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Geometry and dynamics of vortex sheets in 3 dimensions

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Geometry and dynamics of vortex sheets in 3 dimensions. / Burton, David A; Tucker, Robin.
In: Theoretical and Applied Mechanics, Vol. 29, 2002, p. 55-75.

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Burton DA, Tucker R. Geometry and dynamics of vortex sheets in 3 dimensions. Theoretical and Applied Mechanics. 2002;29:55-75. doi: 10.2298/TAM0229055B

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Burton, David A ; Tucker, Robin. / Geometry and dynamics of vortex sheets in 3 dimensions. In: Theoretical and Applied Mechanics. 2002 ; Vol. 29. pp. 55-75.

Bibtex

@article{aa280f102c00467982fc85806755ac20,
title = "Geometry and dynamics of vortex sheets in 3 dimensions",
abstract = "We consider the properties and dynamics of vortex sheets from a geometrical, coordinate-free, perspective. Distribution-valued forms (de Rham currents) are used to represent the fluid velocity and vorticity due to the vortex sheets. The smooth velocities on either side of the sheets are solved in terms of the sheet strengths using the language of double forms. The classical results regarding the continuity of the sheet normal component of the velocity and the conservation of vorticity are exposed in this setting. The formalism is then applied to the case of the self-induced velocity of an isolated vortex sheet. We develop a simplified expression for the sheet velocity in terms of representative curves. Its relevance to the classical Localized Induction Approximation (LIA) to vortex filament dynamics is discussed",
author = "Burton, {David A} and Robin Tucker",
year = "2002",
doi = "10.2298/TAM0229055B",
language = "English",
volume = "29",
pages = "55--75",
journal = "Theoretical and Applied Mechanics",
publisher = "Serbian Society for Mechanics",

}

RIS

TY - JOUR

T1 - Geometry and dynamics of vortex sheets in 3 dimensions

AU - Burton, David A

AU - Tucker, Robin

PY - 2002

Y1 - 2002

N2 - We consider the properties and dynamics of vortex sheets from a geometrical, coordinate-free, perspective. Distribution-valued forms (de Rham currents) are used to represent the fluid velocity and vorticity due to the vortex sheets. The smooth velocities on either side of the sheets are solved in terms of the sheet strengths using the language of double forms. The classical results regarding the continuity of the sheet normal component of the velocity and the conservation of vorticity are exposed in this setting. The formalism is then applied to the case of the self-induced velocity of an isolated vortex sheet. We develop a simplified expression for the sheet velocity in terms of representative curves. Its relevance to the classical Localized Induction Approximation (LIA) to vortex filament dynamics is discussed

AB - We consider the properties and dynamics of vortex sheets from a geometrical, coordinate-free, perspective. Distribution-valued forms (de Rham currents) are used to represent the fluid velocity and vorticity due to the vortex sheets. The smooth velocities on either side of the sheets are solved in terms of the sheet strengths using the language of double forms. The classical results regarding the continuity of the sheet normal component of the velocity and the conservation of vorticity are exposed in this setting. The formalism is then applied to the case of the self-induced velocity of an isolated vortex sheet. We develop a simplified expression for the sheet velocity in terms of representative curves. Its relevance to the classical Localized Induction Approximation (LIA) to vortex filament dynamics is discussed

U2 - 10.2298/TAM0229055B

DO - 10.2298/TAM0229055B

M3 - Journal article

VL - 29

SP - 55

EP - 75

JO - Theoretical and Applied Mechanics

JF - Theoretical and Applied Mechanics

ER -