scholarly journals Gravity effects in the water entry problem

1965 ◽  
Vol 5 (4) ◽  
pp. 427-433 ◽  
Author(s):  
A. G. Mackie
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Boundary Conditions ◽  
Formal Solution ◽  
Water Entry ◽  
Initial State ◽  
Non Linear ◽  
Gravity Effects ◽  
Linearized Theory ◽  
Thin Wedge

The following paper is a sequel to the author's earlier paper [2]. In that paper some general results were obtained which described the motion of a fluid with a free surface subsequent to a given initial state and prescribed boundary conditions of a certain type. The analysis was based on a linearized theory but gravity effects were included. Viscosity, compressibility and surface tension effects were neglected. Among the problems treated was that of the normal symmetric entry of a thin wedge into water at rest. This Water entry problem has attracted a considerable amount of attention since the pioneer paper by Wagner [5]. Both linear and non-linear approximations have been used but all papers apart from [2] neglect gravity on the assumption that in the early stages of the penetration this is unimportant. One of the objects of [2] was to determine the solution with the gravity terms retained. A formal solution was obtained but no attempt was made to analyse this quantitatively. In the present paper we examine the extent of this effect in some detail. It will be of help to the reader to have some familiarity with the first three or four sections of [2] but in order to make the present paper self-contained we shall first reintroduce the notation used there and quote the necessary results from that paper without proof.

scholarly journals Gravity effects in the initial value problems of water wave theory

1968 ◽  
Vol 8 (2) ◽  
pp. 269-274
Author(s):  
A. H. Low
Keyword(s):  
Free Surface ◽  
Power Series ◽  
Wave Theory ◽  
Gravitational Acceleration ◽  
Horizontal Distance ◽  
Initial Value ◽  
Initial State ◽  
Gravity Effects ◽  
The Times ◽  
Thin Wedge

The theory described in this paper is directed towards obtaining a general expression for the development of the free surface of a fluid, subsequent to a given initial state and prescribed boundary conditions, as a power series in g, the gravitational acceleration. In an earlier paper [4], a result, applicable to the particular case of the entry of a thin wedge into an incompressible fluid, was obtained and gave the shape of the free surface as such a power series. This series was valid for values of the ratio ut/x < 1, where u, was the (constant) velocity of entyr of the wedge; x the horizontal distance from the vertex of the wedge; and t the times elapsed after entry. This particular problem was first investigated by Mackie [6] who derived an asymptotic solution.

EFFECTS OF SURFACE TENSION ON TRAPPED MODES IN A TWO-LAYER FLUID

2015 ◽  
Vol 57 (2) ◽  
pp. 189-203 ◽  
Author(s):  
S. SAHA ◽  
S. N. BORA
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Circular Cylinder ◽  
Boundary Value Problems ◽  
Finite Depth ◽  
Trapped Modes ◽  
Trapped Waves ◽  
Linearized Theory ◽  
Horizontal Circular Cylinder ◽  
Effect Of Surface

We consider a two-layer fluid of finite depth with a free surface and, in particular, the surface tension at the free surface and the interface. The usual assumptions of a linearized theory are considered. The objective of this work is to analyse the effect of surface tension on trapped modes, when a horizontal circular cylinder is submerged in either of the layers of a two-layer fluid. By setting up boundary value problems for both of the layers, we find the frequencies for which trapped waves exist. Then, we numerically analyse the effect of variation of surface tension parameters on the trapped modes, and conclude that realistic changes in surface tension do not have a significant effect on the frequencies of these.

scholarly journals Splash jet generated by collision of two liquid wedges

2013 ◽  
Vol 737 ◽  
pp. 132-145 ◽  
Author(s):  
Y. A. Semenov ◽  
G. X. Wu ◽  
J. M. Oliver
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Hodograph Method ◽  
Pressure Distributions ◽  
Wide Range ◽  
Self Similar Solution ◽  
Gravity Effects ◽  
Self Similar ◽  
The Impact ◽  
Analytical Expressions

AbstractA complete nonlinear self-similar solution that characterizes the impact of two liquid wedges symmetric about the velocity direction is obtained assuming the liquid to be ideal and incompressible, with negligible surface tension and gravity effects. Employing the integral hodograph method, analytical expressions for the complex potential and for its derivatives are derived. The boundary value problem is reduced to two integro-differential equations in terms of the velocity modulus and angle to the free surface. Numerical results are presented in a wide range of wedge angles for the free surface shapes, streamline patterns, and pressure distributions. It is found that the splash jet may cause secondary impacts. The regions with and without secondary impacts in the plane of the wedge angles are determined.

scholarly journals Free surface flows over a successive obstacles with surface tension and gravity effects

2019 ◽  
Vol 4 (2) ◽  
pp. 316-326 ◽  
Author(s):  
Abdelkader Laiadi ◽  
◽  
Abdelkrim Merzougui ◽  
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Free Surface Flows ◽  
Surface Flows ◽  
Gravity Effects

On the Effect of Non-Linear Boundary Conditions on the Wave Disturbance and Hydrodynamic Forces of Underwater Vehicles Travelling Near the Free-Surface

2020 ◽  
Author(s):  
William Lambert ◽  
Stefano Brizzolara
Keyword(s):  
Free Surface ◽  
Analytical Solution ◽  
Boundary Conditions ◽  
Energy Content ◽  
Wave Spectrum ◽  
Hydrodynamic Forces ◽  
Wave Resistance ◽  
Wave Disturbance ◽  
Surface Boundary ◽  
Non Linear

Abstract This study compares the effect of non-linear free-surface boundary conditions for a high-order non-linear free-surface Rankine-source boundary element method on wave disturbance and hydrodynamic forces acting on an underwater vehicle travelling near a calm free-surface. In particular, simulations for a steady nonaxisymmetric prolate spheroid using different basis flows and linearization techniques were compared to an analytical method achieved by Chatjigeorgiou using a multipole expansion of Green’s functions. It appears that at low Froude numbers, the basis flow used in the formulation contributes significantly to differences in the steady solutions for wave resistance and pitch, whereas for higher Froude numbers the linearization technique becomes a more defining feature. Upon observation of the analytical solution for wave resistance, one can see that it was formed under a Neumann-Kelvin formulation and this is supported by the Neumann-Kelvin simulations converging well to the analytical solution. Further comparisons were made using a wave directional energy spectrum gathered from transverse wave cuts of the free wave pattern. The spectral analysis allows for a higher level of comparison between all of the different cases, establishing a direct relation between the change in wave resistance and the energy content variation of the particular wave spectrum components.

scholarly journals Note on Ripples in a Viscous Liquid

1891 ◽  
Vol 17 ◽  
pp. 110-115 ◽  
Author(s):  
Tait
Keyword(s):  
Surface Tension ◽  
Surface Layer ◽  
Free Surface ◽  
Boundary Conditions ◽  
Viscous Liquid ◽  
Tuning Fork ◽  
Cartesian Coordinates ◽  
A Current ◽  
Made In

The following investigation was made in consequence of certain peculiarities in the earlier results of some recent measurements of ripples by Prof. Michie Smith, in my Laboratory, which will, I hope, soon be communicated to the Society. These seemed to suggest that viscosity might have some influence on the results, as might also the film of oxide, &c, which soon gathers on a free surface of mercury. I therefore took account of the density, as well as of possible rigidity, of this surface layer, in addition to the surface tension which, was the object of Prof. Smith's work. The later part of the paper, where Cartesian coordinates are employed, runs somewhat on the lines of an analogous investigation in Basset's Hydrodynamics. My original object, however, was different from his, as I sought the effects of viscosity on waves steadily maintained by means of a tuning-fork used as a current interruptor; not on waves once started and then left to themselves. Besides obtaining his boundary conditions in a singular manner, I think that in his § 521 Mr Basset has made an erroneous investigation of the effects of very great viscosity.

The effect of surface tension on the waves produced by a heaving circular cylinder

1968 ◽  
Vol 64 (3) ◽  
pp. 833-847 ◽  
Author(s):  
D. V. Evans
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Circular Cylinder ◽  
Water Waves ◽  
Wave Amplitude ◽  
Velocity Potential ◽  
Linearized Theory ◽  
The Waves ◽  
Energy Argument ◽  
Effect Of Surface

AbstractIn this paper the effect of surface tension on water waves is considered. The usual assumptions of the linearized theory are made. A uniqueness theorem is derived for the waves at infinity for a general class of bounded two-dimensional obstacles in a free surface by means of an energy argument. It is shown how the wave amplitude at infinity depends on the prescribed angle at which the free surface meets the normal to the obstacle. The particular case of a heaving half-immersed circular cylinder is considered in detail, and an expression obtained for the velocity potential in terms of a convergent infinite series, the coefficients of which may be computed.

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