Orateur : Kimiaki Konno, Nihon University (Tokyo)
Titre : On two types of localized induction equation
Résumé : The localized induction equation(LIE), which describes the vortex filament in fluid, is considered. LIE is interesting not only in physics, but also in mathematics because it is an integrable equation and related to other famous equations.
So at first LIE is reviewed. Main interest is that, if the vortex filament is stretched, LIE is still able to describe such a stretched vortex.
Numerical result reveals existence of stretched vortex filament.
Then the derivation of LIE is re-examined and obtained another type of LIE which permits to have solutions of stretched filament. Similarity and difference of properties for these two equations, such as transport property, transformation and scale transformation between two equations and their solutions, are considered from physical and mathematical point of view.
A simple, but useful implicit numerical scheme is presented to calculate LIE.
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CMLA UMR 8536 |
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