Capillary–gravity waves produced by a wavemaker

1991 ◽  
Vol 224 ◽  
pp. 217-226 ◽  
Author(s):  
L. M. Hocking ◽  
D. Mahdmina
Keyword(s):  
Surface Tension ◽  
Contact Angle ◽  
Free Surface ◽  
Surface Waves ◽  
Gravity Waves ◽  
Contact Line ◽  
Dynamic Properties ◽  
Transient Motion ◽  
Infinite Depth ◽  
The Waves

Surface waves in a channel can be produced by the horizontal motion of a plane wavemaker at one end of the channel. The amplitude and the frequency of the waves depend on both surface tension and gravity, as well as on the condition imposed at the contact line between the free surface and the wavemaker. Some of the previous work on the generation of capillary–gravity waves has been based on the unjustified assumption that the slope of the free surface at the contact line can be prescribed. A more acceptable condition is one that relates the slope to the motion of the contact line relative to the wavemaker; in this way the dynamic properties of the contact angle can be incorporated. The waves generated by a plane wavemaker in fluid of infinite depth and in fluid of a depth equal to that of the wavemaker are determined. An important reason for including surface tension is that in its absence the transient motion initiated by an impulsive start is singular; when surface tension is included this singularity is removed.

Anisotropic surface waves under a vertical magnetic force

1969 ◽  
Vol 38 (2) ◽  
pp. 353-364 ◽  
Author(s):  
J. A. Shercliff
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Surface Waves ◽  
Gravity Waves ◽  
Magnetic Force ◽  
Conducting Liquid ◽  
Current Field ◽  
Anisotropic Surface ◽  
Magnetoacoustic Waves ◽  
Deep Fluid

A conducting liquid with a free surface is subjected to a vertical magnetic force due to imposed, horizontal, magnetic and current fields in the liquid. Because the current field is modified differently by differently oriented surface waves, the propagation of gravity waves becomes strongly anisotropic. The cases of shallow and deep fluid are explored. The group velocity shows features that are reminiscent of magnetoacoustic waves. The need for stability of the surface sets limits on the magnetic force which may be imposed. The feasibility of experiments is discussed and the effect of ohmic damping and surface tension is found to be relatively unimportant under suitably chosen conditions.

scholarly journals Non-wetting impact of a sphere onto a bath and its application to bouncing droplets

2017 ◽  
Vol 826 ◽  
pp. 97-127 ◽  
Author(s):  
Carlos A. Galeano-Rios ◽  
Paul A. Milewski ◽  
J.-M. Vanden-Broeck
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Incompressible Fluid ◽  
Surface Waves ◽  
Predictive Model ◽  
Smooth Convex ◽  
Fluid Interface ◽  
Kinematic Constraints ◽  
Infinite Depth ◽  
The Impact

We present a fully predictive model for the impact of a smooth, convex and perfectly hydrophobic solid onto the free surface of an incompressible fluid bath of infinite depth in a regime where surface tension is important. During impact, we impose natural kinematic constraints along the portion of the fluid interface that is pressed by the solid. This provides a mechanism for the generation of linear surface waves and simultaneously yields the pressure applied on the impacting masses. The model compares remarkably well with data of the impact of spheres and bouncing droplet experiments, and is completely free of any of impact parametrisation.

Experimental investigation of capillarity effects on surface gravity waves: non-wetting boundary conditions

1993 ◽  
Vol 246 ◽  
pp. 43-66 ◽  
Author(s):  
Bruno Cocciaro ◽  
Sandro Faetti ◽  
Crescenzo Festa
Keyword(s):  
Contact Angle ◽  
Experimental Investigation ◽  
Free Surface ◽  
Boundary Conditions ◽  
Gravity Waves ◽  
Contact Line ◽  
Surface Gravity ◽  
Surface Gravity Waves ◽  
Damping Rate ◽  
Vertical Walls

Damping and eigenfrequencies of surface capillary—gravity waves greatly depend on the boundary conditions. To the best of our knowledge, so far no direct measurement has been made of the dynamic behaviour of the contact angle at the three-phase interface (fluid—vapour—solid walls) in the presence of surface oscillation. Therefore, theoretical models of surface gravity–capillary waves involve ad hoc phenomenological assumptions as far as the behavior of the contact angle is concerned. In this paper we report a systematic experimental investigation of the static and dynamic properties of surface waves in a cylindrical container where the free surface makes a static contact angle $\theta_{\rm c} = 62^{\circ}$ with the vertical walls. The actual boundary condition relating the contact angle to the velocity of the contact line is obtained using a new stroboscopic optical method. The experimental results are compared with the theoretical expressions to be found in the literature. Two different regimes are observed: (i) a low-amplitude regime, where the contact line always remains at rest and the contact angle oscillates during the oscillation of the free surface; (ii) a higher-amplitude regime, where the contact line slides on the vertical walls. The profile, the eigenfrequency and the damping rate of the first non-axisymmetric mode of the surface gravity waves are investigated. The eigenfrequency and damping rate in regime (i) are in satisfactory agreement with the predictions of the Graham-Eagle theory (1983) of pinned-end edge conditions. The eigenfrequency and damping rate in regime (ii) show a strongly nonlinear dependence on the oscillation amplitude of the free surface. All the experimental results concerning regime (ii) can be explained in terms of the Hocking (1987 a) and Miles (1967, 1991) models of capillary damping by introducing an ‘effective’ capillary coefficient $\lambda_{\rm eft}$. This coefficient is directly obtained for the first time in our experiment from dynamic measurements on the contact line. A satisfactory agreement is found to exist between theory and experiment.

Trapping modes in the theory of surface waves

1951 ◽  
Vol 47 (2) ◽  
pp. 347-358 ◽  
Author(s):  
F. Ursell
Keyword(s):  
Free Surface ◽  
Circular Cylinder ◽  
Total Energy ◽  
Surface Waves ◽  
Radiation Condition ◽  
Finite Width ◽  
Energy Trapping ◽  
Sloping Beach ◽  
The Waves

ABSTRACTIt is shown that a mass of fluid bounded by fixed surfaces and by a free surface of infinite extent may be capable of vibrating under gravity in a mode (called a trapping mode) containing finite total energy. Trapping modes appear to be peculiar to the theory of surface waves; it is known that there are no trapping modes in the theory of sound. Two trapping modes are constructed: (1) a mode on a sloping beach in a semi-infinite canal of finite width, (2) a mode near a submerged circular cylinder in an infinite canal of finite width. The existence of trapping modes shows that in general a radiation condition for the waves at infinity is insufficient for uniqueness.

Surface waves generated by a travelling pressure point

1964 ◽  
Vol 282 (1391) ◽  
pp. 547-558 ◽  
Keyword(s):  
Surface Tension ◽  
Water Surface ◽  
Final Section ◽  
Asymptotic Form ◽  
Wave Theory ◽  
Infinite Depth ◽  
Pressure Point ◽  
The Waves ◽  
Working Out ◽  
Effect Of Surface

Kelvin’s classical ship-wave theory (Thomson 1891) gives an asymptotic form for the waves generated by a pressure point moving over a water surface. This paper presents a method of working out the asymptotic expansions which is simpler than those of the various previous theories, although it does not give new or more accurate results. The technique used is due to Lighthill (1958, 1960). The case in which the water has infinite depth is considered in detail, and corresponding results when the depth is finite are deduced. A final section considers the effect of surface tension.

Refraction of gravity waves by weak current gradients

2001 ◽  
Vol 442 ◽  
pp. 157-159 ◽  
Author(s):  
KRISTIAN B. DYSTHE
Keyword(s):  
Surface Waves ◽  
Group Velocity ◽  
Gravity Waves ◽  
Deep Water ◽  
Current Velocity ◽  
Water Surface ◽  
Simple Formula ◽  
Vertical Component ◽  
Weak Current ◽  
The Waves

When deep water surface waves cross an area with variable current, refraction takes place. If the group velocity of the waves is much larger than the current velocity we show that the curvature of a ray, χ, is given by the simple formula χ = ζ/vg. Here ζ is the vertical component of the current vorticity and vg is the group velocity.

scholarly journals Waves’ Numerical Dispersion and Damping due to Discrete Dispersion Relation

2014 ◽  
Author(s):  
Babak Ommani ◽  
Odd M. Faltinsen
Keyword(s):  
Free Surface ◽  
Dispersion Relation ◽  
Surface Waves ◽  
Boundary Integral ◽  
Panel Method ◽  
Numerical Dispersion ◽  
Finite Difference Schemes ◽  
Rankine Panel Method ◽  
Free Surface Waves ◽  
The Waves

In linear Rankine panel method, the discrete linear dispersion relation is solved on a discrete free-surface to capture the free-surface waves generated due to wave-body interactions. Discretization introduces numerical damping and dispersion, which depend on the discretization order and the chosen methods for differentiation in time and space. The numerical properties of a linear Rankine panel method, based on a direct boundary integral formulation, for capturing two and three dimensional free-surface waves were studied. Different discretization orders and differentiation methods were considered, focusing on the linear distribution and finite difference schemes. The possible sources for numerical instabilities were addressed. A series of cases with and without forward speed was selected, and numerical investigations are presented. For the waves in three dimensions, the influence of the panels’ aspect ratio and the waves’ angle were considered. It has been shown that using the cancellation effects of different differentiation schemes the accuracy of the numerical method could be improved.

Nonlinear interactions between a free-surface flow with surface tension and a submerged cylinder

2010 ◽  
Vol 648 ◽  
pp. 485-507 ◽  
Author(s):  
R. M. MOREIRA ◽  
D. H. PEREGRINE
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Gravity Waves ◽  
Classical Method ◽  
Surface Flow ◽  
Boundary Integral ◽  
Steady Solution ◽  
Small Scale ◽  
Fully Nonlinear ◽  
Submerged Cylinder

A submerged cylinder in a uniform stream flow is approximated by a horizontal doublet, following Lamb's classical method. A linear steady solution including surface tension effects is derived, showing that under certain conditions small-scale ripples are formed ahead of the cylinder, while a train of ‘gravity-like’ waves appear downstream. Surface tension effects and a dipole are included in the fully nonlinear unsteady non-periodic boundary-integral solver described by Tanaka et al. (J. Fluid Mech., vol. 185, 1987, pp. 235–248). Nonlinear effects are modelled by considering a flat free surface or the linear stationary solution as an initial condition for the fully nonlinear irrotational flow programme. Long-run computations show that these unsteady flows approach a steady solution for some parameters after waves have radiated away. In other cases the flow does not approach a steady solution. Interesting features at the free surface such as the appearance of ‘parasitic capillaries’ near the crest of gravity waves and the formation of capillary–gravity waves upstream of the cylinder are found.

scholarly journals Small amplitude capillary-gravity waves in a channel of finite depth

1989 ◽  
Vol 31 (2) ◽  
pp. 142-160 ◽  
Author(s):  
M. C. W. Jones
Keyword(s):  
Integral Equation ◽  
Free Surface ◽  
Gravity Waves ◽  
Small Amplitude ◽  
Unsolved Problem ◽  
Equations Of Motion ◽  
Finite Depth ◽  
Wave Problem ◽  
Infinite Depth ◽  
Existence And Multiplicity

Introductory Remarks. Recently a number of studies (Chen & Saffman [2], Jones & Toland [7,11], Hogan [5]) have been made of periodic capillary-gravity waves which form the free surface of an ideal fluid contained in a channel of infinite depth. However, little work appears to have been done on the corresponding problem when the depth is finite. The most significant contributions appear to be those of Reeder & Shinbrot [9], Barakat & Houston [1] and Nayfeh [8] all of whom confined themselves to Wilton ripples (see §1.3). Yet there are sound reasons why such a study should be made. For quite apart from the unsolved problem regarding the type of capillary-gravity waves which may occur at finite depths, the consideration of the finite depth problem may be regarded as a first step in the study of solitary capillary-gravity waves. In this paper, a new integral equation for the infinite depth problem, due to J. F. Toland and the author, is adapted to be of use in tackling the finite depth problem. Using this we obtain results for the exact equations of motion which answer rigorously the questions of existence and multiplicity of small amplitude solutions of the periodic capillary-gravity wave problem of finite depth.

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