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.
1.pdf - Published Version
Restricted to Registered users only
Download (1169Kb) | Request a copy
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 .
|Item Type:||Journal Article|
|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|
Actions (login required)