Dispersion relations for supersonic multiple virtual jets

Pages: 381 - 390, Issue Special, September 2011

 Abstract        Full Text (162.2K)              

Joshua Du - Department of Mathematics, Kennesaw State University, 1000 Chastain Rd, P.O. Box 1204, Kennesaw, GA 30144, United States (email)
Liancheng Wang - Department of Mathematics & Statistics, Kennesaw State University, Kennesaw, GA 30144, United States (email)

Abstract: In this paper, a special type of circulant matrices, circulant trinity matrices, are first introduced and some properties of these matrices are investigated. Then, in studying a supersonic circular N-jet vortex sheet model, circulant trinity matrices are used to classify the general solutions of the $N$-jet model into 2$N$ families. Finally, the dispersion relations of $N$-jets for each family are derived by using Graf’s Addition Theorem.

Keywords:  Circulant trinity matrix, classification of solutions, dispersion relations
Mathematics Subject Classification:  76J20, 76E99

Received: July 2010;      Revised: April 2011;      Published: October 2011.