Simple Waves and Shocks in Magnetohydrodynamics

Journal Article · Thu Nov 01 04:00:00 EST 1962 · Physics of Fluids (New York)

DOI:https://doi.org/10.1063/1.1706545· OSTI ID:4751806

Bohachevsky, Ihor O.

A theorem due to P. Lax asserts that transition across a weak shock, when expanded in powers of a suitable shockstrength parameter, agrees with the transition across the simple wave of the same kind up to the terms of second order, inclusive. This theorem, however, does not apply to the shock velocity nu ; it is shown that nu can also be determined up to second-order terms from the simple-wave relations. The above result is used to extend Friedrichs' theory of simple wave-weak shock interactions from gas dynamics to a general system of conservation laws. To illustrate the general theory, the treatment of a special system of conservation laws, namely, the Lundquist equations, and an explicit description of simple magnetohydrodynamic waves are given. The latter includes construction of Riemann invariants and the expansion of simple-wave relations into power series up to quadratic terms, inclusive. In connection with this work, a special approximation is proposed to describe the switch-on waves. Shocks are described by analogy with simple waves. To illustrate the necessary modifications of gas-dynamic formulas, the above results are used to discuss in detail the location of the point at which the shock forms. In particular, conditions are given under which the magnetohydrodynamic shocks develop sooner or later than the gas-dynamic. (auth)

• Research Organization: New York Univ., New York
• Sponsoring Organization: USDOE
• NSA Number: NSA-17-005489
• OSTI ID: 4751806
• Journal Information: Physics of Fluids (New York), Journal Name: Physics of Fluids (New York) Journal Issue: 11 Vol. 5; ISSN 0031-9171; ISSN PFLDAS
• Publisher: American Institute of Physics
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

CONSERVATION LAWS
DIFFERENTIAL EQUATIONS
GASES
HYDROMAGNETIC WAVES
LAX THEOREM
MAGNETOHYDRODYNAMICS
MECHANICS
PHYSICS
SHOCK WAVES
TRANSIENTS
VELOCITY