Nonlinear analysis of stretch-twist-fold (STF) flow

In this article, the stretch-twist-fold (STF) flow is numerically studied using phase portraits, sensitive dependence on initial conditions, Lyapunov exponents, power spectrum, and the Poincar, map. The stretch-twist-fold flow is a two-parameter family of Stokes flows defined in a unit sphere that is associated with the fluid particle motion that naturally arises in the dynamo theory, which proposes a mechanism by which celestial bodies, such as earth and sun can maintain and amplify the magnetic field continuously. For this continuous growth of magnetic field, scientists are interested to invent new tools for the nonfuel consumption magnetism propulsion for the low earth orbit of spacecrafts or satellites. General properties of a chaotic dynamical system reference to the stretch-twist-fold flow model are addressed and numerical solutions are generated to explain some of these properties. Analytically, we studied the local behavior at equilibrium points. The predictability of chaos in the STF flow with the numerical calculation of Lyapunov exponents and Poincar, map is presented in this paper.