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.

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.

scholarly journals The effect of surface tension on free surface flow induced by a point sink in a fluid of finite depth

2017 ◽  
Vol 156 ◽  
pp. 526-533
Author(s):  
G.C. Hocking ◽  
H.H.N. Nguyen ◽  
T.E. Stokes ◽  
L.K. Forbes
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Free Surface Flow ◽  
Finite Depth ◽  
Surface Flow ◽  
Effect Of Surface

Boundary Layer Measurements at an Internal Free Surface in a Partially Filled Horizontal and Rapidly-Rotating Container

1989 ◽  
Vol 111 (4) ◽  
pp. 457-463 ◽  
Author(s):  
T. J. Singler
Keyword(s):  
Boundary Layer ◽  
Free Surface ◽  
Circular Cylinder ◽  
Steady Flow ◽  
Symmetry Axis ◽  
Azimuthal Velocity ◽  
Free Surfaces ◽  
Horizontal Circular Cylinder ◽  
Good Agreement

Steady flow in a partially filled horizontal circular cylinder rotating rapidly about its symmetry axis is investigated experimentally. Radial boundary layer profiles of the azimuthal velocity in the neighborhood of the internal free surface are reported for a range of inverse Froude numbers and for two types of free surfaces. Results indicate good agreement with an existing theory.

scholarly journals Hydrodynamic Forces on a Submerged Circular Cylinder in Two-layer Fluid with an Ice-cover

2021 ◽  
Vol 23 (08) ◽  
pp. 282-294
Author(s):  
Manomita Sahu ◽  
◽  
Dilip Das ◽  
Keyword(s):  
Free Surface ◽  
Circular Cylinder ◽  
Flexural Rigidity ◽  
Lower Layer ◽  
Wave Theory ◽  
Finite Depth ◽  
Ice Cover ◽  
Hydrodynamic Forces ◽  
Wave Number ◽  
Infinite Layer

We consider problems based on linear water wave theory concerning the interaction of wave with horizontal circular cylinder submerged in two-layer ocean consisting of a upper layer of finite depth bounded above by an ice-cover and below by an infinite layer of fluid of greater density, the ice-cover being modelled as an elastic plate of very small thickness. Using the method of multipoles, we formulate the problems of hydrodynamic forces on a submerged cylinder in either the upper or the lower layer. The vertical and horizontal forces on the circular cylinder are obtained and depicted graphically against the wave number for various values of flexural rigidity of ice-cover to show the effect of the presence of ice-cover on these quantities. Also when the flexural rigidity and surface density of the ice-cover are taken to be zero, the ice-cover tends to a free-surface. Then all the forces are the same as in the case of two-layer fluid with free surface.

scholarly journals Thermocapillary effects on a thin viscous rivulet draining steadily down a uniformly heated or cooled slowly varying substrate

2001 ◽  
Vol 441 ◽  
pp. 195-221 ◽  
Author(s):  
D. HOLLAND ◽  
B. R. DUFFY ◽  
S. K. WILSON
Keyword(s):  
Surface Tension ◽  
Finite Depth ◽  
Transverse Flow ◽  
Finite Width ◽  
Lubrication Approximation ◽  
Volume Flux ◽  
Infinite Depth ◽  
Surrounding Atmosphere ◽  
Helical Vortices ◽  
Horizontal Circular Cylinder

We use the lubrication approximation to investigate the steady flow of a thin rivulet of viscous fluid with prescribed volume flux draining down a planar or slowly varying substrate that is either uniformly hotter or uniformly colder than the surrounding atmosphere, when the surface tension of the fluid varies linearly with temperature. Utilizing the (implicit) solution of the governing ordinary differential equation that emerges, we undertake a comprehensive asymptotic and numerical analysis of the flow. In particular it is shown that the variation in surface tension drives a transverse flow that causes the fluid particles to spiral down the rivulet in helical vortices (which are absent in the corresponding isothermal problem). We find that a single continuous rivulet can run from the top to the bottom of a large horizontal circular cylinder provided that the cylinder is either warmer or significantly cooler than the surrounding atmosphere, but if it is only slightly cooler then a continuous rivulet is possible only for a sufficiently small flux (though a rivulet with a discontinuity in the free surface is possible for larger values of the flux). Moreover, near the top of the cylinder the rivulet has finite depth but infinite width, whereas near the bottom of the cylinder it has finite width and infinite depth if the cylinder is heated or slightly cooled, but has infinite width and finite depth if the cylinder is significantly cooled.

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 The effect of surface tension in porous wave maker problems

1998 ◽  
Vol 39 (4) ◽  
pp. 539-556 ◽  
Author(s):  
A. Chakrabarti ◽  
T. Sahoo
Keyword(s):  
Surface Tension ◽  
Water Waves ◽  
Eigenfunction Expansion ◽  
Mixed Type ◽  
Finite Depth ◽  
Time Harmonic ◽  
Surface Water Waves ◽  
Wave Maker ◽  
Porous Walls ◽  
Effect Of Surface

AbstractUsing a mixed-type Fourier transform of a general form in the case of water of infinite depth and the method of eigenfunction expansion in the case of water of finite depth, several boundary-value problems involving the propagation and scattering of time harmonic surface water waves by vertical porous walls have been fully investigated, taking into account the effect of surface tension also. Known results are recovered either directly or as particular cases of the general problems under consideration.

scholarly journals scattering of surface waves by a half immersed circular cylinder in fluid of finite depth

1985 ◽  
Vol 8 (1) ◽  
pp. 113-125
Author(s):  
Birendranath Mandel ◽  
Sudip Kumar Goswami
Keyword(s):  
Integral Equation ◽  
Circular Cylinder ◽  
Surface Waves ◽  
Velocity Potential ◽  
Finite Depth ◽  
Reflection Coefficients ◽  
Infinite Depth ◽  
Transmission And Reflection Coefficients ◽  
Linearized Theory ◽  
Transmission And Reflection

A train of surface waves is normally incident on a half immersed circular cylinder in a fluid of finite depth. Assuming the linearized theory of fluid under gravity an integral equation for the scattered velocity potential on the half immersed surface of the cylinder is obtained. It has not been found possible to solve this in closed form even for infinite depth of fluid. Our purpose is to obtain the asymptotic effect of finite depth “h” on the transmission and reflection coefficients when the depth is large. It is shown that the corrections to be added to the infinite depth results of these coefficients can be expressed as algebraic series in powers ofa/hstarting with(a/h)2where “a” is the radius of the circular cylinder. It is also shown that the coefficients of(a/h)2in these corrections do not vanish identically.

Forcing of a bottom-mounted circular cylinder by steep regular water waves at finite depth

2014 ◽  
Vol 755 ◽  
pp. 1-34 ◽  
Author(s):  
Bo T. Paulsen ◽  
H. Bredmose ◽  
H. B. Bingham ◽  
N. G. Jacobsen
Keyword(s):  
Free Surface ◽  
Circular Cylinder ◽  
Water Waves ◽  
Finite Depth ◽  
Load Cycle ◽  
Harmonic Force ◽  
Third Harmonic ◽  
The Third ◽  
Nonlinear Motion ◽  
Secondary Load

AbstractForcing by steep regular water waves on a vertical circular cylinder at finite depth was investigated numerically by solving the two-phase incompressible Navier–Stokes equations. Consistently with potential flow theory, boundary layer effects were neglected at the sea bed and at the cylinder surface, but the strong nonlinear motion of the free surface was included. The numerical model was verified and validated by grid convergence and by comparison to relevant experimental measurements. First-order convergence towards an analytical solution was demonstrated and an excellent agreement with the experimental data was found. Time-domain computations of the normalized inline force history on the cylinder were analysed as a function of dimensionless wave height, water depth and wavelength. Here the dependence on depth was weak, while an increase in wavelength or wave height both lead to the formation of secondary load cycles. Special attention was paid to this secondary load cycle and the flow features that cause it. By visual observation and a simplified analytical model it was shown that the secondary load cycle was caused by the strong nonlinear motion of the free surface which drives a return flow at the back of the cylinder following the passage of the wave crest. The numerical computations were further analysed in the frequency domain. For a representative example, the secondary load cycle was found to be associated with frequencies above the fifth- and sixth-harmonic force component. For the third-harmonic force, a good agreement with the perturbation theories of Faltinsen, Newman & Vinje (J. Fluid Mech., vol. 289, 1995, pp. 179–198) and Malenica & Molin (J. Fluid Mech., vol. 302, 1995, pp. 203–229) was found. It was shown that the third-harmonic forces were estimated well by a Morison force formulation in deep water but start to deviate at decreasing depth.

Sign in / Sign up

Export Citation Format

Share Document