Vortex dynamics: A variational approach using the principle of least action

Vortices are found everywhere around us at every scale. Current models describing vortices are mainly kinematics-based, in which the resulting dynamics are limiting in their nature. Relying on these models, one can predict vortices response for a prescribed initial condition but cannot study their response under generic conditions and external disturbances. That is because current models are a well devised formulation. However, we propose a model from first-variational principles relying on the Principle of Least Action, and not only was it able to predict the vortices response in a generic sense, but also it can be extended to include varying strength vortices or any dynamical constraints.