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Cones of silence, complex rays and catastrophes: high-frequency flow-acoustic interaction effects

Cones of silence, complex rays and catastrophes: high-frequency flow-acoustic interaction effects
Cones of silence, complex rays and catastrophes: high-frequency flow-acoustic interaction effects

In this paper we develop a novel ray solver for the time-harmonic linearized Euler equations used to predict high-frequency flow-acoustic interaction effects from point sources in subsonic mean jet flows. The solver incorporates solutions to three generic ray problems found in free-space flows: the multiplicity of rays at a receiver point, propagation of complex rays and unphysical divergences at caustics. We show that these respective problems can be overcome by an appropriate boundary value reformulation of the nonlinear ray equations, a bifurcation-theory-inspired complex continuation, and an appeal to the uniform functions of catastrophe theory. The effectiveness of the solver is demonstrated for sources embedded in isothermal parallel and spreading jets, with the fields generated containing a wide variety of caustic structures. Solutions are presented across a large range of receiver angles in the far field, both downstream, where evanescent complex rays generate the cone of silence, and upstream, where multiple real rays are organized about a newly observed cusp caustic. The stability of the caustics is verified for both jets by their persistence under parametric changes of the flow and source. We show the continuation of these caustics as surfaces into the near field is complicated due to a dense caustic network, featuring a chain of locally hyperbolic umbilic caustics, generated by the tangency of rays as they are channelled upstream within the jet.

Acoustic Analogies, complex rays, Lilley equation, aeroacoustics, ray solver
0022-1120
37-71
Stone, J.T.
1794a631-0f35-44c3-94dd-68766d0ac401
Self, R.H.
8b96166d-fc06-48e7-8c76-ebb3874b0ef7
Howls, C.J.
66d3f0f0-376c-4f7a-a206-093935e6c560
Stone, J.T.
1794a631-0f35-44c3-94dd-68766d0ac401
Self, R.H.
8b96166d-fc06-48e7-8c76-ebb3874b0ef7
Howls, C.J.
66d3f0f0-376c-4f7a-a206-093935e6c560

Stone, J.T., Self, R.H. and Howls, C.J. (2018) Cones of silence, complex rays and catastrophes: high-frequency flow-acoustic interaction effects. Journal of Fluid Mechanics, 853, 37-71. (doi:10.1017/jfm.2018.544).

Record type: Article

Abstract

In this paper we develop a novel ray solver for the time-harmonic linearized Euler equations used to predict high-frequency flow-acoustic interaction effects from point sources in subsonic mean jet flows. The solver incorporates solutions to three generic ray problems found in free-space flows: the multiplicity of rays at a receiver point, propagation of complex rays and unphysical divergences at caustics. We show that these respective problems can be overcome by an appropriate boundary value reformulation of the nonlinear ray equations, a bifurcation-theory-inspired complex continuation, and an appeal to the uniform functions of catastrophe theory. The effectiveness of the solver is demonstrated for sources embedded in isothermal parallel and spreading jets, with the fields generated containing a wide variety of caustic structures. Solutions are presented across a large range of receiver angles in the far field, both downstream, where evanescent complex rays generate the cone of silence, and upstream, where multiple real rays are organized about a newly observed cusp caustic. The stability of the caustics is verified for both jets by their persistence under parametric changes of the flow and source. We show the continuation of these caustics as surfaces into the near field is complicated due to a dense caustic network, featuring a chain of locally hyperbolic umbilic caustics, generated by the tangency of rays as they are channelled upstream within the jet.

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More information

Submitted date: 21 August 2017
Accepted/In Press date: 3 July 2018
e-pub ahead of print date: 16 August 2018
Published date: 25 October 2018
Keywords: Acoustic Analogies, complex rays, Lilley equation, aeroacoustics, ray solver

Identifiers

Local EPrints ID: 421795
URI: https://eprints.soton.ac.uk/id/eprint/421795
ISSN: 0022-1120
PURE UUID: 8c52acce-11dc-4468-bed3-8d9470967342
ORCID for C.J. Howls: ORCID iD orcid.org/0000-0001-7989-7807

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Date deposited: 27 Jun 2018 16:31
Last modified: 14 Mar 2019 01:47

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