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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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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 -