Baskar, S and Prasad, Phoolan
(2006)
*Formulation of the problem of sonic boom by a maneuvering aerofoil as a one-parameter family of Cauchy problems.*
In: Proceedings Of The Indian Academy Of Sciences-Mathematical Sciences, 116
(1).
pp. 97-119.

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## Abstract

For the structure of a sonic boom produced by a simple aerofoil at it 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 oil the LS and kink-free TS from the numerical solution of the Euler's equations by Inoue, Sakai and Nishida [5].

Item Type: | Journal Article |
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Additional Information: | Copyright of this article belongs to Indian Academy Sciences. |

Keywords: | Sonic boom;shock propagation;ray theory;elliptic equation; conservation laws;Cauchy problem. |

Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |

Date Deposited: | 24 Mar 2009 06:52 |

Last Modified: | 19 Sep 2010 04:56 |

URI: | http://eprints.iisc.ernet.in/id/eprint/17245 |

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