scholarly journals WATER WAVES ON A BILINEAR SHEAR CURRENT

1974 ◽  
Vol 1 (14) ◽  
pp. 36 ◽  
Author(s):  
Robert A. Dalrymple
Keyword(s):  
Water Waves ◽  
Perturbation Technique ◽  
Wave Theory ◽  
Interfacial Velocity ◽  
Shear Current ◽  
Irregular Form ◽  
Vertical Velocity Profile ◽  
Mean Water Level ◽  
The Waves ◽  
A Current

A water wave theory is presented to describe waves propagating on a bilinear shear current flowing in the direction of the waves. The theory is derived assuming an ideal fluid in which a current exists, having a vertical velocity profile which varies linearly from a mean water level velocity of Ug, an interfacial velocity Uj at depth, d, and a bottom velocity Uj$. The theory is developed first for small amplitude waves and then extended to any arbitrary order by a numerical perturbation technique for symmetric waves. For measured waves, an irregular form of the theory is presented to provide a representation of these waves for analysis.

scholarly journals THE INTERACTION OF WAVES AND CURRENTS OVER A LONGSHORE BAR

1986 ◽  
Vol 1 (20) ◽  
pp. 116 ◽  
Author(s):  
I.A. Svendsen ◽  
J. Buhr Hansen
Keyword(s):  
Wave Height ◽  
Wave Motion ◽  
Surf Zone ◽  
Wave Theory ◽  
Runge Kutta Method ◽  
Waves And Currents ◽  
Set Up ◽  
The Waves ◽  
Wave Properties ◽  
A Current

A two-dimensional model for waves and steady currents in the surf zone is developed. It is based on a depth integrated and time averaged version of the equations for the conservation of mass, momentum, and wave energy. A numerical solution is described based on a fourth order Runge-Kutta method. The solution yields the variation of wave height, set-up, and current in the surf zone, taking into account the mass flux in the waves. In its general form any wave theory can be used for the wave properties. Specific results are given using the description for surf zone waves suggested by Svendsen (1984a), and in this form the model is used for the wave motion with a current on a beach with a longshore bar. Results for wave height and set-up are compared with measurements by Hansen & Svendsen (1986).

scholarly journals WAVE BASIN EXPERIMENTS ON BOTTOM FRICTION DUE TO CURRENT AND WAVES

1986 ◽  
Vol 1 (20) ◽  
pp. 61 ◽  
Author(s):  
Paul J. Visser
Keyword(s):  
Laser Doppler Anemometer ◽  
Bottom Friction ◽  
Frictional Stress ◽  
Wave Basin ◽  
New Type ◽  
Mean Water Level ◽  
The Mean ◽  
The Waves ◽  
Mean Current ◽  
A Current

Results are presented of experiments in a wave basin on the increase of the mean bottom frictional stress in a flow when a wave field is superimposed on a current. The bottom friction was derived from the mean water level measured at various places. Measurements of wave orbital and mean current velocities were done both with a micro-propeller and with a new type immersible Laser Doppler Anemometer. The data indicate an increase of the mean bottom shear stress due to the presence of the waves, but less than predicted by Bijker (1967). A suggestion is made to improve the accuracy of this theory. The bottom stresses as predicted by Fredsoe (1984) are somewhat larger than the, experimental results.

scholarly journals Wave and Current Generation in Wave Flumes Using Axial-Flow Pumps

2017 ◽  
Author(s):  
Aurélien Babarit ◽  
Simon Delvoye ◽  
Vincent Arnal ◽  
Laurent Davoust ◽  
Jeroen Wackers ◽  
...  
Keyword(s):  
Water Waves ◽  
Oscillatory Flow ◽  
Axial Flow ◽  
Proof Of Concept ◽  
Experimental Proof ◽  
Current Generation ◽  
Experimental Modelling ◽  
Flow Through ◽  
The Waves ◽  
A Current

We investigate a new concept for wave and current generation. It consists of axial-flow pumps driven such as to generate an oscillatory flow through an orifice located at one end of the flume. Oscillations of the flow lead to the generation of water waves at the free surface. If the average of the flow is different from zero, a current is generated that superposes on the waves. In this study, we explored the technical capabilities of this concept and the influence of geometric parameters on wave and current generation. We used numerical and experimental modelling. Most noticeably, the numerical results indicate that this concept is well suited for the generation of long and high waves. An experimental setup has been designed and built. We used it to make an experimental proof of concept for the wave and current generation, including waves propagating against the current.

DISPERSION IN SEISMIC SURFACE WAVES

Geophysics ◽  
1951 ◽  
Vol 16 (1) ◽  
pp. 63-80 ◽  
Author(s):  
Milton B. Dobrin
Keyword(s):  
Surface Waves ◽  
Water Waves ◽  
Seismic Refraction ◽  
Wave Theory ◽  
Wave Dispersion ◽  
Surface Zone ◽  
Surface Wave Dispersion ◽  
Near Surface ◽  
Arrival Times ◽  
Ground Roll

A non‐mathematical summary is presented of the published theories and observations on dispersion, i.e., variation of velocity with frequency, in surface waves from earthquakes and in waterborne waves from shallow‐water explosions. Two further instances are cited in which dispersion theory has been used in analyzing seismic data. In the seismic refraction survey of Bikini Atoll, information on the first 400 feet of sediments below the lagoon bottom could not be obtained from ground wave first arrival times because shot‐detector distances were too great. Dispersion in the water waves, however, gave data on speed variations in the bottom sediments which made possible inferences on the recent geological history of the atoll. Recent systematic observations on ground roll from explosions in shot holes have shown dispersion in the surface waves which is similar in many ways to that observed in Rayleigh waves from distant earthquakes. Classical wave theory attributes Rayleigh wave dispersion to the modification of the waves by a surface layer. In the case of earthquakes, this layer is the earth’s crust. In the case of waves from shot‐holes, it is the low‐speed weathered zone. A comparison of observed ground roll dispersion with theory shows qualitative agreement, but it brings out discrepancies attributable to the fact that neither the theory for liquids nor for conventional solids applies exactly to unconsolidated near‐surface rocks. Additional experimental and theoretical study of this type of surface wave dispersion may provide useful information on the properties of the surface zone and add to our knowledge of the mechanism by which ground roll is generated in seismic shooting.

Riser Fatigue Due to Currents and Waves

2002 ◽  
Author(s):  
C. Le Cunff ◽  
E. Fontaine ◽  
F. Biolley
Keyword(s):  
Modal Analysis ◽  
Environmental Conditions ◽  
Navier Stokes ◽  
Vortex Induced Vibrations ◽  
Two Factors ◽  
Shedding Frequency ◽  
The Waves ◽  
Structural Mode ◽  
A Current

Fatigue due to environmental conditions is studied on a top-tensioned riser. The fatigue is due to two factors. First, the waves produce a displacement of the top of the riser, which excites the structure. Secondly, currents create vortices behind the structures. The phenomenon is then referred to as vortex-induced vibrations (VIV), whereby the vortices can lock onto a structural mode through the shedding frequency. In the present paper, we have two objectives. The first is to compare the fatigue estimates given either by a modal analysis or by Navier-Stokes calculations for a riser in a current. The second is to determine if studying the wave and current effects separately produces conservative results or if they must be studied together.

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.

Application of Ship-Wave Theory to the Hydrofoil of Finite Span

1957 ◽  
Vol 1 (02) ◽  
pp. 27-55
Author(s):  
John P. Breslin
Keyword(s):  
Wave Theory ◽  
Wave Pattern ◽  
Wave Drag ◽  
Test Results ◽  
Dimensional Theory ◽  
Ship Hydrodynamics ◽  
Finite Span ◽  
Induced Drag ◽  
Load Distributions ◽  
The Waves

It is demonstrated in this paper2 that the deepwater wave drag of a hydrofoil of finite span can be found directly from the theory developed largely for ship hydrodynamics by Havelock and others. The wave drag is then studied at high Froude numbers and from the observed behavior the induced drag of the hydrofoil can be deduced from existing aerodynamic formulas. Evaluation of the resulting formulas is effected for two arbitrary load distributions and a comparison with some model test results is made. A practical approximation which gives the influence of gravity over a range of high Froude numbers is found and from this one can deduce a Froude number beyond which the effects of gravity may be ignored. It is also shown that an expression for the waves at some distance aft of the hydrofoil can be deduced from the general formulas developed for ship hydrodynamics. A discussion of the wave pattern is given with particular emphasis on the centerline profile at high Froude numbers and a contrast is pointed out in regard to the results of the two-dimensional theory for the hydrofoil waves and wave resistance.

scholarly journals A Mild-Slope System for Bragg Scattering of Water Waves by Sinusoidal Bathymetry in the Presence of Vertically Sheared Currents

2019 ◽  
Vol 7 (1) ◽  
pp. 9 ◽  
Author(s):  
Kostas Belibassakis ◽  
Julien Touboul ◽  
Elodie Laffitte ◽  
Vincent Rey
Keyword(s):  
Resonant Frequency ◽  
Water Waves ◽  
Bottom Topography ◽  
Wave System ◽  
Bragg Scattering ◽  
Wave Flume ◽  
Seabed Topography ◽  
Incident Waves ◽  
Slope System ◽  
A Current

Extended mild-slope models (MMSs) are examined for predicting the characteristics of normally incident waves propagating over sinusoidal bottom topography in the presence of opposing shearing currents. It is shown that MMSs are able to provide quite good predictions in the case of Bragg scattering of waves over rippled bathymetry without a current, but fail to provide good predictions concerning the resonant frequency in the additional presence of a current. In order to resolve the above mismatch, a two-equation mild-slope system (CMS2) is derived from a variational principle based on the representation of the wave potential expressed as a superposition of the forward and backward components. The latter system is compared against experimentally measured data collected in a wave flume and is shown to provide more accurate predictions concerning both the resonant frequency and the amplitude of the reflection coefficient. Future work will be devoted to the examination of the derived model for a more general wave system over realistic seabed topography.

Solitons and other solutions of the long-short wave equation

2015 ◽  
Vol 25 (1) ◽  
pp. 129-145 ◽  
Author(s):  
Ghodrat Ebadi ◽  
Aida Mojaver ◽  
Sachin Kumar ◽  
Anjan Biswas
Keyword(s):  
Wave Equation ◽  
Water Waves ◽  
Soliton Solutions ◽  
Expansion Method ◽  
Short Wave ◽  
Shallow Water Waves ◽  
Content Type ◽  
Integration Techniques ◽  
Physical Phenomena ◽  
The Waves

Purpose – The purpose of this paper is to discuss the integrability studies to the long-short wave equation that is studied in the context of shallow water waves. There are several integration tools that are applied to obtain the soliton and other solutions to the equation. The integration techniques are traveling waves, exp-function method, G′/G-expansion method and several others. Design/methodology/approach – The design of the paper is structured with an introduction to the model. First the traveling wave hypothesis approach leads to the waves of permanent form. This eventually leads to the formulation of other approaches that conforms to the expected results. Findings – The findings are a spectrum of solutions that lead to the clearer understanding of the physical phenomena of long-short waves. There are several constraint conditions that fall out naturally from the solutions. These poses the restrictions for the existence of the soliton solutions. Originality/value – The results are new and are sharp with Lie symmetry analysis and other advanced integration techniques in place. These lead to the connection between these integration approaches.

scholarly journals Trapping of water waves by freely floating structures in a channel

2011 ◽  
Vol 467 (2136) ◽  
pp. 3613-3632 ◽  
Author(s):  
Sergey A. Nazarov ◽  
Juha H. Videman
Keyword(s):  
Spectral Problem ◽  
Water Waves ◽  
Variational Principles ◽  
Water Channel ◽  
Coupled System ◽  
Wave Theory ◽  
Operator Pencil ◽  
Geometric Condition ◽  
Trapped Modes ◽  
Floating Structures

This article is concerned with the existence of rigid freely floating structures capable of supporting trapped modes (time-harmonic water waves of finite energy in an unbounded domain). Under the usual assumptions of linear water-wave theory, a condition guaranteeing the existence of trapped modes is derived, and structures satisfying this geometric condition are shown to exist in a three-dimensional water channel. The sufficient condition arises from the application of variational principles to a conveniently formulated linear spectral problem, the main effort being the construction of a reduction scheme that turns the quadnic operator pencil associated with the original coupled system into a linear self-adjoint spectral problem. An example of floating bodies supporting at least four trapped modes is given.

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