Fluid Dynamics & Aerodynamics

Biography

Biography: Przemyslaw Figura

Abstract

We consider flows that preserve lines of a given external field. In particular, we focus on the magneto-fluids flowing in a magnetic field. Moreover, we treat the breakage of the line preservation regime as a process of the magnetic reconnection. To describe the magnetic field, we use the Euler potentials representation. Using this formalism, we formulate a line preserving flows equation that becomes the basis of our further studies. We obtain equations describing the time evolution of the Euler potentials for the considered regime. We provide two approaches to find the special case solutions of the obtained equations, because in general closed-form solutions of the equations do not exist. Also, we consider small perturbations and their implications of our obtained line preserving flows equation as well as perturbations of the Euler potentials time evolution equations. We illustrate them with some simple examples.