Evolution of turbulence in the presence of an obstacle under the control of a PEF with and . (a) PEF ( ) successfully excites waves on big obstacle ( ). (b) Wave cannot be generated from the obstacle ( ) by weak PEF ( ). (c) PEF ( ) applied on medium with small obstacle ( ) cannot induce waves. In the three evolutions, the initial states are identical. The center hollow in every system represents the obstacle.
The process of successful control by a REF with E 0 = 0.8 and TR = 3.3. The radius of obstacle is 3.1.
Development of turbulence with PEF (a) and with REF (b). Parameters: E 0 = 0.4, TP = TR = 3.3, R = 8.0.
Rmin vs. Emin curve when a PEF (squares) and a REF (circles) are applied separately. Rmin and Emin are minimal radius of the obstacle and minimal intensity of the electric field to successfully excite waves, respectively. Inset (a) is the ratio of Rmin (REF/PEF). Inset (b) shows the dependence of minimum period of applied REF on radius of obstacle. The dot line fits the simulation data.
A process shows how a spiral wave is generated from a circular obstacle by a REF. The (yellow) arrows show the direction of the clockwise rotating electric field. The (red) arrows shows the prolonged tips resulted from REF while the (white) arrow denotes another propagating tip of the crescent wave.
The application of REF and PEF results in different time to suppress turbulence. Four points around the obstacle has been shown in Fig. 1(a) (see the pattern at t = 10). The dashed lines show temporary periods of fixed points controlled by REF while the solid lines show that by PEF. (a) Grid on the downside of the obstacle (blue point in Fig. 1(a) ). (b) Grid on the upside of the obstacle (yellow point in Fig. 1(a) ). (c) Grid on the left side of the obstacle (green point in Fig. 1(a) ). (d) Grid on the right side of the obstacle (magenta point in Fig. 1(a) ). The frequency of background turbulence without control, which can be obtained by FFT, is 0.262 (corresponding period 3.82). The period of the electric field is 3.3.
Evolution of turbulence around an elliptic obstacle (The lengths of long-axis and short-axis are 8.0 and 2.0, respectively) under the control of PEF with E 0 = 0.2 and TP = 3.2.
Turbulence suppression around an elliptic obstacle by a REF with E 0 = 0.2 and TR = 3.2.
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