scholarly journals STUDY ON THE PROUDMAN RESONANCE OF WAVES INDUCED BY A MOVING ATMOSPHERIC PRESSURE DISTURBANCE

2018 ◽  
pp. 34
Author(s):  
Xiaojing Niu ◽  
Yixiang Chen ◽  
Haojie Zhou
Keyword(s):  
Shallow Water ◽  
Atmospheric Pressure ◽  
Water Waves ◽  
Impact Factors ◽  
Pressure Disturbance ◽  
Proudman Resonance ◽  
Nonlinear Shallow Water Equations ◽  
Maximum Water ◽  
The Impact ◽  
The Waves

A moving atmospheric pressure disturbance can induce a system of forced water waves. As predicted by the linear theory, an infinite wave height will be induced when the Froude number Fr=1, which is known as the Proudman resonance. Fr is defined as the ratio between the moving speed of an atmospheric pressure disturbance and the phase velocity of shallow water wave. The Proudman resonance is thought to be one of main mechanisms for the destructive meteotsunami (Monserrat et al., 2006). In this study, the nonlinear shallow water equations are used to describe the waves induced by a moving pressure disturbance, and the impact factors to the maximum water elevation in the case of Fr=1 are discussed.

Experiments on strong interactions between solitary waves

1978 ◽  
Vol 85 (3) ◽  
pp. 417-431 ◽  
Author(s):  
P. D. Weidman ◽  
T. Maxworthy
Keyword(s):  
Shallow Water ◽  
Solitary Waves ◽  
Water Waves ◽  
Vries Equation ◽  
Rectangular Channel ◽  
Quantitative Agreement ◽  
Strong Interactions ◽  
Shallow Water Waves ◽  
Qualitative And Quantitative ◽  
The Waves

Experiments on the interaction between solitary shallow-water waves propagating in the same direction have been performed in a rectangular channel. Two methods were devised to compensate for the dissipation of the waves in order to compare results with Hirota's (1971) solution for the collision of solitons described by the Kortewegde Vries equation. Both qualitative and quantitative agreement with theory is obtained using the proposed corrections for wave damping.

Influence of Wave Shape on the Impact of Shallow-Water Waves on Vertical Walls

2006 ◽  
Author(s):  
Claudio Zanzi ◽  
Pablo Go´mez ◽  
Julia´n Palacios ◽  
Joaqui´n Lo´pez ◽  
Julio Herna´ndez
Keyword(s):  
Shallow Water ◽  
Level Set ◽  
Water Waves ◽  
High Speed ◽  
Numerical Study ◽  
Local Level ◽  
Wave Shape ◽  
Shallow Water Waves ◽  
Vertical Walls ◽  
The Impact

A numerical study of the impact of shallow-water waves on vertical walls is presented. The air-liquid flow was simulated using a code for incompressible viscous flow, based on a local level set algorithm and a second-order approximate projection method. The level set transport and reinitialization equations were solved in a narrow band around the interface using an adaptive refined grid. The wave is assumed to be generated by a plunger which is accelerated in an open channel containing water. An arbitrary Lagrangian-Eulerian method was used to take into account the relative movement between the plunger and the end wall of the channel. The evolution of the free surface was visualized using a laser light sheet and a high-speed camera, with a sampling frequency of 1000 Hz. Several simulations were carried out to investigate the influence of the shape of the wave approaching the wall on the relevant quantities associated with the impact. The wave shape just before the impact was changed varying the total length of the channel. The results are compared with experimental results and with results obtained by other authors.

On Lagrangian drift in shallow-water waves on moderate shear

2010 ◽  
Vol 660 ◽  
pp. 221-239 ◽  
Author(s):  
W. R. C. PHILLIPS ◽  
A. DAI ◽  
K. K. TJAN
Keyword(s):  
Boundary Layer ◽  
Shear Flow ◽  
Shallow Water ◽  
Water Waves ◽  
Stokes Drift ◽  
Shallow Water Waves ◽  
Sea Floor ◽  
Langmuir Circulations ◽  
A Minor ◽  
The Waves

The Lagrangian drift in anO(ϵ) monochromatic wave field on a shear flow, whose characteristic velocity isO(ϵ) smaller than the phase velocity of the waves, is considered. It is found that although shear has only a minor influence on drift in deep-water waves, its influence becomes increasingly important as the depth decreases, to the point that it plays a significant role in shallow-water waves. Details of the shear flow likewise affect the drift. Because of this, two temporal cases common in coastal waters are studied, viz. stress-induced shear, as would arise were the boundary layer wind-driven, and a current-driven shear, as would arise from coastal currents. In the former, the magnitude of the drift (maximum minus minimum) in shallow-water waves is increased significantly above its counterpart, viz. the Stokes drift, in like waves in otherwise quiescent surroundings. In the latter, on the other hand, the magnitude decreases. However, while the drift at the free surface is always oriented in the direction of wave propagation in stress-driven shear, this is not always the case in current-driven shear, especially in long waves as the boundary layer grows to fill the layer. This latter finding is of particular interest vis-à-vis Langmuir circulations, which arise through an instability that requires differential drift and shear of the same sign. This means that while Langmuir circulations form near the surface and grow downwards (top down), perhaps to fill the layer, in stress-driven shear, their counterparts in current-driven flows grow from the sea floor upwards (bottom up) but can never fill the layer.

Two-dimensional periodic waves in shallow water

1989 ◽  
Vol 209 ◽  
pp. 567-589 ◽  
Author(s):  
Joe Hammack ◽  
Norman Scheffner ◽  
Harvey Segur
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Two Dimensional ◽  
Reasonable Accuracy ◽  
Kp Equation ◽  
Petviashvili Equation ◽  
Stable Manner ◽  
Genus 2 ◽  
Surface Patterns ◽  
The Waves

Experimental data are presented that demonstrate the existence of a family of gravitational water waves that propagate practically without change of form on the surface of shallow water of uniform depth. The surface patterns of these waves are genuinely two-dimensional and fully periodic, i.e. they are periodic in two spatial directions and in time. The amplitudes of these waves need not be small; their form persists even up to breaking. The waves are easy to generate experimentally, and they are observed to propagate in a stable manner, even when perturbed significantly. The measured waves are described with reasonable accuracy by a family of exact solutions of the Kadomtsev-Petviashvili equation (KP solutions of genus 2) over the entire parameter range of the experiments, including waves well outside the putative range of validity of the KP equation. These genus-2 solutions of the KP equation may be viewed as two-dimensional generalizations of cnoidal waves.

Gravity–capillary rings generated by water drops

1988 ◽  
Vol 197 ◽  
pp. 415-427 ◽  
Author(s):  
Bernard Le Méhauté
Keyword(s):  
Water Waves ◽  
Time History ◽  
Wave Pattern ◽  
Viscous Effects ◽  
Transient Wave ◽  
Linear Superposition ◽  
History Of ◽  
Water Drops ◽  
The Impact ◽  
The Waves

A theory for water waves created by the impact of small objects such as raindrops on an initially quiescent body of water is established. Capillary and dissipative viscous effects are taken into account in addition to gravity. It is shown that the prevailing waves are in a mixed capillary–gravity regime around a wavenumber km which corresponds to the minimum value of the group velocity. The waves are described as function of time and distance by the linear superposition of two transient wave components, a ‘sub-km’ (k < km) component and a ‘super-km’ (k > km) component. The super-km components prevail at a short distance from the drop, whereas only the sub-km ones remain at a larger distance. The relative time history of the wavetrain is independent of the size of the drop, and its amplitude is proportional to the drop momentum when it hits the free surface. The wave pattern is composed of a multiplicity of rings of amplitude increasing towards the drop location and is terminated by a trailing wave with an exponential decay. The number of rings increases with time and distance.

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.

scholarly journals MODELING TURBULENT BORE PROPAGATION IN THE SURF ZONE

1984 ◽  
Vol 1 (19) ◽  
pp. 7
Author(s):  
David R. Basco ◽  
Ib A. Svendsen
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Surf Zone ◽  
Momentum Balance ◽  
Correction Coefficient ◽  
Nonlinear Shallow Water Equations ◽  
Horizontal Momentum ◽  
T Distribution ◽  
The Waves ◽  
Turbulent Bore

Initial efforts to numerically simulate surf zone waves by using a modified form of the nonlinear shallow water equations are described. Turbulence generated at the front of the moving bore-like wave spreads vertically downward to significantly alter the velocity profile and hence the horizontal momentum flux. This influence of turbulence is incorporated into the momentum balance equation through a momentum correction coefficient, a which is prescribed based in part upon the theoretical a(x) distribution beneath stationary hydraulic jumps. The numerical results show that with a suitably chosen a(x) distribution, the equations not only dissipate energy as the waves propagate, but also that the wave shape stabilizes as a realistic profile rather than progressively steepening as when the nonlinear shallow water equations are employed. Further research is needed to theoretically determine the appropriate a(x,t) distribution.

The near-shore behaviour of shallow-water waves with localized initial conditions

2007 ◽  
Vol 591 ◽  
pp. 413-436 ◽  
Author(s):  
DAVID PRITCHARD ◽  
LAURA DICKINSON
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Initial Velocity ◽  
Initial Conditions ◽  
Initial Condition ◽  
Wave Runup ◽  
Shallow Water Waves ◽  
Nonlinear Shallow Water Equations ◽  
Near Shore ◽  
Observed Behaviour

We consider the behaviour of solutions to the nonlinear shallow-water equations which describe wave runup on a plane beach, concentrating on the behaviour at and just behind the moving shoreline. We develop regular series expansions for the hydrodynamic variables behind the shoreline, which are valid for any smooth initial condition for the waveform. We then develop asymptotic descriptions of the shoreline motion under localized initial conditions, in particular a localized Gaussian waveform: we obtain estimates for the maximum runup and drawdown of the wave, for its maximum velocities and the forces it is able to exert on objects in its path, and for the conditions under which such a wave breaks down. We show how these results may be extended to include initial velocity conditions and initial waveforms which may be approximated as the sum of several Gaussians. Finally, we relate these results tentatively to the observed behaviour of a tsunami.

scholarly journals Shallow-Water-Equation Model for Simulation of Earthquake-Induced Water Waves

2017 ◽  
Vol 2017 ◽  
pp. 1-11
Author(s):  
Hongzhou Ai ◽  
Lingkan Yao ◽  
Haixin Zhao ◽  
Yiliang Zhou
Keyword(s):  
Finite Difference Method ◽  
Shallow Water ◽  
Water Waves ◽  
Seismic Waves ◽  
Empirical Equation ◽  
Shallow Water Equation ◽  
Equation Model ◽  
Proposed Model ◽  
Maximum Water ◽  
Water Elevation

A shallow-water equation (SWE) is used to simulate earthquake-induced water waves in this study. A finite-difference method is used to calculate the SWE. The model is verified against the models of Sato and of Demirel and Aydin with three kinds of seismic waves, and the numerical results of earthquake-induced water waves calculated using the proposed model are reasonable. It is also demonstrated that the proposed model is reliable. Finally, an empirical equation for the maximum water elevation of earthquake-induced water waves is developed based on the results obtained using the model, which is an improvement on former models.

scholarly journals Soliton interaction as a possible model for extreme waves in shallow water

2003 ◽  
Vol 10 (6) ◽  
pp. 503-510 ◽  
Author(s):  
P. Peterson ◽  
T. Soomere ◽  
J. Engelbrecht ◽  
E. van Groesen
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Wave System ◽  
Soliton Interaction ◽  
Resonance Case ◽  
Extreme Waves ◽  
Shallow Water Waves ◽  
Near Resonance ◽  
Petviashvili Equation ◽  
The Waves

Abstract. Interaction of two long-crested shallow water waves is analysed in the framework of the two-soliton solution of the Kadomtsev-Petviashvili equation. The wave system is decomposed into the incoming waves and the interaction soliton that represents the particularly high wave hump in the crossing area of the waves. Shown is that extreme surface elevations up to four times exceeding the amplitude of the incoming waves typically cover a very small area but in the near-resonance case they may have considerable extension. An application of the proposed mechanism to fast ferries wash is discussed.

Sign in / Sign up

Export Citation Format

Share Document