Viscosity flux recursion of flow motions in pseudo-hyperbolic space

Abstract

In this study, we examine the time-dependent motion of a particle in pseudo-hyperbolic (p-hyperbolic) space H-0(2) with the help of some flow equations that bring many geometrical solutions to physical problems in areas fluid dynamics, magnetic fluxes, and wave propagation. First, we consider this moving particle as a magnetic flux that makes the Heisenberg ferromagnet spin chain (Hfsc) movement and obtain the p-hyperbolic frame equations representing the flux movement. Then, we obtain some motion equations, assuming that an arbitrary vector field we choose in this space represents the vortex filament flow. Here, we obtain some results by examining the flow motion we have chosen for two different situations, with and without viscosity. More clearly, results such as the time-dependent equation of curvature of an unviscous vortex filament flow and the curvature-dependent equation of the viscosity coefficient of a viscous vortex filament flow are obtained.