A parametric study of breaking bow waves using a 2D + T Technique

2011 ◽  
Vol 687 ◽  
pp. 540-570 ◽  
Author(s):  
Eric Maxeiner ◽  
Mostafa Shakeri ◽  
James H. Duncan
Keyword(s):  
Wave Height ◽  
Contact Point ◽  
Vertical Plane ◽  
Phase Speed ◽  
Wave Crest ◽  
Two Dimensional ◽  
Maximum Wave Height ◽  
Ship Model ◽  
Wave Maker ◽  
Maximum Contact

AbstractA mechanical two-dimensional wave maker with a flexible surface was used to create waves similar to those formed at the bow of a moving ship. Utilizing the two-dimensional plus time (2D + T) approximation, the wave maker was programmed so that its deformable wave board created a time sequence of shapes that simulated the line of intersection between one side of the hull of a slender ship model moving at constant speed and an imaginary vertical plane oriented normal to the ship model track. However, instead of simulating a particular ship hull, the wave maker was set to produce a parametric set of flat plate motions that represent components of typical bow shapes. The resulting surface waves were measured using a cinematic laser-induced fluorescence technique and the resulting wave profiles were analysed. A large variation of wave crest shapes was observed. An assortment of wave characteristics including the maximum contact point height, maximum wave height and plunging jet geometry were measured and related to the corresponding wave maker motion parameters. Despite the variety of wave maker motions and resulting wave crest shapes, it was observed that the gross parameters describing the wave, such as the maximum wave height, maximum contact point height and wave phase speed, correlate strongly with the wave maker velocity along the water line. Details of the crest shape at the moment of incipient breaking showed a stronger dependence on the initial acceleration of the wave board.

scholarly journals Wave Trajectory Study on the Coast of Lhoknga, Aceh Besar, Indonesia: A Numerical Model Approach

2018 ◽  
Vol 20 (1) ◽  
pp. 30 ◽  
Author(s):  
Ichsan Setiawan ◽  
Mohammad Irham
Keyword(s):  
Numerical Model ◽  
Wave Height ◽  
Coastal Waters ◽  
Wave Breaking ◽  
Numerical Study ◽  
High Tide ◽  
Two Dimensional ◽  
Maximum Wave Height ◽  
Wave Refraction ◽  
Model Approach

A numerical model of wave trajectory using shoaling and refraction formula was proposed in the coastal waters of Lhoknga, Aceh Besar, Indonesia. The developed model used a two dimensional (2D) numerical methods for wave trajectory with the input of wave height and period; 0.62 m and 8 second for high tide and 0.47 m and 6 second for low tide. This model was tested on site during low tide and high tide conditions for verification. The purpose of this numerical study is to trace the distribution of wave trajectory because of shoaling, wave breaking, and wave refraction. The model determines the wave height and crest pattern of the ray wave trajectory. The simulation result shows the pattern of the wave propagation at Lhoknga beach moves from the northwest to the east and south of the coast. The model also informs that the maximum wave height during high tide condition is 1.72 m and 1.31 m during low tide condition. The result indicates that the coast of Lhoknga has moderate wave conditions caused by a gentle beach bathymetry slope.

On the structure of bow waves on a ship model

1997 ◽  
Vol 346 ◽  
pp. 77-115 ◽  
Author(s):  
RONALD R. DONG ◽  
JOSEPH KATZ ◽  
THOMAS T. HUANG
Keyword(s):  
Free Surface ◽  
Laser Sheet ◽  
Wave Crest ◽  
Two Dimensional ◽  
Characteristic Structure ◽  
Near Surface ◽  
Ship Model ◽  
Ship Wave ◽  
Bow Wave ◽  
Vorticity Production

Particle image velocitmetry (PIV) measurements and free-surface visualizations around a ship model focus on the flow within the attached liquid sheet, upstream of the point at which the bow wave separates from the model, the origin and structure of the bow wave and the flow downstream of the wave crest. The measurements are performed at Reynolds numbers ranging between 2.8×106 and 7.4×106 and Froude numbers between 0.17 and 0.45 (both are based on ship length L). Representative velocity and vorticity distributions at FrL=0.28 and FrL=0.45 demonstrate the characteristic structure of mild and steep waves, respectively. Very close to the bow the attached sheet is thin and quite unsteady. With increasing distance from the nose the sheet becomes thicker and its development involves considerable vorticity production. In the mild case this vorticity is originated at the free surface, whereas in the steep wave case, boundary layer separation occurs on the model, which also transports vorticity into the sheet. This vorticity and its associated induced lateral flow remain near the model downstream of the bow wave. By calculating the acceleration component tangent to the free surface of the sheet it is shown that the peaks in the near-surface vorticity appear in regions with high viscous flux of vorticity from the surface. Formation of a bow wave also involves considerable production of vorticity. Similar to two-dimensional breakers, the primary origin of this vorticity is at the toe of the breaker. However, unlike the two-dimensional cases, the region containing vorticity in the ship wave does not appear as an extended shear layer. Instead, this vorticity is convected out of the plane of the laser sheet in a series of distinct vortex filaments. The ship wave also has powerful counter-rotating vorticity concentrated near the wave crest that has been observed in two-dimensional waves, but not of the same strength. Breaking becomes weaker, i.e. there is less vorticity production, with increasing distance from the model, but it persists even at the ‘tail’ of the bow wave. The sites of vorticity entrainment of both signs are consistent with the computed near-surface acceleration. Estimates of the three-dimensional velocity distribution and head losses within the wave are also provided.

Theory of the almost-highest wave. Part 2. Matching and analytic extension

1978 ◽  
Vol 85 (4) ◽  
pp. 769-786 ◽  
Author(s):  
M. S. Longuet-Higgins ◽  
M. J. H. Fox
Keyword(s):  
Phase Velocity ◽  
Wave Height ◽  
Water Waves ◽  
Phase Speed ◽  
Wave Crest ◽  
Analytic Extension ◽  
Radius Of Curvature ◽  
Maximum Height ◽  
Branch Points ◽  
Method Of Calculation

Most methods of calculating steep gravity waves (of less than the maximum height) encounter difficulties when the radius of curvature R at the crest becomes small compared with the wavelength L, or some other typical length scale. This paper describes a new method of calculation valid when R/L is small.For deep-water waves, a parameter ε is defined as equal to q/2½c0, where q is the particle speed at the wave crest, in a frame of reference moving with the phase speed c. Hence ε is of order (R/L)½. Three zones are distinguished: (1) an inner zone of linear dimensions ε2L near the crest, where the flow is described by the inner solution found previously by Longuet-Higgins & Fox (1977); (2) an outer zone of dimensions O(L) where the flow is given by a perturbed form of Michell's solution for the highest wave; and (3) a matching zone of width O(L). The matching procedure involves complex powers of ε.The resulting expression for the square of the phase velocity is found to be \[ c^2 = (g/k)\{1.1931-1.18\epsilon^3\cos(2.143\ln \epsilon + 2.22)\} \] (see figures 5a, b), which is in remarkable agreement with independent calculations based on high-order series. In particular, the existence of turning-points in the phase velocity as a function of wave height is confirmed.Similar expressions, valid to order ε3, are found for the wave height, the potential and kinetic energies and the momentum flux or impulse of the wave.The velocity field is extended analytically across the free surface, revealing the existence of branch-points of order ½, as predicted by Grant (1973).

Semi-Empirical Crest Distributions of Long-Crest Nonlinear Waves of Three-Hour Duration

2017 ◽  
Author(s):  
Zhenjia (Jerry) Huang ◽  
Qiuchen Guo
Keyword(s):  
Nonlinear Wave ◽  
Wave Height ◽  
Model Test ◽  
Significant Wave Height ◽  
Spectral Peak ◽  
Wave Crest ◽  
Empirical Formulas ◽  
Peak Period ◽  
Significant Wave ◽  
Semi Empirical

In wave basin model test of an offshore structure, waves that represent the given sea states have to be generated, qualified and accepted for the model test. For seakeeping and stationkeeping model tests, we normally accept waves in wave calibration tests if the significant wave height, spectral peak period and spectrum match the specified target values. However, for model tests where the responses depend highly on the local wave motions (wave elevation and kinematics) such as wave impact, green water impact on deck and air gap tests, additional qualification checks may be required. For instance, we may need to check wave crest probability distributions to avoid unrealistic wave crest in the test. To date, acceptance criteria of wave crest distribution calibration tests of large and steep waves of three-hour duration (full scale) have not been established. The purpose of the work presented in the paper is to provide a semi-empirical nonlinear wave crest distribution of three-hour duration for practical use, i.e. as an acceptance criterion for wave calibration tests. The semi-empirical formulas proposed in this paper were developed through regression analysis of a large number of fully nonlinear wave crest distributions. Wave time series from potential flow simulations, computational fluid dynamics (CFD) simulations and model test results were used to establish the probability distribution. The wave simulations were performed for three-hour duration assuming that they were long-crested. The sea states are assumed to be represented by JONSWAP spectrum, where a wide range of significant wave height, peak period, spectral peak parameter, and water depth were considered. Coefficients of the proposed semi-empirical formulas, comparisons among crest distributions from wave calibration tests, numerical simulations and the semi-empirical formulas are presented in this paper.

Non-Gaussian Extreme Waves in the Central North Sea

1997 ◽  
Vol 119 (3) ◽  
pp. 146-150 ◽  
Author(s):  
J. Skourup ◽  
N.-E. O. Hansen ◽  
K. K. Andreasen
Keyword(s):  
Wave Height ◽  
North Sea ◽  
Upper Bound ◽  
Wave Crest ◽  
Extreme Waves ◽  
Freak Waves ◽  
Freak Wave ◽  
Wave Trains ◽  
Central North Sea ◽  
Crest Height

The area of the Central North Sea is notorious for the occurrence of very high waves in certain wave trains. The short-term distribution of these wave trains includes waves which are far steeper than predicted by the Rayleigh distribution. Such waves are often termed “extreme waves” or “freak waves.” An analysis of the extreme statistical properties of these waves has been made. The analysis is based on more than 12 yr of wave records from the Mærsk Olie og Gas AS operated Gorm Field which is located in the Danish sector of the Central North Sea. From the wave recordings more than 400 freak wave candidates were found. The ratio between the extreme crest height and the significant wave height (20-min value) has been found to be about 1.8, and the ratio between extreme crest height and extreme wave height has been found to be 0.69. The latter ratio is clearly outside the range of Gaussian waves, and it is higher than the maximum value for steep nonlinear long-crested waves, thus indicating that freak waves are not of a permanent form, and probably of short-crested nature. The extreme statistical distribution is represented by a Weibull distribution with an upper bound, where the upper bound is the value for a depth-limited breaking wave. Based on the measured data, a procedure for determining the freak wave crest height with a given return period is proposed. A sensitivity analysis of the extreme value of the crest height is also made.

Searching for Factors that Limit Observed Extreme Maximum Wave Height Distributions in the North Sea

2008 ◽  
pp. 127-138 ◽  
Author(s):  
Gerrit Burgers ◽  
Frits Koek ◽  
Hans de Vries ◽  
Martin Stam
Keyword(s):  
Wave Height ◽  
North Sea ◽  
Maximum Wave Height ◽  
The North ◽  
The North Sea

scholarly journals REPRODUCTION ANALYSIS OF HUMAN DRIFTING BEHAVIOR DURING TSUNAMI USING NUMERICAL CALCULATION

2020 ◽  
pp. 34
Author(s):  
Riko Morita ◽  
Taro Arikawa
Keyword(s):  
Numerical Calculation ◽  
Wave Height ◽  
Prediction Method ◽  
Great East Japan Earthquake ◽  
Numerical Calculations ◽  
Water Tank ◽  
Maximum Wave Height ◽  
Hydraulic Experiment ◽  
Secondary Damage ◽  
Simulation Results

Along with the 2011 Great East Japan Earthquake (Mw 9.0), a huge tsunami exceeding a maximum wave height of 15 m occurred. Many people and objects were destroyed and drifted by the tsunami. In addition, these debris were transported to various places that could not be predicted, resulting in significant secondary damage and increase in the number of missing. Therefore, in order to reduce the amount of damage, it is important to predict the behavior and landing points of person after set adrift in a tsunami. The best way to increase the rescue rate is to predict in advance the area that people will be drifted, and prioritize searching operations at that area. Although there has been considerable number of studies which handle the drifting behavior of containers and ships (e.g., Kaida et al., 2016), the prediction of drifting areas focusing on people has not been conducted. Moreover, a drifting area prediction method has not yet been established. The purpose of this study is to conduct a hydraulic experiment using a flat water tank, and observe the drifting area of the drifting object. Then, we conducted numerical calculations and compared simulation results with the experimental ones.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/1yhKuodhCbg

scholarly journals A Two-Dimensional Coupled Atmosphere-Ice-Sheet-Continent Model Designed for Paleoclimatic Simulations

1990 ◽  
Vol 14 ◽  
pp. 55-57 ◽  
Author(s):  
M.B. Esch ◽  
K. Herterich
Keyword(s):  
Climate Model ◽  
Hydrological Cycle ◽  
Vertical Plane ◽  
Ice Sheet ◽  
Ice Age ◽  
Balance Model ◽  
Two Dimensional ◽  
Geothermal Heat ◽  
The North ◽  
Slow Evolution

We present a two-dimensional climate model to be used for basic dynamic studies on ice-age time scales (103 to 106 years). The model contains an ice sheet, where flow and temperature are calculated in a vertical plane, oriented in the north-south direction. The model ice sheet is forced by a zonally-averaged atmospheric energy-balance model, including a seasonal cycle and a simplified hydrological cycle, which specifies ice temperature and the mass balance at the ice-sheet surface. At the bottom of the ice sheet, the geothermal heat flux is prescribed. In addition, delayed bedrock sinking (or bedrock rising) is assumed.A stationary state is achieved after 200 000 model years. This long time scale is introduced by the slow evolution of the temperature field within the ice sheet. Using reasonable parameter values and presently observed precipitation patterns, modified by ice-sheet orography, the observed thickness to length ratio (4 km/3300 km) of the Laurentide ice sheet can be simulated within a realistic build-up time (40 000 years). Near the ice bottom, temperate regions developed. They may have had an important effect on ice-sheet build-up and ice-sheet decay.

An Experimental Examination of the 2D+T Approximation

2009 ◽  
Vol 53 (02) ◽  
pp. 59-67
Author(s):  
Mostafa Shakeri ◽  
Eric Maxeiner ◽  
Thomas Fu ◽  
James H. Duncan
Keyword(s):  
Froude Number ◽  
Longitudinal Wave ◽  
Contact Line ◽  
Three Dimensional ◽  
Maximum Height ◽  
Hull Form ◽  
Ship Model ◽  
Wave Maker ◽  
Acceleration Of Gravity ◽  
Good Agreement

Measurements of contact line height and longitudinal wave profiles from experiments with a three-dimensional naval ship model and experiments using a 2D+T wave maker with motions approximating the three-dimensional hull form are compared. The shape and maximum height of the contact line in the bow region are nearly the same in the two experiments, and the distance downstream along the hull over which the two measurements agree increases with increasing Froude number, Fn = Um/√gLm, where Um is the ship model speed, g is the acceleration of gravity, and Lm is the ship model waterline length. The comparison of the longitudinal wave profile (wave cut) data from the two experiments shows fairly good agreement for wavelengths and amplitudes at the highest Froude number and the measurement position closest to the hull.

Sign in / Sign up

Export Citation Format

Share Document