than $D_s$ (i.e., $D_s>\pi/k$), the integral would give rise to an average of zero, leaving those that are slowly varying in space (i.e., $\pi/k > D_s$) in $\bar{\Psi}(x)$, and the difference $\delta\Psi \equiv \Psi -\bar\Psi$ characterizes the part of $\Psi$ composed roughly of wavevectors $k\gtrsim \pi/D_s$. Later in Sec. \[sec:BCRStim\], we use the above procedure at each time and exhibit a spacetime diagram of $|\delta\Psi(x,t)|$, in which the slowly-varying part of the background flow ($\Psi_{\rm bf}$ with $k\sim 0$) is removed to bring out $\psi_{\rm HR}$.

Analysis of the simulated experiment {#sec:experiments}
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Formation of the BH-WH cavity 
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In the experiment of [@nphys3104] a BH-WH cavity is established in a quasi-one-dimensional, laboratory BEC held by a confining potential, $U(x)$, as shown in Fig.\[fig:exp\](a). By sweeping a potential step of depth $U_{s}$ at uniform speed $v_{s}$ across the BEC, BH and WH are established ($U_s$ is on the order of $10^{-9}$ K, and $v_s$ is 0.21 mm/s). Atoms are accelerated in the direction opposite to the step motion due to the precipitous drop in the potential. This creates a supersonic flow behind the step and forms a BH at the step edge, $x_{\mathrm{BH}}$. The accelerated atoms gradually slow as they 