Physics – Mathematical Physics

Scientific paper

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1999-12-10

Physics

Mathematical Physics

40 pages, no figures

Scientific paper

10.1016/S0378-4371(00)00223-5

We show that certain infinitesimal operators of the Lie-point symmetries of the incompressible 3D Navier-Stokes equations give rise to vortex solutions with different characteristics. This approach allows an algebraic classification of vortices and throws light on the alignment mechanism between the vorticity and the vortex stretching vector. The symmetry algebra associated with the Navier-Stokes equations turns out to be infinite- dimensional. New vortical structures, generalizing in some cases well-known configurations such as, for example, the Burgers and Lundgren solutions, are obtained and discussed in relation to the value of the dynamic angle. A systematic treatment of the boundary conditions invariant under the symmetry group of the equations under study is also performed, and the corresponding invariant surfaces are recognized.

**Grassi Valerio**

Physics – High Energy Physics – High Energy Physics - Theory

Scientist

**Leo Rosario Antonio**

Mathematics – Analysis of PDEs

Scientist

**Soliani Giulio**

Physics – High Energy Physics – High Energy Physics - Theory

Scientist

**Tempesta Piergiulio**

Physics – Mathematical Physics

Scientist

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