Interfacial solitary waves in a two-fluid medium

by Lloyd R. Walker

Written in English
Published: Pages: 1804 Downloads: 987
Share This

Edition Notes

Statementby Lloyd R. Walker.
Classifications
LC ClassificationsMicrofilm 42309 (Q)
The Physical Object
FormatMicroform
Paginationp. 1796-1804.
Number of Pages1804
ID Numbers
Open LibraryOL2018386M
LC Control Number90950424

This book is a self-contained introduction to the theory of periodic, progressive, permanent waves on the surface of incompressible inviscid fluid. The problem of permanent water-waves has attracted a large number of physicists and mathematicians since Stokes' pioneering papers appeared in and The refraction of internal solitary waves can be due to variations in water depth, nonlinearity, stratification, or shear. This paper addresses the effects of the first two of these effects. Part I of this paper investigated how the amplitude and phase speed of an interfacial solitary wave varied as the wave propagated across a one-dimensional. 1. Introduction [2] Numerous investigations have been conducted to obtain satisfactory theoretical solutions for internal waves in several types of fluid systems having variable bottom geometries. Stokes was the first to develop the theory of internal waves propagating along a boundary between two layers of infinite thickness. Mathematical treatment of the problem is seen in the literature of.   A solitary wave hitting a partially submerged structure. Computational fluid dynamics simulation run with FLOW-3D, developed by Flow Science. For more inform.

  Amazing Solitary Waves: The uniform injection of energy into water can also excite a solitary wave. These are long lived localized disturbances. In this movie you will see examples of . I Fluid Mrch.(). IYJ~. , ~,IJ I’rint~d in Great Rritain On interfacial solitary waves over slowly varying topography By KARL R. HELFRICH, W. K. MELVILLE Ralph M. Parsons I,aboratory, Massachusetts Institute of Technology, Cambridge, MA AND JOHN W. MILES Institute of Geophysics and Planetary Physics, University of California. Considered here are systems of partial differential equations arising in internal wave theory. The systems are asymptotic models describing the two-way propagation of long-crested interfacial waves in the Benjamin-Ono and the Intermediate Long-Wave regimes. Of particular interest will be solitary-wave solutions of these systems. stratification; solitary waves 1 Introduction Global theory of interfacial solitary waves in a two-layer fluid has been developed by Amick & Turner (). Their analytical results predict, in particular, the broadening of solitary waves when the wave speed attains the propagation speed of internal bore. Smooth bore is a steady.

In the case of two-dimensional interfacial deflections, traveling waves of permanent form are constructed and it is shown that solitary waves are possible for a range of physical parameters. All solitary waves are expressed implicitly in terms of incomplete elliptic integrals of the third kind. solitary waves described by (1) is slightly higher. According to Russell’s empirical formula the speed equals q g(h+ k);where kis the height of the peak of the solitary wave above the surface of undisturbed water. As Bullough () has shown, Russell’s approximate speed and the true speed of solitary waves only di er by a term of O(k 2=h). Chen-Yuan, Chen, Cheng-Wu, Chen, I-Fan, Tseng, “Localised mixing due to an interfacial solitary wave breaking on seabed topography in different ridge heights,” Journal of Offshore Mechanics and Arctic Engineering, ASME, Vol. (3), – , August d. The evolution of fluid interfaces in parallel flow in Hele-Shaw cells is studied theoretically and experimentally in the limit of large capillary number. It is shown that such interfaces support wave motion, the amplitude of which for long waves is governed by a set of Korteweg--de Vries and Airy equations.

Interfacial solitary waves in a two-fluid medium by Lloyd R. Walker Download PDF EPUB FB2

The design of a programmed, variable flux wavemaker for efficiently generating interfacial waves is discussed. Solitary waves are generated on the interface between two immiscible liquids with free upper surface; their behavior is generally consistent with that predicted by the Korteweg-de Vries by: Interfacial solitary waves in a two-fluid medium.

The speed difference appears consistent with an interfacial viscous boundary layer. The critical depth ratio separating the elevation and depression modes of the stable gravity solitary wave agrees with prediction in the inviscid limit. The design of a programmed, variable flux wave maker Author: L.

Walker. Interfacial solitary waves in a two-fluid medium: Author(eng) Walker, L. Issue Date: Language: eng: Description: Solitary waves are generated on the interface between two immiscible liquids with free upper surface; their behavior is generally consistent with that predicted by the Korteweg-de Vries equation.

Book Search tips Selecting this option will search all publications across the Scitation platform Selecting this option will search all publications for The role of the free surface on interfacial solitary waves Physics of Flu “ Internal solitary waves in a two Author: G.

la Forgia, G. Sciortino. The results of an experimental investigation dealing with finite-amplitude internal solitary waves in a two-fluid system are presented. Particular attention is paid to characterizing solitons in terms of their shape and amplitude–wavelength scale relationship.

Two cases are considered, viz., a shallow- and a deep-water configuration, in order to study the depth effect upon the propagational characteristics of the by: The oblique interaction of interfacial solitary waves is studied in an inviscid two-layer deep-fluid system.

We first derive the interaction equations correct up to the second order in an amplitude parameter by employing a systematic perturbation method. An experimental study of internal solitary waves in a two-layer liquid. Authors; Authors and affiliations; “Interfacial solitary waves in a two-fluid medium,” Phys.

Interfacial solitary waves in a two-fluid medium book, 16, C. Koop and G. Butler, “An investigation of internal solitary waves in a two-fluid medium,” J. This paper deals with progressing solitary waves at the interface of two superimposed fluids of different densities.

In the case of a two-fluid system bounded above and below by rigid walls, we refer to the wave as guided. If the top wall is absent, that is, the top fluid has its free surface exposed to air, the wave. Steady solitary and generalized solitary waves of a two-fluid problem where the upper layer is under a flexible elastic sheet are considered as a model for internal waves under an ice-covered ocean.

The fluid consists of two layers of constant densities, separated by an interface. Fully nonlinear internal waves in a two-fluid system In particular, for a solitary wave of given amplitude, the new models show that the characteristic wavelength is larger and our equations track only one (interfacial) free surface.

Our techniques would work for. The linear stability of interfacial solitary waves in a two-layer fluid Takeshi Kataoka Department of Mechanical Engineering, Faculty of Engineering, Kobe.

Abstract: In this paper, we discuss the solitary waves at the interface of a two-layer incompressible inviscid fluid confined by two horizontal rigid walls, taking the effect of surface tension into of all, we establish the basic equations suitable for the model considered, and hence derive the Korteweg-de Vries(KdV) equation satisfied by the first-order elevation of the.

After the initial observation by John Scott Russell of a solitary wave in a canal, his insightful laboratory experiments and the subsequent theoretical work of Boussinesq, Rayleigh and Korteweg and de Vries, interest in solitary waves in fluids lapsed until the mid s with the seminal paper of Zabusky and Kruskal, which described the discovery of the soliton.

tion of solitary waves in a three-layer fluid (Rusås and Grue, ) allows for the inv estigation of both mode-1 and mode- 2 waves, including broad flat-centered wav es and extreme. Propagation regimes of interfacial solitary waves in a three-layer fluid Article (PDF Available) in Nonlinear Processes in Geophysics 22(2) March with 55 Reads How we measure 'reads'.

Purchase Waves on Fluid Interfaces - 1st Edition. Print Book & E-Book. ISBNThe selection first elaborates on finite-amplitude interfacial waves, instability of finite-amplitude interfacial waves, and finite-amplitude water waves with surface tension. Solitary Waves on Density Interfaces. This book is devoted to one of the most interesting and rapidly developing areas of modern nonlinear physics and mathematics - the theoretical, analytical and advanced numerical study of the structure and dynamics of one-dimensional as well as two- and three-dimensional solitons and nonlinear waves described by Korteweg-de Vries (KdV), Kadomtsev-Petviashvili (KP), nonlinear Schrödinger (NLS Format: Hardcover.

In all cases, solitary interfacial waves in this numerical theory tally with the experimental data. When the layer thicknesses are almost equal (ratio of lower layer to total depth equal to or ) both the KdV-mKdV and the numerical solutions match the experimental points.

INTERNAL SOLITARY WAVES IN TWO-FLUID SYSTEMS face. The existence of periodic and solitary wave was shown, the latter waves being obtained as the limit of periodic ones with ever-increasing periods. In the present paper, to obtain large amplitude waves in the case of. Free‐surface solitary waves and interfacial solitary waves in a two‐fluid system with a rigid lid are known to satisfy certain exact relations involving integral quantities (mass, kinetic and potential energy, etc.).

It is shown here that similar relations are satisfied by interfacial solitary waves in a two‐fluid system with a free upper surface and by surface solitary waves in a three.

tion of solitary waves in a three-layer fluid (Rusås and Grue, ) allows for the investigation of both mode-1 and mode-2 waves, including broad flat-centered waves and extreme (overhanging) waves.

The similarity of mode-1 waves to the interfacial waves in a two-layer fluid is the probable reason. () Long-wave transverse instability of interfacial gravity–capillary solitary waves in a two-layer potential flow in deep water.

Journal of Engineering Mathematics() Gevrey regularity for a class of water-wave models. Interfacial Wave Motion of Very Large Amplitude: Formulation in Three Dimensions and Numerical Experiments ☆ Author links open overlay panel John Grue Show more.

- On solitary waves in two-fluid systems (to appear). [30] L. Walker, Interfacial solitary waves in a two-fluid medium, Phys. Fluids 16 (), [31] Gordon Thomas Whyburn, Topological analysis, Princeton Mathematical Series. Internal solitary waves are hump-shaped, large-amplitude waves that are physically analogous to surface waves except that they propagate within the fluid, along density steps that typically.

Benney and Luke [3] were among the first to consider oblique interactions of solitary waves, in which the waves approach each other at an angle other than 0or Miles [11] gave the complete second order solution for obliquely interacting surface solitary waves, classifying the interactions as strong (slow) if the angle of approach is near 0and weak (fast) if the angle of approach is near The strong interaction.

Internal waves are gravity waves that oscillate within a fluid medium, rather than on its surface. To exist, the fluid must be stratified: the density must change (continuously or discontinuously) with depth/height due to changes, for example, in temperature and/or the density changes over a small vertical distance (as in the case of the thermocline in lakes and oceans or an.

Steady solitary and generalized solitary waves of a two-fluid problem where the upper layer is under a flexible elastic sheet are considered as a model for internal waves under an ice-covered ocean.

The fluid consists of two layers of constant densities, separated by an interface. The long-wave model describing travelling waves is constructed by means of scaling procedure with a small Boussinesq parameter.

It is demonstrated that solitary wave regimes can be affected by the Kelvin–Helmholtz instability arising due to interfacial velocity shear in the upstream flow. the solitary waves, [18, 22].

Specifically, the presence of surface tension makes an elevation solitary wave narrower than a solitary wave of the Serre equations with the same speed.

Moreover, depending on the value of the Bond number B, the solitary waves can be either of elevation or of depression type. For the short slope the following waves are somewhat less regular.

Again there is no evidence of formation of new solitary wave formation in Figs. 8b and 8d, but a radiating series of dispersive waves is seen. The lead solitary wave is reduced to maximum negative displacements of −19 m by m water depth in all cases.

After the initial observation by John Scott Russell of a solitary wave in a canal, his insightful laboratory experiments and the subsequent theoretical work of Boussinesq, Rayleigh and Korteweg and de Vries, interest in solitary waves in fluids lapsed until the mid s with the seminal paper of Zabusky and Kruskal, which described the discovery of the soliton.In mathematics and physics, a solitary wave can refer to.

The solitary wave (water waves) or wave of translation, as observed by John Scott Russell inthe prototype for a soliton.; A soliton, a generalization of the wave of translation to general systems of partial differential equations; A topological defect, a generalization of the idea of a soliton to any system which is stable.