Kelvin-Helmholtz instability waves of supersonic multiple jets (Q1422512)

From the introduction: This paper deals with three types of circular supersonic multiple jets: 1. Twin unit jets with distance between two centers \(S\); 2. \(N\) unit jets in a row, with distance \(S\) between centers of two consecutive jets; 3. \(N\) unit jets whose centers are uniformly distributed on a circle with radius \(R\). The objective of this work is to determine and to study the characteristics of the acoustic wave modes and the Kelvin-Helmholtz instability waves of multiple supersonic jets. These waves constitute the basic elements of the feedback loop responsible for the generation of resonance tones for jets. In the vortex sheet model, the jets are modeled as \(N\) cylindrical columns bounded by vortex sheets. Instability wave solutions valid inside and outside of the jets can be found. The enforcement of the kinematic and dynamic boundary conditions along the vortex sheets is facilitated by the use of the addition theorem for Bessel functions. The imposition of these conditions leads to a dispersion relation in the form of determinants with dimension infinity by infinity.