recede from the step, due to the rising potential. This causes the flow to become subsonic at a critical distance $L$ behind the step, forming a WH, $x_{\mathrm{WH}}$. Not far beyond $x_{\rm WH}$ the flow velocity in the laboratory frame drops to zero, roughly where $U(x)-U_{s}=U(x_{\mathrm{BH}})$ (this implies that $L$ increases slightly as $x_{\mathrm{BH}}$ moves toward the center of the trap). This procedure produces the flow structure shown in Fig. \[fig:exp\](c).

To determine the flow structure, we implement the spatial WFT described in Sec. \[sec:WFT0\]. Figure \[fig:exp\](b) is a local wavevector spectrum $|\Psi(k,x)|^2$ with $D=5$ $\mu$m, defined in the laboratory frame at a moment during the sweep \[Fig. \[fig:GP1\](e)\]. There is a dominant streak, indicating the background condensate flow, $\Psi_{\rm bf}$, for which the peak position at each $x$ defines the background wavevector, $k_{\rm bf}(x)$. The regions with zero wavevector, $k_{\rm bf}\sim 0$, correspond to the non-accelerated, subsonic BEC; the region behind the step with $k_{\rm bf}\sim -1.4$ $\mu$m$^{-1}$ corresponds to the accelerated, supersonic flow. The blue (dark gray) curve in Fig.\[fig:exp\](c) is minus the flow velocity in the rest frame of the step, $v(x)=v_{\rm bf}(x)-v_{\rm s}$, where $v_{\rm bf}(x)=\hbar k_{\rm bf}(x)/m$ is the background flow velocity in the laboratory 