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1

An effect of electrokinetics phenomena on nonlinear wave propagation in bubbly liquids

Panahov G., Abbasov E., Bakhtiyarov S., Museibli P.

International Journal of Applied Mechanics and Engineering

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2021

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Vol. 26, no. 3

177--186

EN

A study of nonlinear waves in liquid-gas mixtures with the consideration of internal effects is an important problem of both the fundamental and the applied fluid mechanics. Investigation of nonlinear waves in the gas-liquid mixtures with allowance for internal effects is an important task of both fundamental and applied fluid mechanics. These problems often arise in industrial processes such as oil and gas production, hydrocarbons pipeline transportation, gas-saturated fluids flow in pipelines, etc. In this work, we investigate the effect of the internal electric field on the nonlinear wave propagation in a bubbly liquid. Numerical simulations have been conducted to study the nonlinear waves described by the nonlinear Burgers-Korteweg-de Vries equation. The numerical simulations showed that the electrokinetic processes significantly affect the wave propagation process. The amplitude of the waves gradually decreases when the size of the gas bubble is decreasing and the electrical potential increases. A good agreement of obtained results with our previous predictions is found.

2

Water entry of a wedge into waves in three degrees of freedom

Sun Shi Yan, Chen Hai Long, Xu Gang

Polish Maritime Research

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2019

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nr 1

117--124

EN

The hydrodynamic problem of a two-dimensional wedge entering into a nonlinear wave in three degrees of freedom is investigated based on the incompressible velocity potential theory. The problem is solved through the boundary element method in the time domain. To avoid numerical difficulties due to an extremely small contact area at the initial stage, a stretched coordinate system is used based on the ratio of the Cartesian system in the physical space to the distance travelled by the wedge in the vertical direction. The mutual dependence of body motion and wave loading is decoupled by using the auxiliary function method. Detailed results about body accelerations, velocities and displacements at different Froude numbers or different waves are provided, and the mutual effect between body motion and wave loading is analysed in depth.

3

Generation and propagation of nonlinear waves in a towing tank

Drzewiecki Marcin, Sulisz Wojciech

Polish Maritime Research

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2019

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nr 1

125--133

EN

The paper presents the results of the research focused on linear and nonlinear wave generation and propagation in a deepwater towing tank equipped with a single flap-type wavemaker of variable draft. The problem of wave generation and propagation has been theoretically formulated and solved by applying an analytical method; linear and nonlinear solutions were obtained. The linear solution has been verified experimentally. The laboratory experiments confirmed that a linear model can be applied to predict the generation and propagation of water waves of low steepness. However, according to the analysis, the discrepancies between wave profiles predicted by applying the linear and nonlinear models rapidly increases with increasing wave steepness. Additionally, the secondary phenomena which occur in the towing tank, including: disintegration of wave profile, wave reflections from the beach and wave damping, were analyzed. Knowledge on the nonlinear processes and phenomena is essential for modeling the environmental conditions during tests carried out to secure the safety of the naval and offshore constructions. The theoretical formulation was derived and the solution was obtained by the Institute of Hydroengineering of the Polish Academy of Sciences IBW PAN while the experimental research was carried out in Ship Hydromechanics Division of the Ship Design and Research Centre CTO S.A.

4

Linear and nonlinear ΤM polarized surface waves in anisotropic metamaterials

Ali Munazza Zulfiqar

Optica Applicata

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2019

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Vol. 49, nr 3

473--486

EN

The metamaterial with an effective permeability and/or permittivity tensor having elements of different magnitudes and signs is termed as the anisotropic metamaterial. The hyperbolic metamaterial may be considered as a subclass of the anisotropic metamaterial. The dispersion relation for the transverse magnetic surface waves at the interface between a nonlinear dielectric material and an anisotropic metamaterial is derived using the parallel uniaxial approximation of the permittivity tensor. This dispersion relations can be linearized by taking the nonlinear coefficient to be zero. Dispersion curves are plotted for both the linear and the nonlinear cases and are analyzed and compared in different frequency regions.

5

Highly nonlinear solitary wave velocity measurement with a modified Michelson interferometer

Olivares I., Riveros G., Manriquez C., Labbé R., Vergara L.

Optica Applicata

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2017

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Vol. 47, nr 2

257--262

EN

We have measured the velocity of a highly nonlinear solitary wave, generated by the collision of a ball with a linear set of pre-compressed balls of the same material, using a double Michelson interferometer. One of the mirrors of each interferometer was mounted on one of two balls of the array. The measured soliton velocity was u = (346 ± 40) m/s for brass balls with pre-compression force F = (0.8 ± 0.1) N, and u = (102 ± 3) m/s for Teflon balls with pre-compression force F = (0.4 ± 0.1) N.

6

Thermal Waves, Second Sound. Works of Witold Kosiński

Saxton K., Saxton R.

Mathematica Applicanda

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2015

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Vol. 43, No. 2

291--303

EN

This paper is dedicated to Witold Kosiński. Our contribution to this special issue will concentrate on the properties of thermal waves, one of many scientific interests of our friend and collaborator, and this article is dedicated to his memory. Working together with Witold was always an insightful and pleasant experience, and it benefited all of his coworkers including the authors of this note. His scope of research was broad, spanning many disciplines and applications. Here we focus on a few of those aspects to which he applied a deep knowledge of continuum thermodynamics and its mathematical foundations.

PL

Niniejsza praca jest poświęcona pamięci naszego przyjaciela Witolda Kosińskego. Chcielibyśmy przedstawić jego najważniejsze osiągnięcia w dziedzinie propagacji fal termicznych, termodynamiki i teorii hiperbolicznych układów różniczkowych. Zakres badań Kosińskiego był bardzo bogaty. Obejmował wiele dyscyplin na pograniczu mechaniki, matematyki i teorii komputerowych. Współpraca z Witoldem była owocna, zawsze wypełniona entuzjazmem i wzajemnym szacunkiem. Autorzy tego artykułu jak i inni współpracownicy Witolda korzystali z jego wiedzy i zawodowego doświadczenia. Bedzie nam go bardzo brakowało.

7

Reflection and transmission of nonlinear water waves at a semi-submerged dock

Sulisz W.

Archives of Mechanics

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2013

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Vol. 65, nr 3

237--260

EN

A theoretical approach is applied to predict reflection and transmission of nonlinear water waves at a semi-submerged dock. The solution was achieved analytically and by the method of matched eigenfunction expansions. The results show that the dock geometry has a significant effect on the nonlinear components of wave reflection and transmission. The reflection and transmission of nonlinear waves simultaneously increase with increasing dock width for shallow water waves and decrease with increasing dock width for intermediate- and deep-water waves, which is an interesting outcome. A similar simultaneous increase or decrease of nonlinear wave reflection and transmission was observed for the changes of the dock draft. Moreover, the solution reveals that nonlinear wave components may provide a significant contribution to the wave field for a wide range of wave parameters. The nonlinear components of wave reflection and transmission may exceed many times the amplitudes of the corresponding second-order Stokes waves as well as the amplitudes of the corresponding linear components. This phenomenon occurs within the commonly accepted range of the applicability of the second-order wave theory and implies a need to include scattered nonlinear wave components in the analysis of many problems of practical importance, including sediment transport, for which second-order waves have been shown to be the main driving force. Laboratory experiments were conducted to verify nonlinear wave field components. Theoretical results are in reasonable agreement with experimental data.

8

Modeling of the propagation and evolution of nonlinear waves in a wave train

Sulisz W., Paprota M.

Archives of Mechanics

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2011

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Vol. 63, nr 3

311-311

EN

A theoretical approach is applied to predict the propagation and evolution of nonlinear water waves in a wave train. A semi-analytical solution was derived by applying an eigenfunction expansion method. The solution is applied to study the evolution of nonlinear waves in a wave train and the formation of freak waves. The analysis focuses on the changes of wave profile and wave spectrum due to the interaction of wave components in a wave train. The results indicate that for waves of very low steepness, the changes of wave profile and wave spectrum are of secondary importance and weakly nonlinear wave theories can be applied to describe wave propagation in a wave train. For waves of low and moderate steepness, the nonlinear terms in the free-surface boundary conditions are becoming more and more important and weakly nonlinear wave theories cannot be applied to describe substantial changes in wave profile. A train of basically sinusoidal waves may drastically change its form within a relatively short distance from its original position and freak waves are often formed. The interaction between waves in a wave train and significant wave evolution has substantial effects on a wave spectrum. A train of initially very narrow-banded spectrum changes its simple one-peak spectrum to a broad-banded and often multi-peak spectrum in a fairly short period of time. The analysis shows that these phenomena cannot be described properly by the nonlinear Schrödinger equation or its modifications. Laboratory experiments were conducted in a wave flume to verify theoretical approaches. The free-surface elevation recorded by a system of wave gauges was compared with the results provided by the semi-analytical solution. Theoretical results are in a fairly good agreement with experimental data. A reasonable agreement between theoretical results and experimental data is observed, even for complex changes of long wave trains.

9

On the Transformation of Long Gravitational Waves in a Region of Variable Water Depth: a Comparison of Theory and Experiment

Szmidt K.

Archives of Hydro-Engineering and Environmental Mechanics

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2007

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Vol. 54, nr 2

137-158

EN

The paper describes investigations on transformation of long gravitational waves in water of variable depth with reflection of the waves from a shelf barrier. In the model considered, a long water wave arrives from an area of constant water depth to an area of constant, smaller water depth, where it reflects at a vertical wall. The analysis is confined to a finite fluid domain, relevant to experimental investigations in a laboratory flume. In theoretical analysis of the phenomenon, we follow a non-linear shallow water approximation to the problem considered. The fundamental equations of fluid motion are derived with the help of a standard variational procedure in a material system of coordinates. The equations proved to be a reasonable approximation to a description of the long waves propagating in fluid with small variation of its depth. In the discussed case of reflection of such waves from a vertical barrier, however, the motion of the fluid is more complicated and therefore the long water wave theory does not deliver as good results as in the case of pure propagation of the waves. The primary objective of this paper is thus to compare the theoretical solution proposed with data obtained in experiments, and to answer the question about accuracy and applicability of the theoretical model in the description of the problem investigated.

10

Acoustic emission from a dislocation kink accelerated by an external force

Douka E., Polyzos B., Trochidis A.

Archives of Acoustics

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2005

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Vol. 30, No. 2

247-253

EN

The emission of elastic waves from a dislocation kink accelerated by a constant external force is presented. The dynamics of the dislocation kink interacting with longitudinal acoustic waves is described by a sine-Gordon--d'Alembert system, i.e. a sine-Gordon equation nonlinearly coupled with the d'Alembert wave equation. Within the framework of this model, the evolution of velocity of the dislocation kink altered by the applied force is determined, allowing for mechanical couplings. The total energy radiated from the dislocation kink and its spectral composition is calculated numerically and analytically. Computer simulations are presented, which graphically illustrate the analytical considerations and model the acoustic radiation.

11

R-adaptive Trefftz method for steady non-linear water waves

Kołodziej J. A.

Vibrations in Physical Systems

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2002

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Vol. 20

182--183

12

On nonlinear waves in elastic conductors under a magnetic field

Chakraborty S.

Archives of Mechanics

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2002

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Vol. 54, nr 1

3-13

EN

A study of the behavior of magneto-elastic waves in a nonlinear isotropic elastic conductor by applying the method of multiple scales and perturbation has been made for a general displacement wave, under the action of an arbitrarily directed, uniform magnetic field. While in the case of transverse magnetic field the shock the waves are formed, it has been shown here that, under an oblique magnetic field, the wave is distorted without the formation of shocks.