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2011, 2011(Special): 381-390. doi: 10.3934/proc.2011.2011.381

Dispersion relations for supersonic multiple virtual jets

1. 

Department of Mathematics, Kennesaw State University, 1000 Chastain Rd, P.O. Box 1204, Kennesaw, GA 30144

2. 

Department of Mathematics & Statistics, Kennesaw State University, Kennesaw, GA 30144

Received  July 2010 Revised  April 2011 Published  October 2011

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.
Citation: Joshua Du, Liancheng Wang. Dispersion relations for supersonic multiple virtual jets. Conference Publications, 2011, 2011 (Special) : 381-390. doi: 10.3934/proc.2011.2011.381
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