Formulation of the problem of sonic boom by a maneuvering aerofoil as a one-parameter family of Cauchy problems
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- 作者：S. Baskar (1)
Phoolan Prasad (1) prasad@math.iisc.ernet.in - 关键词：Sonic boom ; shock propagation ; ray theory ; elliptic equation ; conservation laws ; Cauchy problem
- 刊名：Proceedings Mathematical Sciences
- 出版时间：February 2006
- 出版年：2006
- 期刊代码：157_0973-7685
- 类别：mat
- 卷：116
- 期：1
- 页码：97-119
- 数据来源：sp
摘要
For the structure of a sonic boom produced by a simple aerofoil at a large distance from its source we take a physical model which consists of a leading shock (LS), a trailing shock (TS) and a one-parameter family of nonlinear wavefronts in between the two shocks. Then we develop a mathematical model and show that according to this model the LS is governed by a hyperbolic system of equations in conservation form and the system of equations governing the TS has a pair of complex eigenvalues. Similarly, we show that a nonlinear wavefront originating from a point on the front part of the aerofoil is governed by a hyperbolic system of conservation laws and that originating from a point on the rear part is governed by a system of conservation laws, which is elliptic. Consequently, we expect the geometry of the TS to be kink-free and topologically different from the geometry of the LS. In the last section we point out an evidence of kinks on the LS and kink-free TS from the numerical solution of the Euler’s equations by Inoue, Sakai and Nishida [5].