Nonlinear Large-Scale Perturbations of Steady Thermal Convective Dynamo Regimes in a Plane Layer of Electrically Conducting Fluid Rotating about the Vertical Axis

Abstract

We present results of numerical investigation of regimes of steady thermal convective dynamo in a plane layer of electrically conducting fluid rotating about the vertical axis and subjected to large-scale perturbations.

Predictability of Magnetic Field Reversals

“…Integration in time has been carried out by the third-order Runge-Kutta method ETD3RK [39] with the exponential time differencing, which was previously successfully used in [37,40,41].…”

“…The nonlinear stability of the space-periodic steady state for Ta = 675 from the branch S R1 8 [42] was studied in [41] allowing for perturbations, whose period in the direction x i is M i times larger for integer M i ≤ 4. The perturbed regime in the unitary periodicity box (for…”

“…which we discuss in the sequel. For these parameter values, the time-stepping with the step length of 0.001 has been performed for N 1 = 255, N 2 = 127, N 3 = 97 -this resolution was found sufficient in computations [41]. Figure 1 presents the kinetic, E v , and magnetic, E b , energies averaged, like in [41], over the volume of the periodicity cell as functions of time.…”

“…For these parameter values, the time-stepping with the step length of 0.001 has been performed for N 1 = 255, N 2 = 127, N 3 = 97 -this resolution was found sufficient in computations [41]. Figure 1 presents the kinetic, E v , and magnetic, E b , energies averaged, like in [41], over the volume of the periodicity cell as functions of time. We observe that the regime consists of what we call segments; each such segment starts when the magnetic energy falls to a local minimum below 10 −6 .…”

“…The flow and the dominant magnetic mode (its growth rate is 0.14) have the symmetry rγ x 2 L 2 /2 . We use the same notation for symmetries, as in [41,42]: γ x n α : (x 1 , x 2 , x 3 ) → (x 1 + α, x 2 , x 3 ) for n = 1, 2 are shifts in the directions of the horizontal Cartesian axes x n (above, the shift α is arbitrary); s 2 : (x 1 , x 2 , x 3 ) → (−x 1 , −x 2 , x 3 ) is the reflection in horizontal planes about the origin (an appropriate horizontal shift of the origin of the coordinate system may be necessary for detecting this symmetry); and r : (x 1 , x 2 , x 3 ) → (x 1 , x 2 , 1 − x 3 ) is the reflection about the horizontal midplane. Finally, the symmetry q : (v, θ, b) → (v, θ, −b) reverses the magnetic field.…”