scholarly journals The resistance of a ship among waves

1937 ◽  
Vol 161 (906) ◽  
pp. 299-308 ◽  
Keyword(s):  
Free Surface ◽  
Surface Waves ◽  
Fluid Velocity ◽  
Wave Length ◽  
Steady Motion ◽  
Degree Of Approximation ◽  
Point Of View ◽  
Similar Degree ◽  
Horizontal Line ◽  
Free Surface Waves

1—The wave resistance of a ship advancing in still water may be calculated under certain assumptions, which amount to supposing the forced wave motion to be small so that squares of the fluid velocity may be neglected; moreover, the ship is supposed to advance with constant velocity in a horizontal line. It does not appear to have been noticed that we may super­ pose on the solution so obtained free surface waves of small amplitude, and that the addition to the resistance may be calculated, to a similar degree of approximation, as the horizontal resultant of the additional fluid pressures due to the free surface waves; this additional resistance, which may be negative, depends upon the position of the ship among the free waves. Various calculations are now made from this point of view. We consider first transverse following waves moving at the same speed as the ship, and then a ship moving in the waves left by another ship in advance moving at the same speed; finally, we examine the more general case of a ship moving through free transverse waves of any wave-length. All the cases are discussed with reference to such experimental results as are available. 2—We treat the problem first as one of steady motion with the ship at rest in a uniform stream of velocity c in the negative direction of Ox ; we take the origin O in the undisturbed water surface, and Oz vertically upwards. The velocity potential is given by ϕ = cx + ϕ 1 , (1)

scholarly journals The method of images in some problems of surface waves

1927 ◽  
Vol 115 (771) ◽  
pp. 268-280 ◽  
Keyword(s):  
Free Surface ◽  
Circular Cylinder ◽  
Surface Waves ◽  
Unit Length ◽  
Wave Length ◽  
Fluid Motion ◽  
Degree Of Approximation ◽  
Image Point ◽  
Horizontal Line ◽  
Image System

1. When a circular cylinder is submerged in a uniform stream, the surface elevation may be calculated, to a first approximation, by a method due originally to Lamb for this case, and later extended to bodies of more general form: the method consists in replacing the cylinder by the equivalent doublet at its centre and then finding the fluid motion due to this doublet. In discussing the problem some years ago, I remarked that if the solution so obtained were interpreted in terms of an image system of sources, we should then be able to proceed to further approximations by the method of successive images, taking images alternately in the surface of the submerged body and in the free surface of the stream. This is effected in the following paper for two-dimensional fluid motion, and the method is applied to the circular cylinder. It provides, theoretically at least, a process for obtaining any required degree of approximation but, of course, the expressions soon become very complicated. It is, however, of interest to examine some cases numerically so as to obtain some idea of the degree of approximation of the first stage. An expression is first obtained for the velocity potential of the fluid motion due to a doublet at a given depth below the surface of a stream, the doublet being of given magnitude with its axis in any direction. A transformation of this expression then gives a simple interpretation in terms of an image system. This system consists of a certain isolated doublet at the image point above the free surface, together with a line distribution of doublets on a horizontal line to the rear of this point; the moment per unit length of the line distribution is constant, but the direction of the axis rotates as we pass along the line, the period of a revolution being equal to the wave-length of surface waves for the velocity of the stream. The contribution of each part of the image system to the surface disturbance is indicated.

scholarly journals Experiments on generation of surface waves by an underwater moving bottom

2015 ◽  
Vol 471 (2178) ◽  
pp. 20150069 ◽  
Author(s):  
Timothée Jamin ◽  
Leonardo Gordillo ◽  
Gerardo Ruiz-Chavarría ◽  
Michael Berhanu ◽  
Eric Falcon
Keyword(s):  
Free Surface ◽  
Surface Waves ◽  
Surface Deformation ◽  
Fluid Layer ◽  
Fluid Velocity ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Low Pass ◽  
Spatio Temporal ◽  
Experimental Findings

We report laboratory experiments on surface waves generated in a uniform fluid layer whose bottom undergoes an upward motion. Simultaneous measurements of the free-surface deformation and the fluid velocity field are focused on the role of the bottom kinematics (i.e. its spatio-temporal features) in wave generation. We observe that the fluid layer transfers bottom motion to the free surface as a temporal high-pass filter coupled with a spatial low-pass filter. Both filter effects are often neglected in tsunami warning systems, particularly in real-time forecast. Our results display good agreement with a prevailing linear theory without any parameter fitting. Based on our experimental findings, we provide a simple theoretical approach for modelling the rapid kinematics limit that is applicable even for initially non-flat bottoms: this may be a key step for more realistic varying bathymetry in tsunami scenarios.

Study on vibration of dragon wash basin and free surface waves inside

2018 ◽  
Vol 35 (1) ◽  
pp. 15-23
Author(s):  
Zi-Yu Guo ◽  
Xiao-Peng Chen ◽  
Lai-Bing Jia ◽  
Bin Xu
Keyword(s):  
Free Surface ◽  
Surface Waves ◽  
Wash Basin ◽  
Free Surface Waves

Pseudo-three-timescale approximation of exponentially modulated free-surface waves

2009 ◽  
Vol 625 ◽  
pp. 435-443 ◽  
Author(s):  
MARK A. KELMANSON
Keyword(s):  
Free Surface ◽  
Surface Waves ◽  
Test Problem ◽  
Evolution Equations ◽  
Film Coating ◽  
Rotating Cylinder ◽  
New Method ◽  
Free Surface Waves ◽  
Numerical Integrations ◽  
Order Of Magnitude

A novel pseudo-three-timescale asymptotic procedure is developed and implemented for obtaining accurate approximations to solutions of an evolution equation arising in thin-film free-surface viscous flow. The new procedure, which employs strained fast and slow timescales, requires considerably fewer calculations than its standard three-timescale counterpart employing fast, slow and slower timescales and may readily be applied to other evolution equations of fluid mechanics possessing wave-like solutions exhibiting exponential decay in amplitude and variations in phase over disparate timescales. The new method is validated on the evolution of free-surface waves on a thin, viscous film coating the exterior of a horizontal rotating cylinder and is shown to yield accurate solutions up to non-dimensional times exceeding by an order of magnitude those of previous related studies. Results of the new method applied to this test problem are demonstrated to be in excellent agreement, over large timescales, with those of corroborative spectrally accurate numerical integrations.

Large amplitude progressive interfacial waves

1979 ◽  
Vol 93 (3) ◽  
pp. 433-448 ◽  
Author(s):  
Judith Y. Holyer
Keyword(s):  
Free Surface ◽  
Surface Wave ◽  
Surface Waves ◽  
Large Amplitude ◽  
Phase Speed ◽  
Maximum Height ◽  
Interfacial Waves ◽  
Free Surface Waves ◽  
Lower Fluid ◽  
Over The Top

This paper contains a study of large amplitude, progressive interfacial waves moving between two infinite fluids of different densities. The highest wave has been calculated using the criterion that it has zero horizontal fluid velocity at the interface in a frame moving at the phase speed of the waves. For free surface waves this criterion is identical to the criterion due to Stokes, namely that there is a stagnation point at the crest of each wave. I t is found that as the density of the upper fluid increases relative to the density of the lower fluid the maximum height of the wave, for fixed wavelength, increases. The maximum height of a Boussinesq wave, which has the density almost the same above and below the interface, is 2·5 times the maximum height of a surface wave of the same wavelength. A wave with air over the top of it can be about 2% higher than the highest free surface wave. The point at which the limiting criterion is first satisfied moves from the crest for free surface waves to the point half-way between the crest and the trough for Boussinesq waves. The phase speed, momentum, energy and other wave properties are calculated for waves up to the highest using Padé approximants. For free surface waves and waves with air above the interface the maximum value of these properties occurs for waves which are lower than the highest. For Boussinesq waves and waves with the density of the upper fluid onetenth of the density of the lower fluid these properties each increase monotonically with the wave height.

scholarly journals Heat transfer in the seabed boundary layer

2021 ◽  
Vol 928 ◽  
Author(s):  
S. Michele ◽  
R. Stuhlmeier ◽  
A.G.L. Borthwick
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Free Surface ◽  
Surface Waves ◽  
Multiple Scales ◽  
Perturbation Expansion ◽  
Phase Speed ◽  
Maximum Heat ◽  
Practical Applications ◽  
Free Surface Waves

We present a theoretical model of the temperature distribution in the boundary layer region close to the seabed. Using a perturbation expansion, multiple scales and similarity variables, we show how free-surface waves enhance heat transfer between seawater and a seabed with a solid, horizontal, smooth surface. Maximum heat exchange occurs at a fixed frequency depending on ocean depth, and does not increase monotonically with the length and phase speed of propagating free-surface waves. Close agreement is found between predictions by the analytical model and a finite-difference scheme. It is found that free-surface waves can substantially affect the spatial evolution of temperature in the seabed boundary layer. This suggests a need to extend existing models that neglect the effects of a wave field, especially in view of practical applications in engineering and oceanography.

A lattice Boltzmann method for viscous free surface waves in two dimensions

2012 ◽  
Vol 71 (2) ◽  
pp. 223-248 ◽  
Author(s):  
Zhuangming Zhao ◽  
Ping Huang ◽  
Yineng Li ◽  
Junmin Li
Keyword(s):  
Free Surface ◽  
Surface Waves ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Two Dimensions ◽  
Free Surface Waves ◽  
Boltzmann Method
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