Asher Yahalom
Ariel University, Israel
Title: Variational principles for topological non-barotropic fluid dynamics
Biography
Biography: Asher Yahalom
Abstract
Ideal barotropic fluid flows with the same circulation structure as steady flows generically have commoving physical surfaces on which the vortex lines lie. These become Bernoullian surfaces when the flow is steady. When these surfaces are nested (vortex line foliation) with the topology of cylinders, toroids or a combination of both, a Clebsch representation of the flow velocity can be introduced. This is then used to reduce the number of functions to be varied in the variational principles for such flows. We then can introduce a three function variational formalism for steady and non-steady barotropic flows. In ideal non barotropic flow, circulation is not conserved in the general case but one has a new commoving variable, that is the entropy itself. We will show how entropy considerations will affect the construction of compact variational principles and what are the unique topological local and global conservation laws associated with non-barotropic flows which are derived from those variational principles. The results are compared with analogous study of variational principles and topological constants of motion in non-barotropic magnetohydrodynamics. Possible applications such as flow stability analysis and numerical simulations will also be mentioned
Recent Publications
1. A Yahalom (2003) Method and system for numerical simulation of fluid flow. US patent 6,516,292.
2. Asher Yahalom and Donald Lynden-Bell (2014) Variational principles for topological barotropic fluid dynamics. Geophysical & Astrophysical Fluid Dynamics. 108(6):667-685.
3. Asher Yahalom (2016) Simplified Variational Principles for non-Barotropic Magnetohydrodynamics. Journal of Plasma Physics doi:10.1017/S0022377816000222.
4.Asher Yahalom (2016) Non-barotropic magnetohydrodynamics as a five-function field theory. International Journal of Geometric Methods in Modern Physics. doi:10.1142/S0219887816501309.
5. Asher Yahalom (2017) A conserved local cross helicity for non-barotropic MHD. Journal of Geophysical & Astrophysical Fluid Dynamics 111(2):131–137.