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

2018 ◽  
Vol 376 (2129) ◽  
pp. 20170347 ◽  
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’.

scholarly journals Solitary flexural–gravity waves in three dimensions

2018 ◽  
Vol 376 (2129) ◽  
pp. 20170345 ◽  
Author(s):  
Olga Trichtchenko ◽  
Emilian I. Părău ◽  
Jean-Marc Vanden-Broeck ◽  
Paul Milewski
Keyword(s):  
Gravity Waves ◽  
Three Dimensional ◽  
Ice Sheet ◽  
Boundary Integral ◽  
Three Dimensions ◽  
Cosserat Theory ◽  
Theme Issue ◽  
Flexural Gravity Waves ◽  
Forced Waves ◽  
Ice Phenomena

The focus of this work is on three-dimensional nonlinear flexural–gravity waves, propagating at the interface between a fluid and an ice sheet. The ice sheet is modelled using the special Cosserat theory of hyperelastic shells satisfying Kirchhoff's hypothesis, presented in (Plotnikov & Toland. 2011 Phil. Trans. R. Soc. A 369 , 2942–2956 ( doi:10.1098/rsta.2011.0104 )). The fluid is assumed inviscid and incompressible, and the flow irrotational. A numerical method based on boundary integral equation techniques is used to compute solitary waves and forced waves to Euler's equations. This article is part of the theme issue ‘Modelling of sea-ice phenomena’.

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.

Influence of snow cover on the parameters flexural-gravity waves in ice cover

2013 ◽  
Vol 54 (3) ◽  
pp. 458-464 ◽  
Author(s):  
V. M. Kozin ◽  
V. L. Zemlyak ◽  
V. Yu. Vereshchagin
Keyword(s):  
Snow Cover ◽  
Gravity Waves ◽  
Ice Cover ◽  
Flexural Gravity Waves

scholarly journals Bending-gravity waves in the sea with an ice cover from moving disturbances

2021 ◽  
pp. 157-161
Author(s):  
Ж.В. Маленко ◽  
А.А. Ярошенко
Keyword(s):  
Gravitational Waves ◽  
Gravity Waves ◽  
Elastic Waves ◽  
Isotropic Plate ◽  
Pure Water ◽  
Three Dimensional ◽  
Ice Cover ◽  
Ship Waves ◽  
Plate Vibrations ◽  
The Waves

В статье проводятся исследования колебаний плавающего ледяного покрова под действием движущихся возмущений. В основу колебаний плавающего ледяного покрова положены линеаризованные уравнения гидромеханики и линейная классическая теория колебаний пластин. Ледяной покров рассматривается как тонкая упругая изотропная пластинка. Анализируются образующиеся при этом трехмерные изгибно-гравитационные волны. Показано, что при движении источника возмущений со скоростью 0<v<v0 изгибно-гравитационные волны не образуются, а наблюдается статический прогиб. Здесь v0 – минимальное значение фазовой скорости. При скорости движения v0<v<v1 образуется одна система изгибно-гравитационных волн. Эти волны распространяются как впереди, так и за источником возмущений. Волны, бегущие впереди источника, обусловлены упругими и массовыми силами пластинки. Волны, распространяющиеся за источником, имеют характер гравитационной волны для чистой воды. При v1<v<(gH)1/2 образуется три системы волн. Упругие волны распространяются впереди источника. Две другие волны распространяются за источником и носят характер поперечной и продольной корабельных волн. При v>(gH)1/2 образуются впереди источника упругие волны, а за источником продольные корабельные волны. Исследовано влияние скорости перемещения нагрузки на амплитуды образующихся волн. The article studies the fluctuations of the floating ice cover under the action of moving perturbations. The vibrations of the floating ice cover are based on the linearized equations of hydro-mechanics and the linear classical theory of plate vibrations. The ice sheet is considered as a thin elastic isotropic plate. The resulting three-dimensional bending-gravity waves are analyzed. It is shown that when the source of disturbances moves at a speed of 0<v<v0, bending-gravitational waves are not formed, but a static deflection is observed. Here v0is the minimum value of the phase velocity. At the speed of motion v0<v<v1, a single system of bending-gravitational waves is formed. These waves propagate both ahead and behind the source of the disturbances. The waves traveling ahead of the source are caused by the elastic and mass forces of the plate. The waves propagating behind the source have the character of a gravitational wave for pure water. At v1<v<(gH)1/2, three wave systems are formed. Elastic waves propagate ahead of the source. The other two waves propagate behind the source and have the character of transverse and longitudinal ship waves. At v>(gH)1/2, elastic waves are formed in front of the source, and longitudinal ship waves are formed behind the source. The influence of the load displacement velocity on the amplitudes of the generated waves is investigated.

scholarly journals Results of modeling the dependence of the height of flexural-gravity waves in a floating plate with a sealed edge on the inclination of the bottom of the reservoir

2021 ◽  
pp. 47-52
Author(s):  
В.М. Козин
Keyword(s):  
Gravitational Waves ◽  
Gravity Waves ◽  
Large Scale ◽  
Ice Cover ◽  
Bottom Slope ◽  
Floating Plate ◽  
Scale Models ◽  
Flexural Gravity Waves ◽  
Resonant Method

На основании проведенных автором экспериментов по разрушению льда амфибийными судами на воздушной подушке (СВП) резонансным методом при их движении в сторону берега, их крупномасштабных моделей в полевых условиях, а также известных случаев разрушения ледяного покрова движущимися в сторону берега транспортными средствами показана возможность существенного увеличения толщины льда, разрушаемого у его береговой кромки. Приведены данные экспериментов, выполненных в опытовом бассейне на моделирующих ледяной покров упругих пленках, подтверждающие эти возможности. В работе представлены результаты моделирования зависимости высоты изгибно-гравитационных волн (ИГВ), возбуждаемых в плавающей пластине движущейся в направлении ее заделанной кромки нагрузкой, от угла наклона дна бассейна. Также приведены рекомендации по использованию наклонности дна для повышения эффективности разрушения ледяного покрова (увеличения толщины разрушаемого льда) путем возбуждения резонансных ИГВ. На основании выполненных экспериментов показано, что приближение к берегу ИГВ, возбуждаемых СВП с последующим их выходом на него, может значительно увеличить толщину разрушаемого льда за счет отрыва от берега его кромки. Отмечена возможность увеличения ледоразрушающей способности ИГВ благодаря последующим проходам судна вдоль нее из-за роста деформаций ослабленного таким образом льда, т.е повышения ледоразрушающей способности СВП. Based on the experiments conducted by the author on ice destruction by amphibious hovercraft using the resonant method when they move towards the shore, their large-scale models in the field, as well as known cases of ice cover destruction by vehicles moving towards the shore, the possibility of a significant increase in the thickness of ice destroyed at its coastal edge is shown. The data of experiments performed in the experimental pool on elastic films modeling the ice cover are presented, confirming these possibilities. The paper presents the results of modeling the dependence of the height of Flexural-gravitational waves excited in a floating plate by a load moving in the direction of its embedded edge on the angle of inclination of the pool bottom. Recommendations are also given for using the bottom slope to increase the efficiency of ice cover destruction (increasing the thickness of the destroyed ice) by exciting resonant Flexural-gravitational waves. Based on the performed experiments, it is shown that the approach to the shore of Flexural-gravitational waves excited by hovercraft with their subsequent exit to it can significantly increase the thickness of the destroyed ice due to the separation of its edge from the shore. The possibility of increasing laboratree the ability of the Flexural-gravitational waves during the next passages of the ship along it due to the growth of deformations weakened the ice.

scholarly journals Three Dimensional Flexural-Gravity Waves

2013 ◽  
Vol 131 (2) ◽  
pp. 135-148 ◽  
Author(s):  
P. A. Milewski ◽  
Z. Wang
Keyword(s):  
Gravity Waves ◽  
Three Dimensional ◽  
Flexural Gravity Waves
Sign in / Sign up

Export Citation Format

Share Document