Visualizations of (from top to bottom) the vorticity , the stream function , the current density , and the vector potential for the square, circular, and elliptic geometries. The three columns correspond to (from left to right) the time instants of series B for which (Fig. 2) is maximal. The time is normalized by the initial turn-over time. Note that the numerical method used in the present work does not impose a zero value of and at the wall of the fluid domain. Thus a constant value was subtracted from and at every point in the fluid domain to impose this.
Influence of the Reynolds number on the spin-up: time dependence of the absolute value of the normalized kinetic angular momentum averaged over ten simulations of series A and series B for the square, circular, and elliptic geometries, from top to bottom. Here and in the following, the angular momentum is always normalized by [and for the magnetic equivalent] corresponding to the angular momentum of a solid-body having the same initial kinetic energy.
Comparison of series B (top) and series C (bottom). Time evolution of the angular momentum (left) and angular field (right) in the square, circular, and elliptic geometries. Only one realization is chosen from each series.
Time evolution of angular momentum for series B . The influence of the magnetic pressure on the spin-up in the square, circle, and ellipse is illustrated by changing the ratio , while keeping fixed. The magnetic pressure is changed by varying , while keeping constant .
Comparison of the time derivative of and the mean current . The run corresponds to one realization in the circle with and .
Parameters of the simulations of series A, B, and C. : number of spin-up. The initial kinetic and magnetic energies are and , respectively, for all simulations. The penalization parameter is chosen for all runs.
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