The TRR 181 seminar is held by Annette Müller (Freie Universität Berlin) on May 2, 11 am at Universität Hamburg, Grindelberg 5, room 008.
The Nambu formulation for two-and three-dimensional fluid dynamics provides a comprised, algebraic description of the structure of vortex dynamics. Nambu mechanics can be seen as a generalization of Hamilton's formulation. The equations of motion are represented in terms of two constitutive conserved quantities: the energy and a vortex-related quantity (helicity (3D), enstrophy (2D)).
By formulating the Helmholtz vorticity equation in terms of Nambu mechanics, a vortex Lie algebra, respectively vortex Lie group of incompressible, inviscid fluids can be found an analyzed. In this way, incompressible, inviscid vortex dynamics can be regarded from a different perspective. A novel matrix representation of the so-called Vortex-Heisenberg Lie algebra, respectively Vortex-Heisenberg Lie group, for two-and three-dimensional vortex dynamics is represented. As an example of the applicability of the corresponding Vortex-Heisenberg Lie group to atmospheric phenomena the onset of splitting storms is analyzed.