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Linear and Non-Linear Waves

We study the evolution of vortex filaments with corners. The dynamics is mainly self-similar as for example the one exhibited by the vortex loops created by the smoke from a cigarette or by the symmetrical pair of vortices generated behind a triangular wing. Corners seem to appear naturally in the process of reconnection of a counterrotating vortex pair.



Vortex loops created by the smoke from a cigarette





Pair of vortices generated behind a triangular wing





Reconnection of a counterrotating vortex pair

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Goal
Describe the dynamics of vortex filaments with corners and measure their fractal dimensions to check up to what extent they are a good toy model of turbulence.
Method
Use well established techniques of Fourier Analysis as Oscillatory Integrals and Gauss Sums to describe the dynamics.
Eusko Jaurlaritza - Gobierno Vasco ikerbasque - Basque Foundation for Science Bizkaia xede. Bizkaiko Foru Aldundia innobasque - Agencia vasca de la innovación Universidad del País Vasco (UPV/EHU) Ayuntamiento de Bilbao - Bilboko Udala