Wave source potentials for two superposed fluids, each of finite depth

1986 ◽  
Vol 100 (3) ◽  
pp. 595-599 ◽  
Author(s):  
S. E. Kassem
Keyword(s):  
Surface Tension ◽  
Internal Waves ◽  
Finite Depth ◽  
Constant Depth ◽  
Wave Source ◽  
Two Fluids ◽  
Different Types ◽  
Superposed Fluids ◽  
Finite Constant

AbstractProblems dealing with the generation of internal waves at the surface separating two fluids involves the consideration of different types of singularities in one of the two fluids. In this paper the velocity potentials describing line sources are obtained for the case when each fluid is of finite constant depth, neglecting effects of surface tension at the surface of separation.

Multipole expansions for two superposed fluids, each of finite depth

1982 ◽  
Vol 91 (2) ◽  
pp. 323-329 ◽  
Author(s):  
S. E. Kassem
Keyword(s):  
Surface Tension ◽  
Internal Waves ◽  
Finite Depth ◽  
Constant Depth ◽  
Two Fluids ◽  
Different Types ◽  
Multipole Expansions ◽  
Superposed Fluids ◽  
Finite Constant

AbstractProblems dealing with the generation of internal waves at the surface separating two fluids involves the consideration of different types of singularities in one of the two fluids. In this paper the velocity potentials describing line and point multipoles are obtained for the case when each fluid is of finite constant depth, neglecting effects of surface tension at the surface of separation.

scholarly journals Basic singularities in the theory of internal waves with surface tension

1986 ◽  
Vol 9 (1) ◽  
pp. 145-159
Author(s):  
M. A. Gorgui ◽  
M. S. Faltas
Keyword(s):  
Surface Tension ◽  
Internal Waves ◽  
Constant Depth ◽  
Two Fluids ◽  
Interface Wave ◽  
Different Types ◽  
Superposed Fluids ◽  
Wave Problems ◽  
Effect Of Surface ◽  
Finite Constant

The study of linearized interface wave problems for two superposed fluids often involves the consideration of different types of singularities in one of the two fluids. In this paper the line and point singularities are investigated for the case when each fluid is of finite constant depth. The effect of surface tension at the surface of separation is included.

The long-wave behaviour of the virtual mass in water of finite depth

1980 ◽  
Vol 372 (1748) ◽  
pp. 65-91 ◽  
Keyword(s):  
Circular Cylinder ◽  
Finite Depth ◽  
Virtual Mass ◽  
Constant Depth ◽  
Long Wave ◽  
Wave Region ◽  
Zero Frequency ◽  
Finite Constant

A half-immersed circular cylinder of radius a undergoes a periodic heaving motion on water of finite constant depth h . The behaviour of the virtual mass is considered in the long-wave region where existing computations are in disagreement. For finite depth Ursell has recently confirmed analytically that the virtual mass remains finite (and is thus a function of a/h ) in the limit Ka = Kh = 0, a/h fixed. His long-wave investigation is now extended by a study of the gradient /d( virtual mass)/d(Aa) for small Ka . It is shown that this gradient is positive in the limit of zero frequency when a/h is sufficiently small, and that in this case the virtual mass has a maximum near Kh = 1. An argument is also given which suggests that this maximum may be expected for bodies of more general sections.

scholarly journals On waves in the presence of vertical porous boundaries

1997 ◽  
Vol 39 (1) ◽  
pp. 104-120 ◽  
Author(s):  
P. F. Rhodes-Robinson
Keyword(s):  
Surface Tension ◽  
Finite Depth ◽  
Wave Source ◽  
Lack Of Information ◽  
Infinite Extent ◽  
Wave Maker ◽  
Incident Waves ◽  
Standard Techniques ◽  
Porous Boundaries ◽  
Effect Of Surface

AbstractIn this paper various wave motions in water of infinite depth containing vertical porous boundaries are determined when the water is of infinite extent on one or both sides. Initially surface tension is ignored and simple solutions for incident waves are obtained before going on to harder wave source and wave-maker solutions. A reduction method is developed to obtain solutions for two-sided boundaries from those for one-sided, which are obtained by standard techniques. The effect of surface tension that precludes simple solutions is also considered, although a present lack of information on dynamical edge behaviour for porous boundaries means that the formal mathematical solutions must be left in terms of arbitrary edge constants. In conclusion, some solutions are noted for finite depth.

On the forced surface waves due to a vertical wave-maker in the presence of surface tension

1971 ◽  
Vol 70 (2) ◽  
pp. 323-337 ◽  
Author(s):  
P. F. Rhodes-Robinson
Keyword(s):  
Surface Tension ◽  
Surface Waves ◽  
Wave Motion ◽  
Velocity Potential ◽  
Vertical Plane ◽  
Finite Depth ◽  
Cylindrical Wave ◽  
Constant Depth ◽  
Classical Wave ◽  
Wave Maker

AbstractThe classical wave-maker problem to determine the forced two-dimensional wave motion with outgoing surface waves at infinity generated by a harmonically oscillating vertical plane wave-maker immersed in water was solved long ago by Sir Thomas Havelock. In this paper we reinvestigate the problem, making allowance for the presence of surface tension which was excluded before, and obtain a solution of the boundary-value problem for the velocity potential which is made unique by prescribing the free surface slope at the wave-maker. The cases of both infinite and finite constant depth are treated, and it is essential to employ a method which is new to this problem since the theory of Havelock cannot be extended in the latter case of finite depth. The solution of the corresponding problem concerning the axisymmetric wave motion due to a vertical cylindrical wave-maker is deduced in conclusion.

scholarly journals Fundamental singularities in the theory of water waves with surface tension

1970 ◽  
Vol 2 (3) ◽  
pp. 317-333 ◽  
Author(s):  
P. F. Rhodes-Robinson
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Water Waves ◽  
Potential Functions ◽  
Fundamental Wave ◽  
Harmonic Waves ◽  
Constant Depth ◽  
Wave Source ◽  
Time Harmonic ◽  
Effect Of Surface

In this paper the forms are obtained for the harmonic potential functions describing the fundamental wave-source and multipole singularities which pertain to the study of infinitesimal time-harmonic waves on the free surface of water when the effect of surface tension is included. Line and point singularities are considered for both the cases of infinite and finite constant depth of water. The method used is an extension of that which has been used to obtain these potentials in the absence of surface tension.

scholarly journals Interactions between an Associative Amphiphilic Block Polyelectrolyte and Surfactants in Water: Effect of Charge Type on Solution Properties and Aggregation

Polymers ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 1729
Author(s):  
Patrizio Raffa
Keyword(s):  
Surface Tension ◽  
Self Assembly ◽  
Interaction Model ◽  
Industrial Applications ◽  
Molecular Organization ◽  
Different Types ◽  
Solution Rheology ◽  
Interesting Class ◽  
First Time

The study of interactions between polyelectrolytes (PE) and surfactants is of great interest for both fundamental and applied research. These mixtures can represent, for example, models of self-assembly and molecular organization in biological systems, but they are also relevant in industrial applications. Amphiphilic block polyelectrolytes represent an interesting class of PE, but their interactions with surfactants have not been extensively explored so far, most studies being restricted to non-associating PE. In this work, interactions between an anionic amphiphilic triblock polyelectrolyte and different types of surfactants bearing respectively negative, positive and no charge, are investigated via surface tension and solution rheology measurements for the first time. It is evidenced that the surfactants have different effects on viscosity and surface tension, depending on their charge type. Micellization of the surfactant is affected by the presence of the polymer in all cases; shear viscosity of polymer solutions decreases in presence of the same charge or nonionic surfactants, while the opposite charge surfactant causes precipitation. This study highlights the importance of the charge type, and the role of the associating hydrophobic block in the PE structure, on the solution behavior of the mixtures. Moreover, a possible interaction model is proposed, based on the obtained data.

scholarly journals Physical Acceptability of the Renyi, Tsallis and Sharma-Mittal Holographic Dark Energy Models in the f(T,B) Gravity under Hubble’s Cutoff

Universe ◽  
2021 ◽  
Vol 7 (3) ◽  
pp. 67
Author(s):  
Salim Harun Shekh ◽  
Pedro H. R. S. Moraes ◽  
Pradyumn Kumar Sahoo
Keyword(s):  
Dark Energy ◽  
Holographic Dark Energy ◽  
Cosmological Parameters ◽  
Field Equations ◽  
Eos Parameter ◽  
Two Fluids ◽  
Gravitational Field Equations ◽  
Energy Models ◽  
Different Types ◽  
The Universe

In the present article, we investigate the physical acceptability of the spatially homogeneous and isotropic Friedmann–Lemâitre–Robertson–Walker line element filled with two fluids, with the first being pressureless matter and the second being different types of holographic dark energy. This geometric and material content is considered within the gravitational field equations of the f(T,B) (where T is the torsion scalar and the B is the boundary term) gravity in Hubble’s cut-off. The cosmological parameters, such as the Equation of State (EoS) parameter, during the cosmic evolution, are calculated. The models are stable throughout the universe expansion. The region in which the model is presented is dependent on the real parameter δ of holographic dark energies. For all δ≥4.5, the models vary from ΛCDM era to the quintessence era.

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