Relaxation of capillary-gravity waves due to contact line nonlinearity: A projection method

Alessandro Bongarzone; Francesco Viola; François Gallaire

doi:10.1063/5.0055898

Capillary–gravity waves produced by a wavemaker

Journal of Fluid Mechanics ◽

10.1017/s0022112091001726 ◽

1991 ◽

Vol 224 ◽

pp. 217-226 ◽

Cited By ~ 14

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.

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Interaction of flexural-gravity waves in ice cover with vertical walls

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.2017.0347 ◽

2018 ◽

Vol 376 (2129) ◽

pp. 20170347 ◽

Cited By ~ 5

Author(s):

A. A. Korobkin ◽

S. Malenica ◽

T. Khabakhpasheva

Keyword(s):

Boundary Conditions ◽

Gravity Waves ◽

Contact Line ◽

Three Dimensional ◽

Ice Cover ◽

Flexural Gravity Waves ◽

Vertical Walls ◽

Vertical Cylinders ◽

Rigid Walls ◽

Ice Phenomena

Diffraction of flexural-gravity waves in an ice cover by a bottom mounted structure with vertical walls is studied. The problem is solved by using the so-called vertical modes corresponding to the roots of the dispersion relation for flexural-gravity waves. These modes reduce the original three-dimensional problem to a set of two-dimensional diffraction problems with non-homogeneous boundary conditions on the rigid walls. Two unknown functions presenting in the boundary conditions for each mode are determined using the conditions at the contact line between the ice cover and the vertical walls. The clamped conditions at the contact line, where the ice cover is frozen to the wall, are considered in this study. The solution of the problem is obtained for a single vertical circular cylinder frozen in the ice cover. A general approach to the problem for vertical cylinders of any shapes is presented. The diffraction problems with vertical walls extended to infinity are discussed. This article is part of the theme issue ‘Modelling of sea-ice phenomena’.

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

Journal of Fluid Mechanics ◽

10.1017/s0022112093000035 ◽

1993 ◽

Vol 246 ◽

pp. 43-66 ◽

Cited By ~ 27

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.

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