Citation
Lynn, YenMow (1961) Isentropic plane waves in magnetohydrodynamics. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd12082005134709
Abstract
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Plane waves propagating in a perfectly electrically conducting polytropic gas of otherwise uniform state in the presence of an arbitrarily oriented uniform magnetic field are studied; they correspond to plane simple waves in magnetohydrodynamics. Riemann invariants across finite amplitude waves in ordinary gasdynamics are generalized herein to take into account all possible magnetohydrodynamics effects. There exist totally seven types of waves, namely, contact surfaces, forward and backward facing transverse simple waves and forward and backward facing coupled (fast and slow) simple waves. But of these only coupled waves are genuinely nonlinear and receive most of our attention. The mathematical theory of simple waves is discussed first to give a general picture of the underlying structure of solutions. Contact surfaces and transverse simple wave solutions are given next with particular emphasis on the case of the contact surface adjacent to a vacuum, region. An exact analytical solution of coupled waves for gases of arbitrary value of [...] is obtained in terms of generalized Riemann invariants; some of these invariants are expressed in terms of definite integrals of a parameter [...]. The invariant relations among several physical quantities are thus expressed in a parametric form. An alternative method of solving coupled waves by graphical means is proposed and some detailed calculations are presented. General properties of physical variables across coupled waves are mentioned. For the special case of gas in a purely transverse magnetic field, a scheme of solving arbitrary flow problems is discussed briefly. The corresponding case of coupled wave solutions is given in terms of a hypergeometric function. Finally, some examples are shown to illustrate the application of the solutions to actual physical problems.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Degree Grantor:  California Institute of Technology 
Division:  Engineering and Applied Science 
Major Option:  Aeronautics 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  1 January 1961 
Record Number:  CaltechETD:etd12082005134709 
Persistent URL:  http://resolver.caltech.edu/CaltechETD:etd12082005134709 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  4863 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  09 Dec 2005 
Last Modified:  26 Dec 2012 03:12 
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