Recurrence in three dimensional magnetohydrodynamic plasma

Abstract

We report on a numerical observation of recurrence phenomenon in a three dimensional magnetohydrodynamic (MHD) plasma for certain classes of initial flow profiles. Our simulations discover such a behaviour for an initial Taylor-Green (TG) type of flow whereas under identical conditions an initial Arnold-Beltrami-Childress (ABC) flow fails to show recurrent behaviour. This difference in the dynamical behaviours is traced to the nature of the Rayleigh quotient in each case. The Rayleigh quotient which is an approximate measure of the number of active degrees of freedom in a dynamical system is found to remain small and bounded in time for the TG flow but grows indefinitely in time for the ABC flow. An estimate of the effective degrees of freedom for the TG flow case is provided and its practical implications for the nonlinear behaviour of the continuum nonlinear MHD plasma system is discussed. *

Revisiting kinematic fast dynamo in three-dimensional magnetohydrodynamicplasmas: dynamo transition from non-helical to helical flows

“…However the investigation of the role of cross-helicity (also called Yoshizawa effect) on YM flow and others, in the context of various dynamo action is beyond the scope of the present work and will be addressed in future communication. The effect of fluid helicity injection in the context of recurrence [39] and quasi-recurrence [40] phenomenon is also an interesting study to investigate out, that will also be reported soon. The role of hydrodynamically unstable shear flow [41] at the largest scale is interesting to investigate in this context.…”

Coherent nonlinear oscillations in magnetohydrodynamic plasma

“…The three dimensional kinetic dynamo effect is matched with Galloway et al [11] in the case of ABC flow for a grid resolution of 64 3 . More benchmarking details and specifications about the code are given in earlier papers [12][13][14].…”