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- Ihor O. Bohachevsky
- Department of Aeronautics and Astronautics, New York University, New York, New York
書誌事項
- 公開日
- 1962-11-01
- DOI
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- 10.1063/1.1706545
- 公開者
- AIP Publishing
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説明
<jats:p>A theorem due to P. Lax asserts that transition across a weak shock, when expanded in powers of a suitable shock-strength 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 v; it is shown that v 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.</jats:p>
収録刊行物
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- The Physics of Fluids
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The Physics of Fluids 5 (11), 1456-1467, 1962-11-01
AIP Publishing