scholarly journals HORIZONTAL WATER PARTICLE VELOCITY OF FINITE AMPLITUDE WAVES

1970 ◽  
Vol 1 (12) ◽  
pp. 19 ◽  
Author(s):  
Yuichi Iwagaki ◽  
Tetsuo Sakai
Keyword(s):  
Particle Velocity ◽  
Wave Length ◽  
Wave Theory ◽  
Approximate Expression ◽  
Finite Amplitude ◽  
Stokes Wave ◽  
Wave Crest ◽  
Amplitude Wave ◽  
Water Particle ◽  
Hot Film

This paper firstly describes two methods to measure vertical distribution and time variation of horizontal water particle velocity induced "by surface waves in a wave tank These two methods consist of tracing hydrogen bubbles and using hot film anemometers, respectively Secondly, the experimental results by the two methods are presented with the theoretical curves derived from the small amplitude wave theory, Stokes wave theory of 3rd order, and the hyperbolic wave theory as an approximate expression of the cnoidal wave theory Finally, based on the comparison of the experimental data with the theoretical curves, the applicability of the finite amplitude wave theories, which has been studied for the wave profile, wave velocity, wave length and wave crest height, is discussed from view point of the water particle velocity.

scholarly journals KINEMATICS OF BREAKING WAVES

1976 ◽  
Vol 1 (15) ◽  
pp. 25 ◽  
Author(s):  
Edward B. Thornton ◽  
James J. Galvin ◽  
Frank L. Bub ◽  
David P. Richardson
Keyword(s):  
Solitary Waves ◽  
Particle Velocity ◽  
Asymptotic Expression ◽  
Breaking Waves ◽  
The Body ◽  
Time Dependent ◽  
Wave Crest ◽  
Periodic Waves ◽  
Water Particle ◽  
Highly Nonlinear

The sight and sound of breaking waves and surf is so familiar and enjoyable that we tend to forget how little we really understand about them. Why is it, that compared to other branches of wave studies our knowledge of breaking waves is so empirical and inexact? The reason must lie partly in the difficulty of finding a precise mathematical description of a fluid flow that is in general nonlinear and time-dependent. The fluid accelerations can no longer be assumed t o be small compared t o gravity, as in Stokes's theory for periodic waves and the theory of cnoidal waves in shallow water, nor is the particle velocity any longer small compared to the phase velocity. The aim of this paper is to bring together s ome recent contributions to the calculation both of steep symmetric waves and of time-dependent surface waves. These have a bearing on the behaviour of whitecaps in deep water and of surf in the breaker zone . Since spilling breakers in gently shoaling water closely resemble solitary waves, we begin with the description of solitary waves of limiting amplitude, then discuss steep waves of arbitrary height. The observed intermittency of whitecaps is discussed in terms of the energy maximum, as a function of wave steepness, In Sections 6 and 7 a simpler description of steady symmetric waves is proposed, using an asymptotic expression for the flow near the wave crest. Finally we describe a new numerical technique (MEL, or mixed Eulerian-Lagrangian) with which it has been found possible to follow the development of periodic waves past the point when overturning takes place. Measurement of waves, and vertical and horizontal water particle velocities were made of spilling, plunging and surging breakers at sandy beaches in the vicinity of Monterey, California. The measured breaking waves, derived characteristically from swell-type waves, can be described as highly nonlinear. Spectra and cross spectra were calculated between waves and velocities. Secondary waves were noted visually and by the strong harmonics in the spectra. The strength of the harmonics is related to the beach steepness, wave height and period. The phase difference between waves and horizontal velocities indicates the unstable crest of the wave leads the velocities on the average by 5-20 degrees. Phase measurements between wave gauges in a line perpendicular to the shore show breaking waves to be frequency nondispersive indicating phase-coupling of the various wave components. The coherence squared values between the sea surface elevation and the horizontal water particle velocity were high in all runs, ranging above 0.8 at the peak of the spectra. The high coherence suggests that most of the motion in the body of breaking waves is wave-induced and not turbulent.

scholarly journals THE EFFECT OF ROUGHNESS ON THE MASS-TRANSPORT OF PROGRESSIVE GRAVITY WAVES

1966 ◽  
Vol 1 (10) ◽  
pp. 11 ◽  
Author(s):  
Arthur Brebner ◽  
J.A. Askew ◽  
S.W. Law
Keyword(s):  
Mass Transport ◽  
Gravity Waves ◽  
Orbital Motion ◽  
Wave Length ◽  
Wave Theory ◽  
Finite Amplitude ◽  
Maximum Value ◽  
Transport Velocity ◽  
Mass Transport Velocity ◽  
The Mean

On the basis of non-viscous small amplitude firstorder theory the maximum value of the horizontal orbital motion at the bed in water of constant depth his given by /U/n yy* »* " r •»** */i where k = /L, H is the wave height crest to trough, T is the period, and L the wave length (L = Sry2jr Arf 2*%/L ). On the basis of finite amplitude wave theory where the particle orbits are not closed ana by the insertion of the viscous laminar boundary layer (the conducti6n solution) the mean drift velocity or mass transport velocity on a perfectly smooth bed is given by Longuet- Higgins (1952) as 7, K H* kcr where

Crest-Height Distribution in Nonlinear Random Wave

2009 ◽  
Author(s):  
Cuilin Li ◽  
Dingyong Yu ◽  
Yangyang Gao ◽  
Junxian Yang
Keyword(s):  
Nonlinear Wave ◽  
Wave Theory ◽  
Distribution Functions ◽  
Theoretical Distribution ◽  
Distribution Model ◽  
Stokes Wave ◽  
Wave Crest ◽  
Linear Wave ◽  
Height Distribution ◽  
Crest Height

Many empirical and theoretical distribution functions for wave crest heights have been proposed, but there is a lack of agreement. With the development of ocean exploitation, waves crest heights represent a key point in the design of coastal structures, both fixed and floating, for shoreline protection and flood prevention. Waves crest height is the dominant parameter in assessing the likelihood of wave-in-deck impact and its resulting severe damage. Unlike wave heights, wave crests generally appear to be affected by nonlinearities; therefore, linear wave theory could not be satisfied to practical application. It is great significant to estimate a new nonlinear wave crest height distribution model correctly. This paper derives an approximation distribution formula based on Stokes wave theory. The resulting theoretical forms for nonlinear wave crest are compared with observed data and discussed in detail. The results are shown to be in good agreement. Furthermore, the results indicate that the new theoretical distribution has more accurate than other methods presented in this paper (e.g. Rayleigh distribution and Weibull distribution) and appears to have a greater range of applicability.

Dynamical Modeling of Deepwater-Type Cylindrical Tuned Liquid Damper With a Submerged Net

1999 ◽  
Vol 122 (1) ◽  
pp. 96-104 ◽  
Author(s):  
Shigehiko Kaneko ◽  
Yasuo Mizota
Keyword(s):  
Wave Theory ◽  
Finite Amplitude ◽  
Hydrodynamic Forces ◽  
Experimental Results ◽  
Shaking Table ◽  
Cylindrical Tank ◽  
Tuned Liquid Damper ◽  
Amplitude Wave ◽  
Modeling Methodology ◽  
Liquid Depth

An analytical model for describing the effectiveness of a deepwater-type cylindrical tuned liquid damper (TLD) with a submerged net for suppressing horizontal vibration of structures is first proposed. In this study, we performed calculations to estimate the effectiveness of a deepwater-type cylindrical TLD based on a proposed dynamical model and compared with experimental results obtained by shaking table experiments and free oscillation tests. In particular, the effect of hydraulic resistance produced by a submerged net and the liquid depth ratio (the ratio of the liquid depth to the diameter of the cylindrical tank) are examined intensively. In the analysis, employing finite amplitude wave theory and Galerkin method in the case of cylindrical tank, we obtained hydrodynamic forces and the free surface elevations. Then, combining the hydrodynamic forces with the equation of motion of the structure, damped transient responses were calculated. The calculated results thus obtained were compared with the experimental results, by which the validity of the modeling methodology was confirmed. [S0094-9930(00)00101-3]

On cnoidal waves and bores

1954 ◽  
Vol 224 (1159) ◽  
pp. 448-460 ◽  
Keyword(s):  
Wave Train ◽  
Wave Length ◽  
Wave Theory ◽  
Finite Amplitude ◽  
Stationary Waves ◽  
Steady Flows ◽  
Left Hand ◽  
Total Head ◽  
The Right ◽  
Supercritical Flows

For a train of gravity waves of finite amplitude in a frame of reference in which they are stationary, it is suggested that, in addition to the volume flow per unit span Q and the total head R , one may usefully study a third constant S , the rate of flow of horizontal momentum(corrected for pressure force, and divided by the density). The values of Q , R and S probably determine the wave-train uniquely; this is proved explicitly for long waves in a new presenta­tion of the ‘cnoidal wave’ theory (§3). The combinations of Q , R and S which are possible in the general case are illustrated by a diagram (figure 2) in which the co-ordinates are r = R / R c and s = S / S c ; here suffix c refers to ‘critical’ flow at the volume rate Q . There are two barriers on this diagram beyond which no stationary waves, or other steady flows, are possible; at the left-hand barrier (corresponding to uniform subcritical flows) the amplitude tends to zero; at the right-hand barrier (corresponding to uniform supercritical flows) the wave-length tends to infinity (case of the solitary wave). The diagram needs to be completed by a third barrier corresponding to ‘waves of greatest height’. This starts at the point marked Z and moves to infinity within the unshaded region without ever intersecting the left-hand barrier. The diagram may be used to determine what losses of momentum and energy a given stream can undergo, without departing from the condition of steady flow. Thus, one can determine the maximum wave resistance on a cylindrical obstacle athwart a given subcritical stream, or on a two-dimensional ‘step’ in the bed, in the absence of energy dissipation. Again, one can study the transition to a wave-train behind a bore. Such a wave-train (present in all but very strong bores) is shown to be capable of absorbing almost the whole energy which according to classical theory is liberated at the bore, although some minute residual dissipation of energy still appears to be necessary.

scholarly journals The Effects on Water Particle Velocity of Wave Peaks Induced by Nonlinearity under Different Time Scales

2021 ◽  
Vol 9 (7) ◽  
pp. 748
Author(s):  
Aifeng Tao ◽  
Shuya Xie ◽  
Di Wu ◽  
Jun Fan ◽  
Yini Yang
Keyword(s):  
Particle Velocity ◽  
Modulation Instability ◽  
Wave Train ◽  
Quadratic Function ◽  
Offshore Structures ◽  
Stokes Wave ◽  
Wave Load ◽  
Freak Waves ◽  
Water Particle ◽  
Generation Mechanisms

The water particle velocity of the wave peaks is closely related to the wave load borne by offshore structures. It is of great value for marine disaster prevention to study the water particle velocity of nonlinear extreme waves represented by Freak waves. This study applies the High-order Spectral Method (HOS) numerical model to analyze the characteristics and influencing factors of the water particle velocity of Freak wave peak with two different generation mechanisms under the initial condition of a weakly modulated Stokes wave train. Our results show that the water particle velocity of the wave peak increases linearly with wave height and initial wave steepness in the evolution stage of modulation instability. While in the later stage, the relationship becomes exponential. Under the condition of similar wave heights, the deformation degrees of Freak waves with different generation mechanisms are distinct, the deformation degree of modulation instability stage is smaller than that of the later stage. The water particle velocity of the wave peaks increases with the deformation degrees. Furthermore, the correlation between wave peak height and water particle velocity is a quadratic function. This provides a theoretical basis for further understanding of nonlinear waves and the prediction of marine disasters.

Conditional Short-Crested Waves in Shallow Water and With Superimposed Current

2002 ◽  
Author(s):  
Jo̸rgen Juncher Jensen
Keyword(s):  
Shallow Water ◽  
Water Depth ◽  
Wave Spectrum ◽  
Wave Theory ◽  
Ocean Waves ◽  
Offshore Structures ◽  
Stokes Wave ◽  
Wave Crest ◽  
Non Linear ◽  
Drilling Rigs

For bottom-supported offshore structures like oil drilling rigs and oil production platforms, a deterministic design wave approach is often applied using a regular non-linear Stokes’ wave. Thereby, the procedure accounts for non-linear effects in the wave loading but the randomness of the ocean waves is poorly represented, as the shape of the wave spectrum does not enter the wave kinematics. To overcome this problem and still keep the simplicity of a deterministic approach, Tromans, Anaturk and Hagemeijer (1991) suggested the use of a deterministic wave, defined as the expected linear Airy wave, given the value of the wave crest at a specific point in time or space. In the present paper a derivation of the expected linear short-crested wave riding on a uniform current is given. The analysis is based on the conventional shallow water Airy wave theory and the direction of the main wind direction can make any direction with the current. A consistent derivation of the wave spectrum taking into account current and finite water depth is used. The numerical results show a significant effect of the water depth, the directional spreading and the current on the conditional mean wave profile. Extensions to higher order waves are finally discussed.

A presentation of cnoidal wave theory for practical application

1960 ◽  
Vol 7 (2) ◽  
pp. 273-286 ◽  
Author(s):  
R. L. Wiegel
Keyword(s):  
Particle Velocity ◽  
Wave Theory ◽  
Periodic Waves ◽  
Cnoidal Wave ◽  
Laboratory Measurements ◽  
Practical Application ◽  
Water Particle ◽  
Wave Celerity

Cnoidal wave theory is appropriate to periodic waves progressing in water whose depth is less than about one-tenth the wavelength. The leading results of existing theories are modified and given in a more practical form, and the graphs necessary to their use by engineers are presented. As well as results for the wave celerity and shape, expressions and graphs for the water particle velocity and local acceleration fields are given. A few comparisons between theory and laboratory measurements are included.

scholarly journals TRANSMISSION OF REGULAR WAVES PAST FLOATING PLATES

1974 ◽  
Vol 1 (14) ◽  
pp. 112
Author(s):  
Uygur Sendil ◽  
W.H. Graf
Keyword(s):  
Water Depth ◽  
Wave Length ◽  
Wave Theory ◽  
Finite Amplitude ◽  
Linear Wave ◽  
Regular Waves ◽  
Transmission Coefficients ◽  
Wave Flume ◽  
Wave Heights ◽  
Incident Waves

Theoretical solutions for the transmission beyond and reflection of waves from fixed and floating plates are based upon linear wave theory, as put forth by John (1949), and Stoker (1957), according to which the flow is irrotational, the fluid is incompressible and frictionless, and the waves are of small amplitude. The resulting theoretical relations are rather complicated, and furthermore, it is assumed that the water depth is very small in comparison to the wave length. Wave transmissions beyond floating horizontal plates are studied in a laboratory wave flume. Regular (harmonic) waves of different heights and periods are generated. The experiments are carried out over a range of wave heights from 0.21 to 8.17 cm (0.007 to 0.268 ft), and wave periods from 0.60 to 4.00 seconds in water depth of 15.2, 30.5, and 45.7 cm (0.5, 1.0 and 1.5 ft). Floating plates of 61, 91 and 122 cm (2, 3 and 4 ft) long were used. From the analyses of regular waves it was found that: (1) the transmission coefficients, H /H , obtained from the experiments are usually less than those obtained from the theory. This is due to the energy dissipation by the plate, which is not considered in the theory. (2) John's (1949) theory predicts the transmission coefficients, H /H , reasonably well for a floating plywood plate, moored to the bottom and under the action of non-breaking incident waves of finite amplitude. (3) a floating plate is less effective in damping the incident waves than a fixed plate of the same length.

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