Correlations on weakly time-dependent transcritical white-hole flows

Johan Fourdrinoy (1) , Scott Robertson (2, 3) , Nicolas James (4) , Alessandro Fabbri (5, 2) , Germain Rousseaux (1)

1 PPrime [Poitiers] - Institut Pprime [UPR 3346]
2 IJCLab - Laboratoire de Physique des 2 Infinis Irène Joliot-Curie
3 Laboratoire Charles Fabry / Gaz Quantiques
4 LMA [Poitiers] - Laboratoire de mathématiques et applications [UMR 7348]
5 Dep. de Fisica Teorica and IFIC

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 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 is 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. In gated flows, however, the undulation is ``attached'' to the obstacle, and the correlation pattern is likely due to the scattering of a stochastic ensemble of surface waves.

Domaines: Relativité Générale et Cosmologie Quantique [gr-qc]; Dynamique des Fluides [physics.flu-dyn]

Johan Fourdrinoy, Scott Robertson, Nicolas James, Alessandro Fabbri, Germain Rousseaux. Correlations on weakly time-dependent transcritical white-hole flows. 2021. ⟨hal-03491809v1⟩