scholarly journals Multiple resonances of a moving oscillating surface disturbance on a shear current

2016 ◽  
Vol 808 ◽  
pp. 668-689 ◽  
Author(s):  
Yan Li ◽  
Simen Å. Ellingsen
Keyword(s):  
Free Surface ◽  
Dispersion Relation ◽  
Constant Velocity ◽  
Critical Value ◽  
Far Field ◽  
Gravitational Acceleration ◽  
Ship Waves ◽  
Infinite Depth ◽  
Shear Current ◽  
Surface Disturbance

We consider waves radiated by a disturbance of oscillating strength moving at constant velocity along the free surface of a shear flow, which, when undisturbed, has uniform horizontal vorticity of magnitude $S$. When no current is present the problem is a classical one and much studied, and in deep water a resonance is known to occur when $\unicode[STIX]{x1D70F}=|\boldsymbol{V}|\unicode[STIX]{x1D714}_{0}/g$ equals the critical value $1/4$ ($\boldsymbol{V}$: velocity of disturbance, $\unicode[STIX]{x1D714}_{0}$: oscillation frequency, $g$: gravitational acceleration). We show that the presence of a subsurface shear current can change this picture radically. Not only does the resonant value of $\unicode[STIX]{x1D70F}$ depend strongly on the angle between $\boldsymbol{V}$ and the current’s direction and the ‘shear-Froude number’ $\mathit{Fr}_{s}=|\boldsymbol{V}|S/g$; when $\mathit{Fr}_{s}>1/3$, multiple resonant values – as many as four – can occur for some directions of motion. At sufficiently large values of $\mathit{Fr}_{s}$, the smallest resonance frequency tends to zero, representing the phenomenon of critical velocity for ship waves. We provide a detailed analysis of the dispersion relation for the moving oscillating disturbance, in both finite and infinite water depth, including for the latter case an overview of the different far-field waves which exist in different sectors of wave-vector space under different conditions. Owing to the large number of parameters, a detailed discussion of the structure of resonances is provided for infinite depth only, where analytical results are available.

scholarly journals Ship waves in the presence of uniform vorticity

2014 ◽  
Vol 742 ◽  
Author(s):  
Simen Å. Ellingsen
Keyword(s):  
Shear Flow ◽  
Finite Depth ◽  
Critical Value ◽  
Wave Problem ◽  
Transverse Waves ◽  
Ship Waves ◽  
Striking Result ◽  
Constant Vorticity ◽  
Shear Current ◽  
Half Angle

AbstractLord Kelvin’s result that waves behind a ship lie within a half-angle $\phi _{\mathit{K}}\approx 19^{\circ }28'$ is perhaps the most famous and striking result in the field of surface waves. We solve the linear ship wave problem in the presence of a shear current of constant vorticity $S$, and show that the Kelvin angles (one each side of wake) as well as other aspects of the wake depend closely on the ‘shear Froude number’ $\mathit{Fr}_{\mathit{s}}=VS/g$ (based on length $g/S^2$ and the ship’s speed $V$), and on the angle between current and the ship’s line of motion. In all directions except exactly along the shear flow there exists a critical value of $\mathit{Fr}_{\mathit{s}}$ beyond which no transverse waves are produced, and where the full wake angle reaches $180^\circ $. Such critical behaviour is previously known from waves at finite depth. For side-on shear, one Kelvin angle can exceed $90^\circ $. On the other hand, the angle of maximum wave amplitude scales as $\mathit{Fr}^{-1}$ ($\mathit{Fr}$ based on size of ship) when $\mathit{Fr}\gg 1$, a scaling virtually unaffected by the shear flow.

Effect of Anisotropic Shape on Ship Wakes in Presence of Shear Current of Uniform Vorticity

2016 ◽  
Author(s):  
Yan Li ◽  
Simen Å. Ellingsen
Keyword(s):  
Aspect Ratio ◽  
Three Dimensional ◽  
Ship Waves ◽  
Aspect Ratios ◽  
Asymptotic Expressions ◽  
Shear Current ◽  
Ship Wakes ◽  
Surface Disturbance ◽  
Dimensional Shape ◽  
Three Dimensional Shape

We analyze the interactions between a subsurface shear current of uniform vorticity and a moving surface disturbance of anisotropic shape which generates surface gravity waves. The problem extends previous analysis of ship waves in the presence of a shear current varying linearly with depth, now also accounting for the three dimensional shape of real ships, in order to study the interplay of aspect ratio and the shear current. Based on general solutions derived previously, we apply an elliptical Gaussian pressure disturbance at the surface moving at constant velocity as a model for a real “ship”. Wave contributions in the far field and expressions for the Mach angle (of maximum wave amplitude) based on asymptotic expressions for high Froude numbers, are derived thereafter. Through numerical calculations we present wave patterns, as well as Kelvin and Mach angles, at moderate Froude numbers under different shear strenghts and aspect ratios. Results show that the aspect ratio has negligible effect on the value of the critical shear vorticity and Kelvin angle, whereas a subtle interplay of aspect ratio and shear strenght is found to affect the Mach angle at moderate Froude numbers.

Ship Waves in a Stratified Fluid

2001 ◽  
Vol 45 (01) ◽  
pp. 1-12 ◽  
Author(s):  
Timour Radko
Keyword(s):  
Free Surface ◽  
Present Model ◽  
Stratified Fluid ◽  
Moving Object ◽  
Far Field ◽  
Ship Waves ◽  
Linear Waves ◽  
Different Types ◽  
Density Interfaces

The far-field asymptotics of the linear waves excited by a moving object are obtained for a fluid consisting of n density layers (n is arbitrary). The structure of the perturbations of free surface and density interfaces is analyzed as a function of the depth of the object and its velocity. The amplitudes of different types of waves are compared. The present model also confirms and generalizes the features of the ship waves that were known previously only for the cases of one-layer and two-layer fluids.

scholarly journals Surface Waves Generated by a Translating and Oscillating Source Atop Realistic Shear Flows

2018 ◽  
Author(s):  
Yan Li ◽  
Simen Å. Ellingsen
Keyword(s):  
Surface Waves ◽  
River Estuary ◽  
Dimensionless Frequency ◽  
Gravitational Acceleration ◽  
Columbia River Estuary ◽  
Depth Dependence ◽  
Shear Current ◽  
Surface Disturbance ◽  
Numerical Tools ◽  
A Current

We analyze surface waves generated by a translating, oscillating surface disturbance atop a horizontal background flow of arbitrary depth dependence, with a focus on determining the Doppler resonance. For a critical value of the dimensionless frequency τ = ωV/g (ω: oscillation frequency, V: source velocity, g: gravitational acceleration) at which generated waves cannot escape. In the absence of shear the resonant value is famously 1/4; the presence of a shear current modifies this. We derive the theoretical and numerical tools for studying this problem, and present the first calculation of the Doppler resonance for a source atop a real, measured shear current to our knowledge. Studying graphical solutions to the (numerically obtained) dispersion relation allows derivation of criteria determining the number of far-field waves that exist in different sectors of propagation directions, from which the criteria for Doppler resonance follow. As example flows we study a typical wind-driven current, and a current measured in the Columbia River estuary. We show that modeling these currents as uniform or with a linear depth dependence based on surface measures may lead to large discrepancies, in particular for long and moderate wavelengths.

scholarly journals WAVES GENERATED BY TWO OR MORE SHIPS IN A CHANNEL

2011 ◽  
Vol 1 (32) ◽  
pp. 60 ◽  
Author(s):  
Maria Francisca Nascimento ◽  
Claudio Freitas Neves ◽  
Geraldo De Freitas Maciel
Keyword(s):  
Free Surface ◽  
Numerical Model ◽  
Surface Pattern ◽  
Ship Waves ◽  
Wave Trains

The numerical model FUNWAVE+Ship simulates the generation and propagation of ship waves to shore, including phenomena such as refraction, diffraction, currents and breaking of waves. The interaction of two wave trains, generated by ships moving either in the same direction at different speeds or in opposite directions, is studied. Focus is given to the wave orbital velocities and to the free surface pattern.

Reflection and Transmission of Ship Waves by Floating Barriers

2002 ◽  
Author(s):  
Quan-Ming Miao ◽  
Allen T. Chwang
Keyword(s):  
Free Surface ◽  
Energy Density ◽  
Wave Energy ◽  
Outer Region ◽  
Wave Pattern ◽  
Transmission Performance ◽  
Reflection And Transmission ◽  
Ship Waves ◽  
Wave Energy Density

The reflection and transmission of ship waves by vertical floating barriers located on both sides of a fairway are investigated by the modified Dawson’s method in this paper. The free surface is specially treated to take into account the floating barriers. The wave pattern and the wave energy density between and outside the barriers are obtained. It is found that the reflection and transmission performance of a barrier is associated with its width and height. For a wider or higher barrier, more ship waves are reflected by it. A vertical floating barrier with a reasonable width and height can reduce ship waves in the outer region very efficiently.

scholarly journals On generation and propagation of tsunamis in a shallow running ocean

1978 ◽  
Vol 1 (3) ◽  
pp. 373-390
Author(s):  
Lokenath Debnath ◽  
Uma Basu
Keyword(s):  
Free Surface ◽  
Three Dimensional ◽  
Relative Magnitude ◽  
Ocean Floor ◽  
Surface Elevation ◽  
Free Surface Elevation ◽  
Surface Disturbance ◽  
Fourier And Laplace Transforms ◽  
The Given ◽  
Integral Solutions

A theory is presented of the generation and propagation of the two and the three dimensional tsunamis in a shallow running ocean due to the action of an arbitrary ocean floor or ocean surface disturbance. Integral solutions for both two and three dimensional problems are obtained by using the generalized Fourier and Laplace transforms. An asymptotic analysis is carried out for the investigation of the principal features of the free surface elevation. It is found that the propagation of the tsunamis depends on the relative magnitude of the given speed of the running ocean and the wave speed of the shallow ocean. When the speed of the running ocean is less than the speed of the shallow ocean wave, both the two and the three dimensional free surface elevation represent the generation and propagation of surface waves which decay asymptotically ast−12for the two dimensional case and ast−1for the three dimensional tsunamis. Several important features of the solution are discussed in some detail. As an application of the general theory, some physically realistic ocean floor disturbances are included in this paper.

From Bulbous Bow to Free-Surface Shock Wave—Trends of 20 Years’ Research on Ship Waves at the Tokyo University Tank

1981 ◽  
Vol 25 (03) ◽  
pp. 147-180
Author(s):  
Takao Inui
Keyword(s):  
Shock Wave ◽  
Free Surface ◽  
Field Measurements ◽  
Wave Pattern ◽  
Ship Waves ◽  
Second Stage ◽  
Initial Stage ◽  
Man And Nature ◽  
Bulbous Bow ◽  
The Relationship

Trends of 20 years' research on ship waves at the Tokyo University Tank since 1960 are briefly sketched. Stress is focused on the importance of dialogues between man and nature. The process of these dialogues is exemplified by some typical cases, including the development of bulbous bows and the finding of free-surface shock waves. Wave-pattern pictures are shown to be indispensable for the initial stage of the di alogues, while wave contours and velocity-field measurements serve well in the second stage. The current wave analysis and wake survey may be the third. The relationship between "wavebreaking" and the "free-surface shock wave" is also discussed.

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