results, which is just between the slow and fast contraction investigated in the work by @hanke13.

![Average PNS radius (defined by a fiducial density of $10^{11}~ {\rm g}~{\rm cm}^{-3}$) for the 1D (blue line), 2D (green line), and 3D models (red line), respectively. The gray lines labeled as “fit” corresponds to the prescribed PNS evolution with three different values of $R_{\rm f} = 10, 12, $ and 15 km (see text for more details). []{data-label="pns"}](pns.eps){width=".8\linewidth"}

![Top panel shows radial profiles of angle-averaged entropy at 100 ms postbounce for the 1D, 2D-H-1, 3D-H-1 model, respectively. Bottom panel shows spectra of the turbulent kinetic energy as a function of wavenumber ($k$) between our 2D (green line) and 3D (red line) model, respectively. []{data-label="fig:r-s"}](r-ent.eps "fig:"){width=".8\linewidth"}\
![Top panel shows radial profiles of angle-averaged entropy at 100 ms postbounce for the 1D, 2D-H-1, 3D-H-1 model, respectively. Bottom panel shows spectra of the turbulent kinetic energy as a function of wavenumber ($k$) between our 2D (green line) and 3D (red line) model, respectively. []{data-label="fig:r-s"}](sed100ms.eps "fig:"){width=".8\linewidth"}\

Top panel of Figure \[fig:r-s\] shows angle-averaged entropy profile at 100 ms postbounce, after when the difference of the subsequent shock evolution between our 1D, 2D, and 3D models becomes remarkable 