Motion of vortices with buoyancy – Stefan Llewellyn Smith, Department of Mechanical and Aerospace Engineering, UCSD

November 4, 2019 @ 1:00 pm – 2:00 pm
Centre for Mathematical Sciences
Dr. Jerome Neufeld

In this talk I will discuss vortical flows with density variations in the presence of gravity. Explicit calculations of the motion of non-trivial vortices in the presence of density differences and surface tension are not as common as one might expect. Three topics are presented. An asymptotic model for the evolution of a thin-core vortex filament with density variations is discussed, using a formulation based on forces due to Moore and Saffman that allows buoyancy and surface tension forces to be incorporated in a natural manner. A contour dynamics method for axisymmetric vortex rings with density differences is presented, which requires following the evolution of a vortex sheet on the boundary generated by baroclinic torques. Finally a formulation of contour dynamics applicable to helical vortices is outlined.