Periodic Shock Waves in Resonating Gas Columns

1960 ◽  
Vol 32 (8) ◽  
pp. 961-970 ◽  
Author(s):  
R. Alfred Saenger ◽  
George E. Hudson
Keyword(s):  
Shock Waves ◽  
Periodic Shock

Particle motion in resonance tubes

1998 ◽  
Vol 360 ◽  
pp. 1-20 ◽  
Author(s):  
A. GOLDSHTEIN ◽  
K. SHUSTER ◽  
P. VAINSHTEIN ◽  
M. FICHMAN ◽  
C. GUTFINGER
Keyword(s):  
Relaxation Time ◽  
Shock Waves ◽  
Particle Motion ◽  
Small Particle ◽  
Oscillation Amplitude ◽  
Weak Shock ◽  
Transport Processes ◽  
Resonance Oscillation ◽  
Particle Drift ◽  
Periodic Shock

Small particle motions in standing or travelling acoustic waves are well known and extensively studied. Particle motion in weak shock waves has been studied much less, especially particle motion in periodic weak shock waves which as yet has not been dealt with.The present study considers small particle motions caused by weak periodic shock waves in resonance tubes filled with air. A simple mathematical model is developed for resonance gas oscillations under the influence of a vibrating piston with a finite amplitude at the first acoustic resonance frequency. It is shown that a symmetrical sinusoidal piston motion generates non-symmetric periodic shock waves. A model of particle motion in such a flow field is suggested. It is found that non-symmetric shock waves cause particle drift from the middle cross-section toward the ends of the resonance tube. The velocity of particle drift is found to be of the order of Dpρp/ Trρg, where Dp is the particle diameter, Tr the period of the resonance oscillation, ρp and ρg are the particle and gas density, respectively. At the same time, the velocity drift strongly depends on the ratio τ/Tr, where τ is the particle relaxation time. Particle drift is vigorous when τ/Tr∼1 and insignificant when τ/Tr 1. Theoretical predictions of particle drift in resonance tubes are verified numerically as well as experimentally.When the particle relaxation time is much smaller than period of the resonance oscillations particles perform oscillations around their equilibrium positions with amplitude of the order of Dpρp/ρg. It is shown that the difference in oscillation amplitude of particle of difference sizes explains coalescence of aerosol droplets observed in experiments of Temkin (1970).The importance of the phenomena for particle separation, coagulation and transport processes is discussed.

Wave breaking and shock waves for a periodic shallow water equation

2007 ◽  
Vol 365 (1858) ◽  
pp. 2281-2289 ◽  
Author(s):  
Joachim Escher
Keyword(s):  
Shock Waves ◽  
Shallow Water ◽  
Wave Breaking ◽  
Blow Up ◽  
Shallow Water Equation ◽  
Strong Solutions ◽  
Global Weak Solutions ◽  
Initial Profile ◽  
And Shock Waves ◽  
Periodic Shock

This paper is devoted to the study of a recently derived periodic shallow water equation. We discuss in detail the blow-up scenario of strong solutions and present several conditions on the initial profile, which ensure the occurrence of wave breaking. We also present a family of global weak solutions, which may be viewed as global periodic shock waves to the equation under discussion.

scholarly journals Winds in late-type stars: Mechanisms of mass outflow

1981 ◽  
Vol 59 ◽  
pp. 187-212
Author(s):  
Jeffrey L. Linsky
Keyword(s):  
Shock Waves ◽  
Mass Loss ◽  
Alfven Waves ◽  
Alfvén Waves ◽  
Pressure Gradients ◽  
Late Type ◽  
Periodic Shock ◽  
Thermally Driven ◽  
Mass Outflow ◽  
Field Lines

AbstractFour basic mechanisms have been proposed to explain the acceleration of winds in late-type stars –– thermal pressure gradients, radiation pressure on circumstellar dust grains, momentum addition by Alfvén waves, and momentum addition by periodic shock waves. In this review I describe recent work in applying these mechanisms to stars, and consider whether these mechanisms can work even in principle and whether they are consistent with recent ultraviolet and X-ray data from the IUE and Einstein spacecraft. Thermally-driven winds are likely important for late-type dwarfs, where the mass loss rates are small, and perhaps also in G giants and supergiants, but they cannot operate alone in the K and M giants and supergiants. Radiatively-driven winds are probably unimportant for all cool stars, even the M supergiants with dusty circumstellar envelopes. In principle, Alfvén waves can accelerate winds to high speeds provided the field lines are initially open or forced open by some mechanism, but detailed calculations are needed. Magnetic reconnection is an interesting suggestion for an acceleration mechanism when the field lines are initially closed. For the Mras and semiregular variable supergiants, periodic shock waves provide a simple way of producing rapid mass loss. Thus we are making some progress in understanding mass loss mechanisms for the cool half of the H-R diagram.

Periodic shock waves in a gas

1970 ◽  
Vol 5 (2) ◽  
pp. 223-230 ◽  
Author(s):  
Sh. U. Galiev ◽  
M. A. Il'gamov ◽  
A. V. Sadykov
Keyword(s):  
Shock Waves ◽  
Periodic Shock
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