کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1897199 1534068 2008 8 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Kinematic variational principle for motion of vortex rings
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Kinematic variational principle for motion of vortex rings
چکیده انگلیسی
We show how the ideas of topology and variational principle, opened up by Euler, facilitate the calculation of motion of vortex rings. Kelvin-Benjamin's principle, as generalised to three dimensions, states that a steady distribution of vorticity, relative to a moving frame, is the state that maximizes the total kinetic energy, under the constraint of constant hydrodynamic impulse, on an iso-vortical sheet. By adapting this principle, combined with an asymptotic solution of the Euler equations, we make an extension of Fraenkel-Saffman's formula for the translation velocity of an axisymmetric vortex ring to third order in a small parameter, the ratio of the core radius to the ring radius. Saffman's formula for a viscous vortex ring is also extended to third order.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Physica D: Nonlinear Phenomena - Volume 237, Issues 14–17, 15 August 2008, Pages 2210-2217
نویسندگان
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