scholarly journals Generation of Surface Waves Due to Initial Axisymmetric Surface Disturbance in Water with a Porous Bottom

2019 ◽  
Vol 24 (3) ◽  
pp. 625-644 ◽  
Author(s):  
P. Kundu ◽  
B.N. Mandal
Keyword(s):  
Free Surface ◽  
Asymptotic Form ◽  
Velocity Potential ◽  
Hankel Transform ◽  
Initial Surface ◽  
Initial Value ◽  
Poisson Problem ◽  
Different Types ◽  
Surface Disturbance ◽  
Infinite Integral

Abstract A two-dimensional Cauchy Poisson problem for water with a porous bottom generated by an axisymmetric initial surface disturbance is investigated here. The problem is formulated as an initial value problem for the velocity potential describing the motion in the fluid. The Laplace and Hankel transform techniques have been used in the mathematical analysis to obtain the form of the free surface in terms of a multiple infinite integral. This integral is then evaluated asymptotically by the method of stationary phase. The asymptotic form of the free surface is depicted graphically in a number of figures for different values of the porosity parameter and for different types of initial disturbances.

scholarly journals The cauchy-poisson waves in an inviscid rotating stratified liquid

1990 ◽  
Vol 3 (1) ◽  
pp. 57-64
Author(s):  
Lokenath Debnath ◽  
Uma B. Guha ◽  
Manjusri Basu
Keyword(s):  
Free Surface ◽  
Gravity Waves ◽  
Large Time ◽  
Boussinesq Approximation ◽  
Free Surface Flows ◽  
Phase Method ◽  
Stationary Phase Method ◽  
Initial Value ◽  
Surface Disturbance ◽  
Stratified Liquid

Based upon the Boussinesq approximation, an initial value investigation is made of the axisymmetric free surface flows generated in an inviscid rotating stratified liquid of infinite depth by the prescribed free surface disturbance. The asymptotic analysis of the integral solution is carried out by the stationary phase method to describe the solution for large time and large distance from the source of the disturbance. The asymptotic solution is found to consist of the classical free surface gravity waves and the internal-inertial waves.

scholarly journals Water waves generated by disturbances at an ice cover

2005 ◽  
Vol 2005 (5) ◽  
pp. 737-746 ◽  
Author(s):  
Paramita Maiti ◽  
B. N. Mandal
Keyword(s):  
Water Waves ◽  
Velocity Potential ◽  
Ice Cover ◽  
Unsteady Motion ◽  
Initial Disturbance ◽  
Thin Elastic Plate ◽  
Initial Value ◽  
Long Time ◽  
Infinite Integral ◽  
Special Case

This paper is concerned with two-dimensional unsteady motion of water waves generated by an initial disturbance created at an ice sheet covering the water. The ice cover is modeled as a thin elastic plate. Using linear theory, the problem is formulated as an initial value problem for the velocity potential describing the motion in the liquid. In the mathematical analysis, the Laplace and Fourier transform techniques have been utilized to obtain the depression of the ice-covered surface in the form of an infinite integral. For the special case of initial disturbance concentrated at the origin, taken on the ice cover, this integral is evaluated asymptotically by the method of a stationary phase for a long time and large distance from the origin. The form of the ice-covered surface is graphically depicted for two types of initial disturbances.

Nonlinear instability of liquid jets with thermocapillarity

1995 ◽  
Vol 283 ◽  
pp. 97-123 ◽  
Author(s):  
F. Mashayek ◽  
N. Ashgriz
Keyword(s):  
Ambient Temperature ◽  
Liquid Jets ◽  
Stable Configuration ◽  
Initial Surface ◽  
Breakup Mechanism ◽  
Capillary Flows ◽  
First Case ◽  
Satellite Drops ◽  
Thermal Disturbance ◽  
Surface Disturbance

The breakup mechanism of a capillary jet with thermocapillarity is investigated. Effects of the heat transfer from the liquid to the surrounding ambient, the liquid thermal conductivity, and the temperature-dependent surface tension coefficient on the jet instability and the formation of satellite drops are considered. Two different disturbances are imposed on the jet. In the first case, the jet is exposed to a spatially periodic ambient temperature. In addition to the thermal boundary condition, an initial surface disturbance with the same wavenumber as the thermal disturbance is also imposed on the jet. Both in-phase and out-of-phase thermal disturbances with respect to surface disturbances are considered. For the in-phase thermal disturbances, a parameter set is obtained at which capillary and thermocapillary effects can cancel each other and the jet attains a stable configuration. No such parameter set can be obtained when the thermocapillary flows are in the same direction as the capillary flows, as in the out-of-phase thermal disturbances. In the second case, only an initial thermal disturbance is imposed on the surface of the liquid while the ambient temperature is kept spatially and temporally uniform.

A METHOD FOR THE DIRECT INTERPRETATION OF ELECTRICAL SOUNDINGS MADE OVER A FAULT OR DIKE

Geophysics ◽  
1973 ◽  
Vol 38 (4) ◽  
pp. 762-770 ◽  
Author(s):  
Terry Lee ◽  
Ronald Green
Keyword(s):  
Bessel Functions ◽  
Direct Analysis ◽  
Hankel Transform ◽  
Approximation Technique ◽  
Polarization Data ◽  
Resistivity Data ◽  
Vertical Fault ◽  
Direct Interpretation ◽  
Electrical Soundings ◽  
Infinite Integral

The potential function for a point electrode in the vicinity of a vertical fault or dike may be expressed as an infinite integral involving Bessel functions. Beginning with such an expression, two methods are presented for the direct analysis of resistivity data measured both normal and parallel to dikes or faults. The first method is based on the asymptotic expansion of the Hankel transform of the field data and is suitable for surveys done parallel to the strike of the dike or fault. The second method is based on a successive approximation technique which starts from an initial approximate solution and iterates until a solution with prescribed accuracy is found. Both methods are suitable for programming on a digital computer and some illustrative numerical results are presented. These examples show the limitations of the methods. In addition, the application of resistivity data to the interpretation of induced‐polarization data is pointed out.

scholarly journals LISMA_HDS language for modeling heterogeneous dynamic systems

2021 ◽  
pp. 103-122
Author(s):  
Evgeny Popov ◽  
◽  
Yury Shornikov ◽  
Keyword(s):  
Dynamic Systems ◽  
Initial Value Problems ◽  
Method Of Lines ◽  
System Of Equations ◽  
Modeling Languages ◽  
Cauchy Problems ◽  
Systems Of Equations ◽  
Initial Value ◽  
Algebraic Systems ◽  
Different Types

Heterogeneous dynamic systems (HDS) simultaneously describe processes of different physical nature. Systems of this kind are typical for numerous applications. HDSs are characterized by the following features. They are often multimode or hybrid systems. In general, their modes are defined as initial value problems (Cauchy problems) for implicit differential-algebraic systems of equations. Due to the presence of heterogeneous dynamic components or processes evolving in both time and space, the dimension of the complete system of equations may be pretty high. In some cases, the system of equations has an internal structure, for instance, the differential-algebraic system of equations approximating a partial differential equation by the method of lines. An original huge system of equations can then be algorithmically rewritten in a compact form. Moreover, heterogeneous hybrid dynamical systems can generate events of qualitatively different types. Therefore one has to use different numerical event detection algorithms. Nowadays, HDSs are modeled and simulated in computer environments. The modeling languages widely used by engineers do not allow them to fully specify all the properties of the systems of this class. For instance, they do not include event typing constructs. That is why a declarative general-purpose modeling language named LISMA_HDS has been developed for the computer-aided modeling and ISMA simulation environment. The language takes into account all of the characteristic features of HDSs. It includes constructs for plain or algorithmic declaration of model constants, initial value problems for explicit differential-algebraic systems of equations, and initial guesses for variables. It also allows researchers to define explicit time events, modes and transitions between them upon the occurrence of events of different types, to use macros and implement event control. LISMA_HDS is defined by a generative grammar in an extended Backus-Naur form and semantic constraints. It is proved that the grammar belongs to the LL(2) subclass of context-free grammars.

scholarly journals On generation and propagation of tsunamis in a shallow running ocean

1978 ◽  
Vol 1 (3) ◽  
pp. 373-390
Author(s):  
Lokenath Debnath ◽  
Uma Basu
Keyword(s):  
Free Surface ◽  
Three Dimensional ◽  
Relative Magnitude ◽  
Ocean Floor ◽  
Surface Elevation ◽  
Free Surface Elevation ◽  
Surface Disturbance ◽  
Fourier And Laplace Transforms ◽  
The Given ◽  
Integral Solutions

A theory is presented of the generation and propagation of the two and the three dimensional tsunamis in a shallow running ocean due to the action of an arbitrary ocean floor or ocean surface disturbance. Integral solutions for both two and three dimensional problems are obtained by using the generalized Fourier and Laplace transforms. An asymptotic analysis is carried out for the investigation of the principal features of the free surface elevation. It is found that the propagation of the tsunamis depends on the relative magnitude of the given speed of the running ocean and the wave speed of the shallow ocean. When the speed of the running ocean is less than the speed of the shallow ocean wave, both the two and the three dimensional free surface elevation represent the generation and propagation of surface waves which decay asymptotically ast−12for the two dimensional case and ast−1for the three dimensional tsunamis. Several important features of the solution are discussed in some detail. As an application of the general theory, some physically realistic ocean floor disturbances are included in this paper.

On Line Distributions of Kelvin Sources

1964 ◽  
Vol 8 (04) ◽  
pp. 45-52
Author(s):  
E. O. Tuck
Keyword(s):  
Free Surface ◽  
Physical Properties ◽  
Velocity Potential ◽  
Fourier Transforms ◽  
Point Sources ◽  
Straight Line ◽  
On Line ◽  
New Form ◽  
Line Of Singularities

The velocity potential for the flow due to point sources distributed arbitrarily along a straight line near to or at a linearized gravitational free surface is obtained in a new form by use of Fourier transforms. Such a method of representing the potential facilitates the determination of its behavior near to the line of singularities; this behavior is derived formally and its physical properties discussed. A brief illustration is given of a method of using this result in o theory for the motion of a slender ship.

scholarly journals Study on liquid sloshing characteristics of a swaying rectangular tank with a rolling baffle

2019 ◽  
Vol 119 (1) ◽  
pp. 23-41 ◽  
Author(s):  
Jing-Han Wang ◽  
Shi-Li Sun
Keyword(s):  
Free Surface ◽  
Present Method ◽  
Velocity Potential ◽  
Solution Procedure ◽  
Liquid Sloshing ◽  
Published Data ◽  
Free Surface Elevation ◽  
Separate Variable ◽  
Rectangular Tank ◽  
Vertical Baffle

Abstract This study addresses the sloshing characteristics of a liquid contained in a tank with a vertical baffle mounted at the bottom of the tank. Liquid sloshing characteristics are studied through an analytical solution procedure based on the linear velocity potential theory. The tank is forced to sway horizontally and periodically, while the baffle is fixed to the tank or rolling around a hinged point. The rectangular tank flow field is divided into a few sub-domains. The potentials are solved by a separate variable method, and the boundary conditions and matching requirements between adjacent sub-domains are used to determine the sole solution. The free surface elevations with no baffle or a low fixed baffle are compared with those in published data, and the correctness and reliability of the present method are verified. Then the baffle is forced to rotate around the bottom-mounted point. It is found that the baffle’s motion, including the magnitude and the phase together, can be adjusted to suppress the free surface elevation, and even the sloshing wave can be almost eliminated.

scholarly journals SURFACE TENSION OF SERUM

1922 ◽  
Vol 35 (5) ◽  
pp. 707-735 ◽  
Author(s):  
P. Lecomte du Noüy
Keyword(s):  
Surface Tension ◽  
Surface Layer ◽  
Free Surface ◽  
Organic Compounds ◽  
Sodium Oleate ◽  
Mean Value ◽  
Physiological Solution ◽  
Optimum Concentration ◽  
Initial Value ◽  
Ring Method

The application of the ring method to the measurement of solutions of serum and of certain organic compounds has brought forth new facts, mainly the decrease of the surface tension of such solutions in function of time. 1. In serum diluted at such a low concentration as 1:1,000,000 in NaCl, physiological solution, the surface tension of the liquid is lowered by 3 or 4 dynes in 2 hours; at 1:100,000, by about 11 dynes (mean value) in 2 hours, and by 20 dynes in 24 hours; at 1:10,000 by about 13 to 16 dynes in 2 hours. 2. The drop in surface tension is much more rapid in the first 30 minutes and follows generally the law of adsorption in the surface layer in function of the time. 3. Stirring or shaking after the drop causes the surface tension to rise, but generally below its initial value. 4. The same phenomena occur when using sodium oleate, glycocholate, or saponin instead of serum. 5. For every serum, as well as for the substances mentioned above a maximum drop occurs in certain conditions at a given optimum concentration. 6. Not only are the substances which lower the surface tension adsorbed in the surface layer, in the case in which they are present with crystalloids, but also the crystalloids themselves, in contradiction to Gibbs' statement. This is plainly shown by the evaporation of such solutions in watch-glasses which, instead of a small group of sharp, large, well defined crystals at the bottom, leaves a white disc almost as large as the initial free surface itself, due to the liberation of the salt by the surface layer as it crawls down the concave surface of the glass. 7. In these conditions, solutions of serum are characterized by a very peculiar periodic and concentric distribution of the crystals, at a concentration of 1:100 only. The same ring-like aspect is observed with sodium oleate, glycocholate, and saponin, but not at the same concentration, as was to be expected, since serum is a solution in itself.

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