Speaker
Description
Analogue Gravity [1] enables the replication and investigation of phenomena normally associated with (Quantum) Field Theory in Curved Spacetime through meticulously controlled tabletop experiments. In the particular system of a classical open channel flow, gravity waves on the surface of an inviscid, incompressible and irrotational fluid serve as a means to simulate phenomena akin to those observed around black holes within laboratory settings [2]. The flow, if transcritical, plays the role of an effective spacetime featuring a horizon. This approach provides a pathway to experimentally investigate various classical instabilities associated with black (and white) holes [3-7].
While the assumption of an irrotational flow is necessary to construct the analogy, it is in practice a strong assumption. Friction on the bottom of the channel tends to induce a boundary layer where the flow velocity drops rapidly to zero [6], while flow recirculation tends to occur in the downstream wake of an obstacle [7]. It is thus an experimentally relevant question to determine how the wave propagation is altered by a non-trivial depth-dependence of the flow.
In this presentation, we propose a novel approach to construct an analog model incorporating gravity waves while considering the effects of vorticity. Our model involves an incompressible and inviscid fluid flowing in two layers: one characterised by constant vorticity at the bottom and another with vanishing vorticity at the top, with perturbations applied to the interface between the layers and
on the free surface. Using this method, we derive new equations of motion for both the scalar field associated with the potential velocity and a new scalar field linked to the variation of vorticity. We
develop a new Lagrangian, define a novel scalar product, and deduce WKB-like solutions [8] for the fields. Finally, we compute the scattering coefficients associated with modes falling into an analogue
black hole [6].
[1] C. Barceló, S. Liberati, and M. Visser, “Analogue gravity,” Living Reviews in Relativity, vol. 8, Dec. 2005.
[2] R. Schützhold and W. G. Unruh, “Gravity wave analogues of black holes,” Phys. Rev. D, vol. 66, p. 044019, Aug 2002.
[3] G. Rousseaux, C. Mathis, P. Maïssa, T. G. Philbin, and U. Leonhardt, “Observation of negative-frequency waves in a water tank: a classical analogue to the hawking effect?,” New Journal of Physics, vol. 10, p. 053015, may 2008.
[4] S. Weinfurtner, E. W. Tedford, M. C. J. Penrice, W. G. Unruh, and G. A. Lawrence, “Measurement of stimulated hawking emission in an analogue system,” Phys. Rev. Lett., vol. 106, p. 021302, Jan 2011.
[5] L.-P. Euvé, F. Michel, R. Parentani, T. G. Philbin, and G. Rousseaux, “Observation of noise correlated by the hawking effect in a water tank,” Phys. Rev. Lett., vol. 117, p. 121301, Sep 2016.
[6] L.-P. Euvé, S. Robertson, N. James, A. Fabbri, and G. Rousseaux, “Scattering of co-current surface waves on an analogue black hole,” Physical Review Letters, vol. 124, Apr. 2020.
[7] J. Fourdrinoy, S. Robertson, N. James, A. Fabbri, and G. Rousseaux, “Correlations on weakly time-dependent transcritical white-hole flows,” Phys. Rev. D, vol. 105, p. 085022, Apr 2022.
[8] L. C. Baird, “New integral formulation of the schrödinger equation,” J. Math. Phys., vol. 11, pp. 2235–2242, Aug 1970.
