Geometry and dynamics of vortex sheets in 3 dimensions

Burton, David A and Tucker, Robin (2002) Geometry and dynamics of vortex sheets in 3 dimensions. Theoretical and Applied Mechanics, 29. pp. 55-75.

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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

Item Type:
Journal Article
Journal or Publication Title:
Theoretical and Applied Mechanics
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Deposited On:
27 Oct 2011 09:25
Last Modified:
18 Feb 2024 00:37