Dual cylinder inviscid vortex sound of low Mach number

Emphasizing physical pictures with a minimum of analysis, an introductory account is presented as to how vortices generate sound. Based on the observation that a vortex ring induces the same hydrodynamic (incompressible) flow as does a dipole sheet of the same shape, simple physical arguments for sound generation by vorticity are presented, first in terms of moving vortex rings of fixed strength and then of fixed rings of variable strength. These lead to the formal results of the theory of vortex sound, with the source expressed in terms of the vortex force ρ(u∧ ζ) and of the form introduced by Mo¨hring in terms of the vortex moment (y∧ ζ′), (ρ is the constant fluid density, u the flow velocity, ζ = ∇ ∧u the vorticity and y is the flow coordinate). The simple “Contiguous Method” of finding the contiguous acoustic field surrounding an acoustically compact hydrodynamic (incompressible) field is also discussed. Some very simple vortex flows illustrate the various ideas. These are all for acoustically compact, low Mach number flows of an inviscid fluid, except that a simple argument for the effect of viscous dissipation is given and its relevance to the “dilatation” of a vortex is mentioned.

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Two-dimensional model of low Mach number vortex sound generation in a lined duct

The Journal of the Acoustical Society of America ◽

10.1121/1.3192332 ◽

2009 ◽

Vol 126 (3) ◽

pp. 1005-1014 ◽

Cited By ~ 2

Author(s):

S. K. Tang ◽

C. K. Lau

Keyword(s):

Mach Number ◽

Two Dimensional ◽

Sound Generation ◽

Dimensional Model ◽

Low Mach Number ◽

Vortex Sound ◽

Two Dimensional Model

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Vortex sound due to a flexible boundary backed by a cavity in a low Mach number mean flow

The Journal of the Acoustical Society of America ◽

10.1121/1.2434240 ◽

2007 ◽

Vol 121 (3) ◽

pp. 1345-1352 ◽

Cited By ~ 5

Author(s):

S. K. Tang ◽

R. C. K. Leung ◽

R. M. C. So

Keyword(s):

Mach Number ◽

Mean Flow ◽

Low Mach Number ◽

Vortex Sound

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Why Do Vortices Generate Sound?

Journal of Mechanical Design ◽

10.1115/1.2836464 ◽

1995 ◽

Vol 117 (B) ◽

pp. 252-260 ◽

Cited By ~ 4

Author(s):

Alan Powell

Keyword(s):

Mach Number ◽

Incompressible Flow ◽

Vortex Rings ◽

Inviscid Fluid ◽

Fluid Density ◽

Sound Generation ◽

Simple Argument ◽

Low Mach Number ◽

Vortex Sound ◽

Moving Vortex

Emphasizing physical pictures with a minimum of analysis, an introductory account is presented as to how vortices generate sound. Based on the observation that a vortex ring induces the same hydrodynamic (incompressible) flow as does a dipole sheet of the same shape, simple physical arguments for sound generation by vorticity are presented, first in terms of moving vortex rings of fixed strength and then of fixed rings of variable strength. These lead to the formal results of the theory of vortex sound, with the source expressed in terms of the vortex force ρ(u∧ ζ) and of the form introduced by Mo¨hring in terms of the vortex moment (y∧ ζ′), (ρ is the constant fluid density, u the flow velocity, ζ = ∇ ∧u the vorticity and y is the flow coordinate). The simple “Contiguous Method” of finding the contiguous acoustic field surrounding an acoustically compact hydrodynamic (incompressible) field is also discussed. Some very simple vortex flows illustrate the various ideas. These are all for acoustically compact, low Mach number flows of an inviscid fluid, except that a simple argument for the effect of viscous dissipation is given and its relevance to the “dilatation” of a vortex is mentioned.

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On vortex sound at low Mach number

Journal of Fluid Mechanics ◽

10.1017/s0022112078000865 ◽

1978 ◽

Vol 85 (4) ◽

pp. 685-691 ◽

Cited By ~ 179

Author(s):

W. Möhring

Keyword(s):

Mach Number ◽

Sound Source ◽

Vortex Rings ◽

Spherically Symmetric ◽

Correlation Tensor ◽

Low Mach Number ◽

Vortex Sound ◽

Flow Vorticity ◽

Number Flow ◽

Low Mach Number Flow

A transformation is described which relates the sound generated by low Mach number flow to the flow vorticity. For compact flow fields the apparent sound source is of quadrupole type and linear in the vorticity and therefore also linear in the flow velocity. This scheme is applied to the sound generated by the interaction of two identical thin vortex rings. Then a flow field with a number of compact vortices is discussed. It is found that each vortex can be replaced acoustically by a dipole related to the impulse of the vortex, plus the quadrupole just mentioned plus a spherically symmetric sound source related to the energy of the vortex. An application to low Mach number free-space turbulence shows that the generated sound is related to the vorticity correlation tensor.

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