On expansion waves generated by the refraction of a plane shock at a gas interface

1967 ◽  
Vol 30 (2) ◽  
pp. 385-402 ◽  
Author(s):  
L. F. Henderson
Keyword(s):  
Expansion Wave ◽  
Plane Shock ◽  
Wave System ◽  
Expansion Waves ◽  
Reflected Wave ◽  
Expansion Fan ◽  
New Type ◽  
Self Similar ◽  
Fixed Boundaries ◽  
Mapping Theory

The paper deals with the regular refraction of a plane shock at a gas interface for the particular case where the reflected wave is an expansion fan. Numerical results are presented for the air–CH4 and air–CO2 gas combinations which are respectively examples of ‘slow–fast’ and ‘fast–slow’ refractions. It is found that a previously unreported condition exists in which the reflected wave solutions may be multi-valued. The hodograph mapping theory predicts a new type of regular–irregular transition for a refraction in this condition. The continuous expansion wave type of irregular refraction is also examined. The existence of this wave system is found to depend on the flow being self-similar. By contrast the expansion wave becomes centred when the flow becomes steady. Transitions within the ordered set of regular solutions are examined and it is shown that they may be either continuous or discontinuous. The continuous types appear to be associated with fixed boundaries and the discontinuous types with movable boundaries. Finally, a number of almost linear relations between the wave strengths are noted.

On the irregular refraction of a plane shock wave at a Mach number interface

1968 ◽  
Vol 32 (1) ◽  
pp. 185-202 ◽  
Author(s):  
L. F. Henderson ◽  
A. K. Macpherson
Keyword(s):  
Shock Wave ◽  
Mach Number ◽  
Speed Of Sound ◽  
Expansion Wave ◽  
Plane Shock Wave ◽  
Plane Shock ◽  
Irregular Wave ◽  
Self Similar ◽  
Irregular Systems ◽  
Mach Reflexion

The paper considers the refraction of a plane shock wave at an interface between two streams of different Mach number. Particular attention is paid to the irregular wave systems. It is found that when the interface is slow-fast, that is when the speed of sound a0 in the first or incident wave medium is less than the speed of sound aB in the second or transmitted wave medium, then there are two irregular systems, one being a double Mach reflexion type and the other being a four-wave confluence type. There are also two irregular systems when the refraction is fast-slow; these are a single Mach reflexion type and an expansion wave type. This last system has a central expansion wave when the flow is steady and a continuous band expansion wave when the flow is self-similar. Only two of the irregular wave systems have been observed experimentally in the fully developed state. Possible degeneracies are discussed.

scholarly journals Interaction of linear modulated waves and unsteady dispersive hydrodynamic states with application to shallow water waves

2019 ◽  
Vol 875 ◽  
pp. 1145-1174 ◽  
Author(s):  
T. Congy ◽  
G. A. El ◽  
M. A. Hoefer
Keyword(s):  
Water Waves ◽  
Large Scale ◽  
Kdv Equation ◽  
Linear Wave ◽  
Mean Flow ◽  
Undular Bore ◽  
Expansion Waves ◽  
Flow Interaction ◽  
The Kdv Equation ◽  
New Type

A new type of wave–mean flow interaction is identified and studied in which a small-amplitude, linear, dispersive modulated wave propagates through an evolving, nonlinear, large-scale fluid state such as an expansion (rarefaction) wave or a dispersive shock wave (undular bore). The Korteweg–de Vries (KdV) equation is considered as a prototypical example of dynamic wavepacket–mean flow interaction. Modulation equations are derived for the coupling between linear wave modulations and a nonlinear mean flow. These equations admit a particular class of solutions that describe the transmission or trapping of a linear wavepacket by an unsteady hydrodynamic state. Two adiabatic invariants of motion are identified that determine the transmission, trapping conditions and show that wavepackets incident upon smooth expansion waves or compressive, rapidly oscillating dispersive shock waves exhibit so-called hydrodynamic reciprocity recently described in Maiden et al. (Phys. Rev. Lett., vol. 120, 2018, 144101) in the context of hydrodynamic soliton tunnelling. The modulation theory results are in excellent agreement with direct numerical simulations of full KdV dynamics. The integrability of the KdV equation is not invoked so these results can be extended to other nonlinear dispersive fluid mechanic models.

Movement, Sound, and Body in the Postapartheid City

2012 ◽  
Author(s):  
Thomas Blom Hansen
Keyword(s):  
Youth Culture ◽  
Urban Landscape ◽  
Sound System ◽  
Physical Mobility ◽  
Urban Music ◽  
New Type ◽  
Taxi Industry ◽  
Fixed Boundaries ◽  
Cultural Mobility ◽  
The City

This chapter focuses on the rise of new forms of cultural mobility in the postapartheid city, particularly, the rise of the kombi taxi and its massive sound system as the most striking innovation in the urban landscape. While the private taxi industry has been at the center of much violence and criminal networks, it has also been important in providing new forms of agile physical mobility across the fixed boundaries in the city. More importantly, the taxis have also been the vehicles and symbols of a new type of music and youth culture that begins to cut across boundaries of class and race. The chapter explores the particular form of taxi industry in Chatsworth and looks at the wider phenomenon of the new sonic taste alliances forged by kwaito and other forms of urban music after apartheid.

Localized Excitations in a Dispersive Long Water-Wave System via an Extended Projective Approach

2007 ◽  
Vol 62 (3-4) ◽  
pp. 140-146 ◽  
Author(s):  
Jin-Xi Fei ◽  
Chun-Long Zheng
Keyword(s):  
Coherent Structures ◽  
Water Wave ◽  
Wave System ◽  
Variable Separation ◽  
Localized Excitations ◽  
Complex Wave ◽  
New Type ◽  
03.65 Ge

By means of an extended projective approach, a new type of variable separation excitation with arbitrary functions of the (2+1)-dimensional dispersive long water-wave (DLW) system is derived. Based on the derived variable separation excitation, abundant localized coherent structures such as single-valued localized excitations, multiple-valued localized excitations and complex wave excitations are revealed by prescribing appropriate functions. - PACS numbers: 03.65.Ge, 05.45.Yv

Applications of Ultrasound to Materials Chemistry

MRS Bulletin ◽  
1995 ◽  
Vol 20 (4) ◽  
pp. 29-34 ◽  
Author(s):  
Kenneth S. Suslick
Keyword(s):  
Physical Phenomenon ◽  
Direct Interaction ◽  
Acoustic Cavitation ◽  
Expansion Wave ◽  
Materials Chemistry ◽  
Metal Powders ◽  
Heterogenous Catalysis ◽  
Compression Waves ◽  
Expansion Waves ◽  
Chemical Effects

This article will begin with an introduction to acoustic cavitation, the physical phenomenon responsible for the chemical effects of ultrasound. Some recent applications of sonochemistry to the synthesis of nanophase and amorphous metals, as well as to heterogenous catalysis, will then be highlighted. Finally, we will examine the effects of ultrasound on metal powders in liquid-solid slurries.The chemical effects of ultrasound do not come from a direct interaction of sound with molecular species. Ultrasound has frequencies from around 15 kilohertz to tens of megahertz. In liquids, this means wavelengths from centimeters down to microns, which are not molecular dimensions. Instead, when sound passes through a liquid, the formation, growth, and implosive collapse of bubbles can occur, as depicted in Figure 1. This process is called acoustic cavitation.More specifically, sound passing through a liquid consists of expansion waves and compression waves. As sound passes through a liquid, if the expansion wave is intense enough (that is, if the sound is loud enough), it can pull the liquid apart and form a bubble (a cavity). The compression wave comes along and compresses this cavity, then another expansion wave re-expands it. So we have an oscillating bubble going back and forth, say, 20,000 times a second.

scholarly journals The speed, reflection and intensity of waves propagating in flexible tubes with aneurysm and stenosis: Experimental investigation

2019 ◽  
Vol 233 (10) ◽  
pp. 979-988 ◽  
Author(s):  
Wisam S Hacham ◽  
Ashraf W Khir
Keyword(s):  
Reflection Coefficient ◽  
Wave Speed ◽  
Expansion Waves ◽  
Reflected Wave ◽  
Compression And Expansion ◽  
Contracting Heart ◽  
Propagation Of Waves ◽  
Flexible Tubes ◽  
Mother Tube

A localized stenosis or aneurysm is a discontinuity that presents the pulse wave produced by the contracting heart with a reflection site. However, neither wave speed ( c) in these discontinuities nor the size of reflection in relation to the size of the discontinuity has been adequately studied before. Therefore, the aim of this work is to study the propagation of waves traversing flexible tubes in the presence of aneurysm and stenosis in vitro. We manufactured different sized four stenosis and four aneurysm silicone sections, connected one at a time to a flexible ‘mother’ tube, at the inlet of which a single semi-sinusoidal wave was generated. Pressure and velocity were measured simultaneously 25 cm downstream the inlet of the respective mother tube. The wave speed was measured using the PU-loop method in the mother tube and within each discontinuity using the foot-to-foot technique. The stenosis and aneurysm dimensions and c were used to determine the reflection coefficient ( R) at each discontinuity. Wave intensity analysis was used to determine the size of the reflected wave. The reflection coefficient increased with the increase and decrease in the size of the aneurysm and stenosis, respectively. c increased and decreased within stenosis and aneurysms, respectively, compared to that of the mother tube. Stenosis and aneurysm induced backward compression and expansion waves, respectively; the size of which was related to the size of the reflection coefficient at each discontinuity, increases with smaller stenosis and larger aneurysms. Wave speed is inversely proportional to the size of the discontinuity, exponentially increases with smaller stenosis and aneurysms and always higher in the stenosis. The size of the compression and expansion reflected wave depends on the size of R, increases with larger aneurysms and smaller stenosis.

On self-similarity of waves in tropical cyclones

2021 ◽  
Author(s):  
Maria Yurovskaya ◽  
Vladimir Kudryavtrsev ◽  
Bertrand Chapron
Keyword(s):  
Wave Field ◽  
Tropical Cyclones ◽  
Numerical Solutions ◽  
Parametric Model ◽  
Linear Wave ◽  
Wave System ◽  
Large Computer ◽  
State Assignment ◽  
Self Similar ◽  
Similar Solutions

<p>Wave fields generated by tropical cyclones (TC) are of strong interest for marine engineering, navigation safety, determination of coastal sea levels and coastal erosion. Considerable efforts have been made to improve knowledge about the surface waves in TC, both from measurements and numerical experiments. Full sophisticated spectral wave models certainly have the capability to provide detailed wave information, but they require large computer power, precise well-resolved surface winds and/or needs to consider large ensembles of solutions. In this context, more simplified but robust solutions are demanded.</p><p>This work is based on 2D-parametric model of waves evolution forced by wind field varying in space and time, non-linear wave interactions and wave breaking dissipation [submitted to J. Geoph. Res., see also preprint DOI: https://doi.org/10.1002/essoar.10504620.1]. Numerical solutions of model provide efficient visualization on how waves develop under TC and leave it as swell. Superposition of wave-rays exhibits coherent spatial patterns of wave parameters depending on TC characteristics, - maximal wind speed (um), radius (Rm), and translation velocity (V).</p><p>In this presentation we demonstrate how solutions of 2D-parametric model can be described analytically through self-similar functionsusing proper scaling involving the main TC parameters: um, Rm, and V. These self-similar solutions can be treated as TC-wave Geophysical Model Function (TC-wave GMF), to help analytically derive azimuthal-radial distributions of the primary wave system parameters (SWH, wavelength, direction) under TC characterized by arbitrary sets of um, Rm and V conditions. Self-similar solutions describe the main properties of wave field under TC, in particular: right-to-left half asymmetry of wave field under TC; strong dependence of wave energy and wavelength on V, um and Rm caused by group velocity resonance; division of TCs on “slow” and “fast” when TC-induced waves outrun TC and form wake of swell trailing TC.</p><p>Comparisons between self-similar solutions and measurements of TC-generated waves reported in the literature, demonstrate excellent agreement to warrant their use for research and practical applications.</p><p>The core support for this work was provided by the Russian Science Foundation through the Project №21-47-00038 at RSHU. The support of the Ministry of Science and Education of the Russian Federation under State Assignment No. 0555-2021-0004 at MHI RAS, and State Assignment No. 0736-2020-0005 at RSHU are gratefully acknowledged.</p>

Impact of drops on solid surfaces: self-similar capillary waves, and splashing as a new type of kinematic discontinuity

1995 ◽  
Vol 283 ◽  
pp. 141-173 ◽  
Author(s):  
A. L. Yarin ◽  
D. A. Weiss
Keyword(s):  
Experimental Data ◽  
Capillary Waves ◽  
Low Velocity Impact ◽  
Low Velocity ◽  
Charge Coupled Device ◽  
New Type ◽  
Self Similar ◽  
Onset Velocity ◽  
A Charge ◽  
The Impact

The impact of drops impinging one by one on a solid surface is studied experimentally and theoretically. The impact process is observed by means of a charge-coupled-device camera, its pictures processed by computer. Low-velocity impact results in spreading and in propagation of capillary waves, whereas at higher velocities splashing (i.e. the emergence of a cloud of small secondary droplets, absent in the former case) sets in. Capillary waves are studied in some detail in separate experiments. The dynamics of the extension of liquid lamellae produced by an impact in the case of splashing is recorded. The secondary-droplet size distributions and the total volume of these droplets are measured, and the splashing threshold is found as a function of the impact parameters.The pattern of the capillary waves is predicted to be self-similar. The calculated wave profile agrees well with the experimental data. It is shown theoretically that the splashing threshold corresponds to the onset of a velocity discontinuity propagating over the liquid layer on the wall. This discontinuity shows several aspects of a shock. In an incompressible liquid such a discontinuity can only exist in the presence of a sink at its front. The latter results in the emergence of a circular crown-like sheet virtually normal to the wall and propagating with the discontinuity. It is predicted theoretically and recorded in the experiment. The crown is unstable owing to the formation of cusps at the free rim at its top edge, which results in the splashing effect. The onset velocity of splashing and the rate of propagation of the kinematic discontinuity are calculated and the theoretical results agree fairly well with the experimental data. The structure of the discontinuity is shown to match the outer solution.

Expansion Waves in Two-Phase Pipelines

2006 ◽  
Author(s):  
Alessandro Terenzi
Keyword(s):  
Sound Velocity ◽  
Slip Flow ◽  
Expansion Wave ◽  
Two Phase ◽  
Expansion Waves ◽  
Internal Fluid ◽  
Pressurized Pipelines ◽  
The Impact ◽  
Phase Fluid ◽  
Wave Calculation

The analysis of the expansion wave propagation generated by full-bore ruptures of pressurized pipelines containing compressible fluids must be carried out during the assessment of the possible use of crack arrestors. If the internal fluid is two-phase, the sound velocity dependence from the local void fraction and flow regime has to be taken into account, by considering that it may be much lower than for single phase gases, thus promoting crack propagation. In this paper a model for the simulation of an expansion wave in a two-phase fluid pipeline is presented; this model includes several possible descriptions of the thermodynamics and flow regimes, ranging from the simpler homogeneous equilibrium approach to the non-equilibrium slip flow evaluation. The sound velocity trend inside a rarefaction wave can give rise to particular phenomena as curve inversions and jumps. The impact of different formulations on the expansion wave calculation is discussed, giving hints for the design of the pipelines under consideration.

Sign in / Sign up

Export Citation Format

Share Document