The trailing vorticity field behind a line source in two-dimensional incompressible linear shear flow

S.W. Rienstra, M. Darau, E.J. Brambley

Research output: Contribution to journalArticleAcademicpeer-review

9 Citations (Scopus)

Abstract

The explicit exact analytic solution for harmonic perturbations from a line mass source in an incompressible inviscid two-dimensional linear shear is derived using a Fourier transform method. The two cases of an infinite shear flow and a semi-infinite shear flow over an impedance boundary are considered. For the free-field and hard-wall configurations, the pressure field is (in general) logarithmically diverging and its Fourier representation involves a diverging integral that is interpreted as an integral of generalized functions; this divergent behaviour is not present for a finite impedance boundary or if the frequency equals the mean flow shear rate. The dominant feature of the solution is the hydrodynamic wake caused by the shed vorticity of the source. For linear shear over an impedance boundary, in addition to the wake, (at most) two surface modes along the wall are excited. The implications for duct acoustics with flow over an impedance wall are discussed. Keywords: aeroacoustics, general fluid mechanics, vortex shedding
Original languageEnglish
Pages (from-to)618-636
JournalJournal of Fluid Mechanics
Volume720
DOIs
Publication statusPublished - 2013

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Shear flow
Vorticity
shear flow
vorticity
impedance
Aeroacoustics
Acoustic impedance
Vortex shedding
Fluid mechanics
wakes
Ducts
Shear deformation
Fourier transforms
Hydrodynamics
acoustic ducts
Acoustics
shear
sheds
aeroacoustics
vortex shedding

Cite this

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abstract = "The explicit exact analytic solution for harmonic perturbations from a line mass source in an incompressible inviscid two-dimensional linear shear is derived using a Fourier transform method. The two cases of an infinite shear flow and a semi-infinite shear flow over an impedance boundary are considered. For the free-field and hard-wall configurations, the pressure field is (in general) logarithmically diverging and its Fourier representation involves a diverging integral that is interpreted as an integral of generalized functions; this divergent behaviour is not present for a finite impedance boundary or if the frequency equals the mean flow shear rate. The dominant feature of the solution is the hydrodynamic wake caused by the shed vorticity of the source. For linear shear over an impedance boundary, in addition to the wake, (at most) two surface modes along the wall are excited. The implications for duct acoustics with flow over an impedance wall are discussed. Keywords: aeroacoustics, general fluid mechanics, vortex shedding",
author = "S.W. Rienstra and M. Darau and E.J. Brambley",
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The trailing vorticity field behind a line source in two-dimensional incompressible linear shear flow. / Rienstra, S.W.; Darau, M.; Brambley, E.J.

In: Journal of Fluid Mechanics, Vol. 720, 2013, p. 618-636.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - The trailing vorticity field behind a line source in two-dimensional incompressible linear shear flow

AU - Rienstra, S.W.

AU - Darau, M.

AU - Brambley, E.J.

PY - 2013

Y1 - 2013

N2 - The explicit exact analytic solution for harmonic perturbations from a line mass source in an incompressible inviscid two-dimensional linear shear is derived using a Fourier transform method. The two cases of an infinite shear flow and a semi-infinite shear flow over an impedance boundary are considered. For the free-field and hard-wall configurations, the pressure field is (in general) logarithmically diverging and its Fourier representation involves a diverging integral that is interpreted as an integral of generalized functions; this divergent behaviour is not present for a finite impedance boundary or if the frequency equals the mean flow shear rate. The dominant feature of the solution is the hydrodynamic wake caused by the shed vorticity of the source. For linear shear over an impedance boundary, in addition to the wake, (at most) two surface modes along the wall are excited. The implications for duct acoustics with flow over an impedance wall are discussed. Keywords: aeroacoustics, general fluid mechanics, vortex shedding

AB - The explicit exact analytic solution for harmonic perturbations from a line mass source in an incompressible inviscid two-dimensional linear shear is derived using a Fourier transform method. The two cases of an infinite shear flow and a semi-infinite shear flow over an impedance boundary are considered. For the free-field and hard-wall configurations, the pressure field is (in general) logarithmically diverging and its Fourier representation involves a diverging integral that is interpreted as an integral of generalized functions; this divergent behaviour is not present for a finite impedance boundary or if the frequency equals the mean flow shear rate. The dominant feature of the solution is the hydrodynamic wake caused by the shed vorticity of the source. For linear shear over an impedance boundary, in addition to the wake, (at most) two surface modes along the wall are excited. The implications for duct acoustics with flow over an impedance wall are discussed. Keywords: aeroacoustics, general fluid mechanics, vortex shedding

U2 - 10.1017/jfm.2013.2

DO - 10.1017/jfm.2013.2

M3 - Article

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SN - 0022-1120

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