scholarly journals MACH-REFLECTION AS A DIFFRACTION PROBLEM

1976 ◽  
Vol 1 (15) ◽  
pp. 45 ◽  
Author(s):  
Udo Berger ◽  
Soren Kohlhase
Keyword(s):  
Wave Height ◽  
Incident Wave ◽  
Water Waves ◽  
Gas Dynamics ◽  
Mach Reflection ◽  
Diffraction Problem ◽  
Vertical Wall ◽  
Oblique Wave ◽  
Wave Heights ◽  
The Waves

As under oblique wave approach water waves are reflected by a vertical wall, a wave branching effect (stem) develops normal to the reflecting wall. The waves progressing along the wall will steep up. The wave heights increase up to more than twice the incident wave height. The £jtudy has pointed out that this effect, which is usually called MACH-REFLECTION, is not to be taken as an analogy to gas dynamics, but should be interpreted as a diffraction problem.

scholarly journals Wave Breaker Model of Transmission Waves

2021 ◽  
Vol 2 (1) ◽  
pp. 35-40
Author(s):  
Phetthanan Sukaphone ◽  
Buonkun Ounlesy Yaxasiht
Keyword(s):  
Wave Height ◽  
Incident Wave ◽  
Wave Energy ◽  
Water Waves ◽  
Wave Reflection ◽  
Reflection Coefficients ◽  
The Waves ◽  
Incident Wave Energy

The wavelength, the wave height, and the depth of the water under which the waves travel are critical criteria for describing water waves. According to previous research, the depth and period of the waves have a significant effect on the propagation and reflection coefficients. The hollow breakwater's varied model is supposed to minimize wave reflection and propagation in addition to reducing wave reflection, due to its capacity to capture and reduce incident wave energy. 

LARGE SCALE EXPERIMENTS ON EVOLUTION AND RUN-UP OF BREAKING SOLITARY WAVES

2007 ◽  
Vol 01 (03) ◽  
pp. 257-272 ◽  
Author(s):  
KAO-SHU HWANG ◽  
YU-HSUAN CHANG ◽  
HWUNG-HWENG HWUNG ◽  
YI-SYUAN LI
Keyword(s):  
Solitary Wave ◽  
Wave Height ◽  
Solitary Waves ◽  
Water Depth ◽  
Large Scale ◽  
Scale Effects ◽  
Wave Heights ◽  
Run Up ◽  
Hydraulics Laboratory ◽  
The Waves

The evolution and run-up of breaking solitary waves on plane beaches are investigated in this paper. A series of large-scale experiments were conducted in the SUPER TANK of Tainan Hydraulics Laboratory with three plane beaches of slope 0.05, 0.025 and 0.017 (1:20, 1:40 and 1:60). Solitary waves of which relative wave heights, H/h0, ranged from 0.03 to 0.31 were generated by two types of wave-board displacement trajectory: the ramp-trajectory and the solitary-wave trajectory proposed by Goring (1979). Experimental results show that under the same relative wave height, the waveforms produced by the two generation procedures becomes noticeably different as the waves propagate prior to the breaking point. Meanwhile, under the same relative wave height, the larger the constant water depth is, the larger the dimensionless run-up heights would be. Scale effects associated with the breaking process are discussed.

scholarly journals Reflection of nonlinear deep-water waves incident onto a wedge of arbitrary angle

1990 ◽  
Vol 32 (1) ◽  
pp. 61-96 ◽  
Author(s):  
T. R. Marchant ◽  
A. J. Roberts
Keyword(s):  
Deep Water ◽  
Water Waves ◽  
Wave Reflection ◽  
Mach Reflection ◽  
Wedge Angle ◽  
Arbitrary Angle ◽  
Weakly Nonlinear ◽  
Progressive Waves ◽  
The Waves ◽  
Wave Properties

AbstractWave reflection by a wedge in deep water is examined, where the wedge can represent a breakwater of finite length or the bow of a ship heading directly into the waves. In addition, the form of the solution allows the results to apply to ships heading at an angle into the waves. We consider a deep-water wavetrain approaching the wedge head on from infinity and being reflected. Far from the wedge there is a field of progressive waves (the incident wavetrain) while close to the wedge there is a short-crested wavefield (the incident and reflected wavetrains). A weakly-nonlinear slowly-varying averaged Lagrangian theory is used to describe the problem (see Whitham [16]) as the theory includes the nonlinear interaction between the incident and reflected wavetrains. This modelling of a short-crested wavefield allows the nonlinear wavefield to be found for broad wedges, as opposed to previous theories which are applicable to thin wedges only.It is shown that the governing partial differential equations are hyperbolic and that the solution comprises two regions, within which the wave properties are constant separated by a wave jump. Given the wedge angle and the incident wavefield, the jump angle and the wave steepness and wavenumber of the short-crested wave-field behind the wave jump can be determined. Two solution branches are found to exist: one corresponds to regular reflection, while for small amplitudes the other is similar to Mach-reflection and so it is called near Mach-reflection. Results are presented describing both solution branches and the transition between them.

scholarly journals MEASUREMENT OF INCIDENT WAVE HEIGHT IN COMPOSITE WAVE TRAINS

1974 ◽  
Vol 1 (14) ◽  
pp. 21
Author(s):  
Ake Sandstrom
Keyword(s):  
Wave Height ◽  
Incident Wave ◽  
Wave Train ◽  
Wave Length ◽  
Wave Theory ◽  
Arithmetic Mean ◽  
Reflected Waves ◽  
Wave Heights ◽  
Wave Trains ◽  
Composite Wave

A method is proposed for measurement of the incident wave height in a composite wave train. The composite wave train is assumed to consist of a superposition of regular incident and reflected waves with the same wave period. An approximate value of the incident wave height is obtained as the arithmetic mean of the wave heights measured "by two gauges separated a quarter of a wave length. The accuracy of the method in relation to the location of the gauges and the wave parameters is investigated using linear and second order wave theory. Results of the calculations are presented in diagrams.

scholarly journals WAVES GENERATED BY A PISTON-TYPE WAVEMAKER

1970 ◽  
Vol 1 (12) ◽  
pp. 36 ◽  
Author(s):  
Ole Secher Madsen
Keyword(s):  
Mathematical Model ◽  
Finite Number ◽  
Wave Height ◽  
Finite Amplitude ◽  
Governing Equations ◽  
Approximate Evaluation ◽  
Large Wave ◽  
Wave Heights ◽  
The Waves ◽  
Theoretical Results

When a wavemaker generates a finite number of waves, it has been found that one of the first and one of the last waves in such a burst is considerably larger than the average A mathematical model, based on the linearized governing equations, is used for the particular problem of the waves generated by a sinusoidally moving piston-type wavemaker starting from rest Theoretical results for the magnitude of the large wave relative to the average agree fairly well with experiments, however, the actual wave height is smaller in the experiments than predicted by theory It is shown, by extending the classical wavemaker theory to second order, that finite amplitude effects do not offer an explanation However, pistons rarely fit the tank dimensions exactly, and an approximate evaluation indicates that the discrepancy between predicted and observed wave heights can be attributed to the effects of leakage around the piston.

scholarly journals GENERALIZED WAVE DIFFRACTION DIAGRAMS

2000 ◽  
Vol 1 (2) ◽  
pp. 2
Author(s):  
J. W. Johnson
Keyword(s):  
Wave Height ◽  
Wave Diffraction ◽  
Water Waves ◽  
Electromagnetic Waves ◽  
Wave Train ◽  
Diffraction Theory ◽  
Long Beach ◽  
Practical Application ◽  
Diffraction Of Light ◽  
Wave Heights

Wave diffraction is the phenomenon in which water waves are propagated into a sheltered region formed by a breakwater or similar barrier which interrupts a portion of a regular wave train (Fig. 1). The principles of diffraction have considerable practical application in connection with the design of breakwaters as discussed by Dunham (1951) at the Long Beach Conference. The phenomenon is analogous to the diffraction of light, sound, and electromagnetic waves. Two general types of diffraction problems usually are encountered: one, the passage of waves around the end of a semi-infinite impermeable breakwater (Putnam and Arthur, 1948), and, second, the passage of waves through a gap in a breakwater (Blue and Johnson, 1949t Carr and Stelzriede, 1951). In general, the theoretical solutions have been found to apply with conservative results, that is, the predicted wave heights in the lee of a breakwater are found to be slightly larger than the height of waves that may be expected under actual conditions. The use of the diffraction theory in breakwater design is made convenient when summarized in the form of diagrams with curves of equal values of diffraction coefficients on a coordinate system in which the origin of the Bystem is at the tip of a single breakwater (Figs. 2a-2b, and 3) or at the center of a gap (Figs. 2c, and 4-6). The diffraction coefficient in this instance is defined as the ratio of the diffracted wave height to the incident wave height and usually is designated by the symbol K». The procedure in preparing diffraction diagrams appears elsewhere (Johnson, 1950). The purpose of this paper is to present diffraction diagrams to supplement the material of Dunham (1951). For complete details on the application of diffraction diagrams to typical harbor problems the reader is referred to this latter paper.

scholarly journals WAVE INVESTIGATIONS IN SHALLOW WATER

1970 ◽  
Vol 1 (12) ◽  
pp. 10 ◽  
Author(s):  
Winfried Siefert
Keyword(s):  
Shallow Water ◽  
Wave Height ◽  
Wind Direction ◽  
Tidal Flat ◽  
Propagation Direction ◽  
Elbe Estuary ◽  
Zero Crossing ◽  
Wave Heights ◽  
The Mean ◽  
The Waves

Examination of the significant heights of zero-crossing waves in the Elbe Estuary has yielded two noteworthy results: 1 In the deeper water of the estuary, the value of the quotient relating the significant and the mean wave heights is larger than on the bordering tidal flat. 2. The value of this function is dependent on the height of the waves; on the tidal flat this dependency is considerably more sensitive than in deeper water. With increasing wave height the value of significant wave height divided by mean height becomes smaller The propagation direction of waves moving onto the tidal flat is contingent upon the position of intertidal channels Such channels sharply reduce the possible propagation directions The waves nearly always move up-channel regardless of the wind direction It is possible to derive special wave period and wave height distributions representing the conditions m very shallow water.

scholarly journals MODEL STUDIES OF IMPULSIVELY-GENERATED WATER WAVES

1966 ◽  
Vol 1 (10) ◽  
pp. 26 ◽  
Author(s):  
Jan M. Jordaan
Keyword(s):  
Water Waves ◽  
Wave Train ◽  
Sudden Change ◽  
Underwater Explosion ◽  
Model Studies ◽  
Wave Basin ◽  
Wave Heights ◽  
Time Of Travel ◽  
The Impact ◽  
The Waves

The wave action due to a sudden impulse in a body of water was studied in a wave basin with beach in the laboratory. Waves were impulsively generated in the 90 ft. tank of water, 3 ft. deep, by the impact or sudden withdrawal of a paraboloidal plunger 14 ft. in diameter. The waves had a dominant height of 2 inches and period of 3 seconds, respectively, at a distance of 50 ft. from the plunger. Such waves are scale representations of those generated by sudden impulses in the ocean, such as an underwater nuclear explosion, a sudden change in the ocean bed due to earthquakes, or the impact of a land slide. The waves produced by a downward impulse, or by an underwater explosion, form a dispersive system: whose properties are not constant as in a uniform progressive wave train. Wave periodicities, celerities and wave lengths increase with time of travel and wave heights decrease with travel distance. Theory has already been developed to predict the wave properties at a given travel time and distance for given source energy, displacement and travel path depth profile (Jordaan 1965). Measurements agree fairly well with predictions.

Forced small-amplitude water waves: a comparison of theory and experiment

1960 ◽  
Vol 7 (1) ◽  
pp. 33-52 ◽  
Author(s):  
F. Ursell ◽  
R. G. Dean ◽  
Y. S. Yu
Keyword(s):  
Wave Height ◽  
Water Waves ◽  
Small Amplitude ◽  
Experimental Error ◽  
Wave Motion ◽  
Wave Theory ◽  
Finite Amplitude ◽  
Uniform Density ◽  
Wave Channel ◽  
Wave Heights

This paper describes an attempt to verify experimentally the wavemaker theory for a piston-type wavemaker. The theory is based upon the usual assumptions of classical hydrodynamics, i.e. that the fluid is inviscid, of uniform density, that motion starts from rest, and that non-linear terms are neglected. If the water depth, wavelength, wave period, and wavemaker stroke (of a harmonically oscillating wavemaker) are known, then the wavemaker theory predicts the wave motion everywhere, and in particular the wave height a few depths away from the wavemaker.The experiments were conducted in a 100 ft. wave channel, and the wave-height envelope was measured with a combination hook-and-point gauge. A plane beach (sloping 1:15) to absorb the wave energy was located at the far end of the channel. The amplitude-reflexion coefficient was usually less than 10%. Unless this reflexion effect is corrected for, it imposes one of the most serious limitations upon experimental accuracy. In the analysis of the present set of measurements, the reflexion effect is taken into account.The first series of tests was concerned with verifying the wavemaker theory for waves of small steepness (0.002 ≤ H/L ≤ 0.03). For this range of wave steepnesses, the measured wave heights were found to be on the average 3.4% below the height predicted by theory. The experimental error, as measured by the scatter about aline 3.4% below the theory, was of the order of 3%. The systematic deviation of 3.4% is believed to be partly due to finite-amplitude effects and possibly to imperfections in the wavemaker motion.The second series of tests was concerned with determining the effects of finite amplitude. For therange of wave steepnesses 0.045 ≤ H/L ≤ 0.048, themeasured wave heights were found to be on the average 10% below the heightspredictedfrom the small-amplitude theory. The experimental error was again of the order of 3%.It is considered that these measurements confirm the validity of the small-amplitude wave theory. No confirmation of this accuracy has hitherto been given for forced motions.

scholarly journals EXPERIMENTAL DATA ON THE OVERTOPPING OF SEAWALLS BY WAVES

2011 ◽  
Vol 1 (7) ◽  
pp. 36
Author(s):  
A. Paape
Keyword(s):  
Wave Height ◽  
Know How ◽  
The Past ◽  
Maximum Value ◽  
Wave Heights ◽  
Run Up ◽  
Materials Used ◽  
The Stability ◽  
The Waves ◽  
Made In

In the past it has been found that serious damage and breaching of seawalls is most frequently caused by overtopping. Hence for the design of seawalls data must be available about the overtopping by waves of the different profiles that might be possible. Naturally the conditions under which damage is caused to the seawall also depend on the type of construction and the materials used, for example: the stability of grass covered dikes can be endangered seriously by water flowing over the inner slope. In many designs the necessary height of a seawall has been defined such that not more than 2% of the waves overtop the crest, under chosen design conditions. This criterion has been determined on the assumption that the overtopping must remain very small. Some overtopping has to be accepted because no maximum value for wave height and wave run-up can be given, unless of course the wave height is limited by fore-shore conditions. Unfortunately this criterion gives no information about the volume and concentration of water overtopping the crest in each instance. Moreover it is of interest to know how this overtopping varies with other conditions, such as changes in the significant wave height. Information about the overtopping by waves was obtained from model investigations on simple plane slopes w^th inclinations varying from 1 : 8 to 1 : 2. The experiments were made in a windflume where wind generated waves as well as regular waves were employed. Using wind generated waves, conditions from nature regarding the distribution of wave heights could be reproduced. It appeared that the overtopping depends on the irregularity of the waves and that the same effects cannot be reproduced using regular paddle generated waves. In this paper a description of the model and the results of these tests are given. Investigations are m progress on composite slopes, including the reproduction of conditions for a seawall which suffered much overtopping but remained practically undamaged during the flood of 1953.

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