Correlations on weakly time-dependent transcritical white-hole flows

Abstract

We report on observations made on a run of transcritical flows over an obstacle in a narrow channel. Downstream from the obstacle, the flows decelerate from supercritical to subcritical, typically with an undulation on the subcritical side (known in hydrodynamics as an undular hydraulic jump). In the Analogue Gravity context, this transition corresponds to a white-hole horizon. Free surface deformations are analyzed, mainly via the two-point correlation function which shows the presence of a checkerboard pattern in the vicinity of the undulation. In non-gated flows where the white-hole horizon occurs far downstream from the obstacle, this checkerboard pattern is shown to be due to low-frequency fluctuations associated with slow longitudinal movement of the undulation. It can thus be considered as an artifact due to a time-varying background. In gated flows, however, the undulation is typically "attached" to the obstacle, and the fluctuations associated with its movement are strongly suppressed. In this case, the observed correlation pattern is likely due to a stochastic ensemble of surface waves, scattering on a background that is essentially stationary.

Logarithmic catastrophes and Stokes’s phenomenon in waves at horizons

“…This situation is capable of mimicking many aspects of black hole physics where the effective spacetime metric depends on the fluid flow and acoustic waves play the role of light [11][12][13][14][15]. Analogue event horizons for classical waves, including the classical analogue of Hawking radiation, have been observed in water tank experiments [16][17][18][19][20][21][22] and also in optical fibres [23][24][25]. Another system where analogue event horizons can be created is a flowing Bose-Einstein condensate (BEC) formed from ultracold atoms.…”