scholarly journals LIMITING CONDITION FOR STANDING WAVE THEORIES BY PERTURBATION METHOD

1970 ◽  
Vol 1 (12) ◽  
pp. 32 ◽  
Author(s):  
Yoshito Tsuchiya ◽  
Masataka Yamaguchi
Keyword(s):  
Free Surface ◽  
Perturbation Method ◽  
Standing Wave ◽  
Vertical Wall ◽  
Standing Waves ◽  
Finite Amplitude ◽  
Surface Conditions ◽  
Wave Pressure ◽  
Wave Characteristics ◽  
Limiting Condition

The purpose of this paper is to make clear the validity and limiting condition for the application of the finite amplitude standing wave theories by the perturbation method In a numerical example, the errors of each order solution of these theories for two non-linear free surface conditions are computed for various kinds of wave characteristics and compared with each other Some experiments on the wave pressure on a vertical wall by standing waves were carried out and a plot of the limiting condition for the application of these theories is proposed based on the comparison with theoretical curves In addition, as an example of the application of these theories, the change of characteristics of wave pressure of standing waves accompanying the overtopping wave on a vertical wall is discussed.

scholarly journals PRESSURE UPON VERTICAL WALL PROM STANDING WAVES

1972 ◽  
Vol 1 (13) ◽  
pp. 87
Author(s):  
V.K. Shtencel
Keyword(s):  
Experimental Data ◽  
Standing Wave ◽  
Vertical Wall ◽  
Standing Waves ◽  
Finite Depth ◽  
Theoretical Solution ◽  
Stable Mode ◽  
Wave Pressure ◽  
Additional Criterion ◽  
Structure Result

When surge waves approach a vertical wall a standing wave is formed ahead of the latter. This is the only case when the interaction between waves and structure result in a stable mode of motion with distinct kinematic characteristics. Such motion can be described by equations of hydromechanics without the introduction of any hydraulic coefficients; a comparison of various theoretical solutions with experimental data can serve as an additional criterion for evaluating the accuracy of this or that solution. The first theoretical solution for wave pressure acting upon a vertical wall under the effect of standing waves at a finite depth has been published by Sainflou in 1928 (1).

On the form of the highest progressive and standing waves in deep water

1973 ◽  
Vol 331 (1587) ◽  
pp. 445-456 ◽  
Keyword(s):  
Free Surface ◽  
Numerical Integration ◽  
Gravity Wave ◽  
Standing Wave ◽  
Deep Water ◽  
Standing Waves ◽  
Infinite Depth ◽  
Single Term

The form of a progressive gravity wave on deep water, which generally must be found by numerical integration (Michell 1893) is shown to be approximated with remarkable accuracy by a single term. Six consecutive waves are transformed conformally so as to surround the point corresponding to infinite depth. The free surface then corresponds closely to the boundary of a hexagon. In a similar way the profile of a standing wave is closely approximated to by transforming four consecutive waves conformally and taking the profile as the boundary of a square. The profile agrees closely with that calculated by Penney & Price (1952) and with the experiments of Taylor (1953).

On cross-waves

1970 ◽  
Vol 41 (4) ◽  
pp. 837-849 ◽  
Author(s):  
C. J. R. Garrett
Keyword(s):  
Free Surface ◽  
Steady State ◽  
Standing Waves ◽  
Order Theory ◽  
Finite Amplitude ◽  
Second Order ◽  
Mathieu’S Equation ◽  
Wave Maker ◽  
The Cross ◽  
Cross Waves

Cross-waves are standing waves with crests at right angles to a wave-maker. They generally have half the frequency of the wave-maker and reach a steady state at some finite amplitude. A second-order theory of the modes of oscillation of water in a tank with a free surface and wave-makers at each end leads to a form of Mathieu's equation for the amplitude of the cross-waves, which are thus an example of parametric resonance and may be excited at half the wave-maker frequency if this is within a narrow band. The excitation depends on the amplitude of the wave-maker at the surface and the integral over depth of its amplitude. Cross-waves may be excited even if the mean free surface is stationary. The effects of finite amplitude are that the cross-waves approach a steady state such that a given amplitude is achieved at a frequency greater than that for free waves by an amount proportional to the amplitude of the wave-maker. The theory agrees reasonably well with the experimental results of Lin & Howard (1960). The amplification of the cross-waves may be understood in terms of the rate of working of the wave-maker against transverse stresses associated with the cross-waves, one located at the surface and the other equal to Miche's (1944) depth-independent second-order pressure. The theory applies to the situation where the primary motion consists of standing waves and the cross-waves are constant in amplitude away from the wave-maker, but certain generalizations may be made to the situation where the primary waves are progressive and the cross-waves decay away from the wave-maker.

On the Kapitza instability and the generation of capillary waves

2016 ◽  
Vol 789 ◽  
pp. 368-401 ◽  
Author(s):  
Georg F. Dietze
Keyword(s):  
Free Surface ◽  
Large Amplitude ◽  
Vertical Wall ◽  
Classical Problem ◽  
Finite Amplitude ◽  
Capillary Waves ◽  
Smooth Transition ◽  
Cutoff Wavelength ◽  
Integral Boundary ◽  
Low Dimensional

We revisit the classical problem of a liquid film falling along a vertical wall due to the action of gravity, i.e. the Kapitza paradigm (Kapitza, Zh. Eksp. Teor. Fiz., vol. 18, 1948, pp. 3–28). The free surface of such a flow is typically deformed into a train of solitary pulses that consists of large asymmetric wave humps preceded by small precursory ripples, designated as ‘capillary waves’. We set out to answer four fundamental questions. (i) By what mechanism do the precursory ripples form? (ii) How can they travel at the same celerity as the large-amplitude main humps? (iii) Why are they designated as ‘capillary waves’? (iv) What determines their wavelength and number and why do they attenuate in space? Asymptotic expansion as well as direct numerical simulations and calculations with a low-dimensional integral boundary-layer model have yielded the following conclusions. (i) Precursory ripples form due to an inertia-based mechanism at the foot of the leading front of the main humps, where the local free-surface curvature is large. (ii) The celerity of capillary waves is matched to that of the large humps due to the action of surface tension, which speeds up the former and slows down the latter. (iii) They are justly designated as ‘capillary waves’ because their wavelength is systematically shorter than the visco-capillary cutoff wavelength of the Kapitza instability. Due to a nonlinear effect, namely that their celerity decreases with decreasing amplitude, they nonetheless attain/maintain a finite amplitude because of being continuously compressed by the pursuing large humps. (iv) The number and degree of compression of capillary waves is governed by the amplitude of the main wave humps as well as the Kapitza number. Large-amplitude main humps travel fast and strongly compress the capillary waves in order for these to speed up sufficiently. Also, the more pronounced the first capillary wave becomes, the more (spatially attenuating) capillary waves are needed to allow a smooth transition to the back of the next main hump. These effects are amplified by decreasing the Kapitza number, whereby, at very small values, streamwise viscous diffusion increasingly attenuates the amplitude of the capillary waves.

On the use of tensor paths to estimate the nonproportionality factor of multiaxial stress or strain histories under free-surface conditions

2015 ◽  
Vol 227 (11) ◽  
pp. 3087-3100 ◽  
Author(s):  
Marco Antonio Meggiolaro ◽  
Jaime Tupiassú Pinho de Castro ◽  
Hao Wu
Keyword(s):  
Free Surface ◽  
Multiaxial Stress ◽  
Surface Conditions

Nonlinear Wave Crest Distribution on a Vertical Breakwater

2018 ◽  
Author(s):  
Valentina Laface ◽  
Giovanni Malara ◽  
Felice Arena ◽  
Ioannis A. Kougioumtzoglou ◽  
Alessandra Romolo
Keyword(s):  
Experimental Data ◽  
Free Surface ◽  
Vertical Wall ◽  
Surface Elevation ◽  
Wave Crest ◽  
Height Distribution ◽  
Free Surface Elevation ◽  
Pressure Transducers ◽  
Pressure Time ◽  
Time Histories

The paper addresses the problem of deriving the nonlinear, up to the second order, crest wave height probability distribution in front of a vertical wall under the assumption of finite spectral bandwidth, finite water depth and long-crested waves. The distribution is derived by relying on the Quasi-Deterministic representation of the free surface elevation in front of the vertical wall. The theoretical results are compared against experimental data obtained by utilizing a compressive sensing algorithm for reconstructing the free surface elevation in front of the wall. The reconstruction is pursued by starting from recorded wave pressure time histories obtained by utilizing a row of pressure transducers located at various levels. The comparison shows that there is an excellent agreement between the proposed distribution and the experimental data and confirm the deviation of the crest height distribution from the Rayleigh one.

Distribution of Wave Impact Forces From Breaking and Non-Breaking Waves

2009 ◽  
Author(s):  
Anne M. Fullerton ◽  
Thomas C. Fu ◽  
Edward S. Ammeen
Keyword(s):  
Free Surface ◽  
Wave Height ◽  
Breaking Waves ◽  
Qualitative Assessment ◽  
Total Force ◽  
Impact Loads ◽  
Wave Impact ◽  
Data Set ◽  
Wave Characteristics ◽  
Wide Range

Impact loads from waves on vessels and coastal structures are highly complex and may involve wave breaking, making these changes difficult to estimate numerically or empirically. Results from previous experiments have shown a wide range of forces and pressures measured from breaking and non-breaking waves, with no clear trend between wave characteristics and the localized forces and pressures that they generate. In 2008, a canonical breaking wave impact data set was obtained at the Naval Surface Warfare Center, Carderock Division, by measuring the distribution of impact pressures of incident non-breaking and breaking waves on one face of a cube. The effects of wave height, wavelength, face orientation, face angle, and submergence depth were investigated. A limited number of runs were made at low forward speeds, ranging from about 0.5 to 2 knots (0.26 to 1.03 m/s). The measurement cube was outfitted with a removable instrumented plate measuring 1 ft2 (0.09 m2), and the wave heights tested ranged from 8–14 inches (20.3 to 35.6 cm). The instrumented plate had 9 slam panels of varying sizes made from polyvinyl chloride (PVC) and 11 pressure gages; this data was collected at 5 kHz to capture the dynamic response of the gages and panels and fully resolve the shapes of the impacts. A Kistler gage was used to measure the total force averaged over the cube face. A bottom mounted acoustic Doppler current profiler (ADCP) was used to obtain measurements of velocity through the water column to provide incoming velocity boundary conditions. A Light Detecting and Ranging (LiDAR) system was also used above the basin to obtain a surface mapping of the free surface over a distance of approximately 15 feet (4.6 m). Additional point measurements of the free surface were made using acoustic distance sensors. Standard and high-speed video cameras were used to capture a qualitative assessment of the impacts. Impact loads on the plate tend to increase with wave height, as well as with plate inclination toward incoming waves. Further trends of the pressures and forces with wave characteristics, cube orientation, draft and face angle are investigated and presented in this paper, and are also compared with previous test results.

scholarly journals Instability of standing waves for non-linear Schrödinger-type equations

1988 ◽  
Vol 8 (8) ◽  
pp. 119-138 ◽  
Keyword(s):  
Dynamical Systems ◽  
Standing Wave ◽  
Optical Waveguides ◽  
Standing Waves ◽  
Positive Eigenvalue ◽  
Shooting Argument ◽  
Wave Solutions ◽  
Non Linear ◽  
Linearized Operator

AbstractA theorem is proved giving a condition under which certain standing wave solutions of non-linear Schrödinger-type equations are linearly unstable. The eigenvalue equations for the linearized operator at the standing wave can be analysed by dynamical systems methods. A positive eigenvalue is then shown to exist by means of a shooting argument in the space of Lagrangian planes. The theorem is applied to a situation arising in optical waveguides.

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