse of the nondimensional experimental velocity profiles is found. This is also true with the fully nonlinear computations of transient waves. There is excellent agreement between the present measurements and previously published Laser Doppler Anemometry data. A surprising result, obtained by comparison, is that the nondimensional experimental velocities fit with the exponential profile, i.e. e ky ; y the vertical coordinate, with y ¼ 0 in the mean water level. q

Nonlinear Effects in Gravity Waves Propagating in Shallow Water

Coastal Engineering Journal, 2012

Nonlinear energy transfers due to triad interactions change the characteristics of the wave-field in the shoaling region. The degree of nonlinear coupling is examined using numerical simulations based on an accurate set of deterministic evolution equations for the propagation of fully dispersive weakly nonlinear waves. The model validation, using existing experimental measurements for wave transformation over a shoal, showed that it accurately predicts nonlinear energy transfer for irregular waves with large wave-numbers. The bound higher harmonics and nonlinear statistical measures, i.e. the wave skewness and asymmetry, are well simulated by the model in both the shoaling and deshoaling regions. Numerical simulation of steep waves in shallow water with the Ursell number O(1), showed that nonlinear dispersion and phase locking lead to triad interactions even on a horizontal bottom. Nonlinear energy transfers in monochromatic waves lead to rapid spatial recurrence of the primary wave amplitudes. This is in contrast to the case of irregular waves where the Fourier coefficients of the wave-field do not recur due to the presence of innumerable interactions, which are expected to cancel resulting in no spatial evolution of the wave spectrum.

Experimental velocities and accelerations in very steep wave events in deep water

European Journal of Mechanics - B/Fluids, 2006

The entire experimental velocity and acceleration fields in the six steepest cases of a campaign of totally 122 large wave events in deep water are documented. From observations in these six waves, totally 36000 experimental velocity vectors are put on nondimensional form using a suitable reference velocity defined by √ g/k, where k and are obtained as follows: from the wave record at a fixed position the local trough-to-trough period, T TT and the maximal elevation of the event above mean sea level, ζ m are defined. The local wavenumber, k and the wave slope, are evaluated from ω 2 /(gk) = 1 + 2 and kζ m = + 1 2 2 + 1 2 3

Crest speeds of unsteady surface water waves

Journal of Fluid Mechanics

Intuitively, crest speeds of water waves are assumed to match their phase velocities. However, this is generally not the case for natural waves within unsteady wave groups. This motivates our study, which presents new insights into the generic behavior of crest speeds of linear to highly nonlinear unsteady waves. While our major focus is on gravity waves where a generic crest slowdown occurs cyclically, results for capillary-dominated waves are also discussed, for which crests cyclically speed up. This curious phenomenon arises when the theoretical constraint of steadiness is relaxed, allowing waves to change their form, or shape. In particular, a kinematic analysis of both simulated and observed open ocean gravity waves reveals a forward-to-backward leaning cycle for each individual crest within a wave group. This is clearly manifest during the focusing of dominant wave groups essentially due to the dispersive nature of waves. It occurs routinely for focusing linear (vanishingly small steepness) wave groups, and it is enhanced as the wave spectrum broadens. It is found to be relatively insensitive to the degree of phase coherence and focusing of wave groups. The nonlinear nature of waves limits the crest slowdown. This reduces when gravity waves become less dispersive, either as they steepen or as they propagate over finite water depths. This is demonstrated by numerical simulations of the unsteady evolution of 2D and 3D dispersive gravity wave packets in both deep and intermediate water depths, and by open ocean space-time measurements.

Measurements of velocities and accelerations in steep irregular water waves by

2000

An extended PIV system is employed to measure the velocities and accelerations in steep irregular waves in a laboratory wave tank. In parts of the experiments a complementary theoretical description provides a comparison with the measurements. The theoretical model is very precise, with an error term being less than 0.5% relative to the primary wave for the conditions of the experiments. The purpose with the comparison is to test the accuracy of the wave experiments under realistic and controllable conditions in the laboratory. The experimental acceleration field is calculated from the difference between two consecutive velocity fields. The latter are measured using directionally resolved Digital Particle Image Velocimetry (DPIV). The system uses two separate cameras viewing the same region of flow to acquire PIV images with no limitation on the time between individual velocity measurements. Both cameras record the same field of view with a small angle between their respective viewi...

Groups of waves in shallow water

Journal of Geophysical Research, 1984

Wave group statistics predicted by linear theories are compared to numerical simulations, thus determining ranges of spectral shapes for which the theories are valid. It is found that these theories are not generally valid for ocean data because of many assumptions and simplifications beyond linearity and random phase or because their range of applicability does not include the vast majority of ocean conditions. The simulations also provide quantitative information about the variability of linear wave group statistics which is useful when examining ocean field data. The simulation technique is used to show that important ocean gravity wave group statistics are not inconsistent with an underlying wave field composed of linearly superposed random waves. The majority of the field data examined were collected in 10 m depth; significant wave heights varied from about 20 to 200 cm, and the spectral shapes ranged from fairly narrow to broad (1 < Q•, < 6). For the 10-m depth data, the observed mean run length, variance of run length, and probabilities of runs of a given number of waves were statistically consistent with the simulations. In contrast to the apparently linear groups observed in 10 m depth, waves in 2-3 m depth showed marked departures from the linear simulations.

Measurements of velocities and accelerations in steep irregular water waves

An extended PIV system is employed to measure the velocities and accelerations in steep irregular waves in a laboratory wave tank. In parts of the experiments a complementary theoretical description provides a comparison with the measurements. The theoretical model is very precise, with an error term being less than 0.5% relative to the primary wave for the conditions of the experiments. The purpose with the comparison is to test the accuracy of the wave experiments under realistic and controllable conditions in the laboratory.

Calculations of kinematics underneath measured time histories of steep water waves

Applied Ocean Research, 2010

The present paper is concerned with the problem of estimating fluid particle velocities underneath a measured wave profile at a single spatial position. Second-order calculations are compared with measurements of wave particle kinematics underneath both irregular waves (Skjelbreia et al. (1991) [17]) and focused wave groups (Johannessen & Swan (2001) [16]). It is found that second-order theory is capable of describing the kinematics at the free surface very accurately provided that the local underlying regime of free waves can be identified. At the free surface, estimates of the crest velocities are nearly independent of the cutoff frequency even for broad continuous spectra. Since the velocities at the free surface can be calculated accurately, it is found that the simplest and most reliable method to obtain the velocities below the surface is to use the exponentially decaying velocity potential directly also above the still water level. In a continuous spectrum, the solution will necessarily break down for large enough frequencies but since the velocities at the surface are known, this is strictly an interpolation and the frequency cutoff may be controlled. A directional wave field is not defined uniquely from measurements of the surface elevation at one spatial position. Comparisons between measurements of steep directional wave groups and calculations of unidirectional waves based on the measured surface elevation, however, indicate that the unidirectional case may provide very useful predictions also for short crested wave groups.