Figure 19: (a) Temporal evolution of the volume averaged magnetic energy, Maxwell and Reynolds stresses in the fiducial run are represented by thick, dashed, and dash-dotted curves, respectively. The vertical axis is normalized by the initial magnetic energy , that is , , and where single bracket denotes the volume average of the physical variables. Horizontal axis is normalized by the rotational period . Three typical evolutionary stages, (i) exponential growth stage, (ii) transition stage, and (iii) nonlinear turbulent stage, are denoted by white, dark gray, and light gray shaded regions. (b) The amplitude of power spectra of the magnetic energy along the and axes. The dashed and dotted curves describes the and components respectively. The vertical axis is normalized by the initial magnetic energy . The wave-numbers shown in the horizontal axis are normalized by the . The upper thick curve demonstrates the Kolmogorov slope for isotropic incompressible turbulence . The lower slope is proportional to just for the reference. In our local simulations, we prepare a 2D shearing box which is threaded by the initial vertical field G with imposing initial gas pressure , angular velocity and shear parameter , respectively. Here the shear parameter represents the degree of differential rotation as with being the radial coordinate. The other parameters are fixed to mimic the properties in the vicinity of the PNS’s surface in the postbounce phase (i.e., the density is taken to be and the box size is taken to be (horizontal) (vertical)).