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

Dispersion relations for supersonic multiple virtual jets

Joshua Du 1, and  Liancheng Wang 2,

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