6.1 Wave tank experiments

As we have seen, waves in shallow water can be considered to be a particularly simple analogue gravity system. (See Section 4.1.3.) Experimentally, water basins are relatively cheap and easy to construct and handle. In particular, shallow water basins (more precisely, wave tanks or wave flumes) have acquired a prominent role in recent years. In particular, such technology underlay the 1983 work of Badulin et al. [17Jump To The Next Citation Point], and such wave tanks are currently used by groups in Nice, France [532Jump To The Next Citation Point] and Vancouver, Canada [682Jump To The Next Citation Point]. The Nice experiments have been carried out using a large wave-tank 30 m long, 1.8 m wide and 1.8 m deep. The simplest set-up with such a device is to send water waves (e.g., produced by a piston) against a fluid flow produced by a pump. To generate a water-wave horizon, a ramp is placed in the water, with positive and negative slopes separated by a flat section. When a train of waves is sent against the reverse fluid flow there will be a place where the flow speed equals the group velocity of the waves – there a group velocity horizon will be created. (Remember that in the shallow-water regime the low momentum co-moving dispersion relation for surface water waves is 2 ω = gk tanh(kh ) where g denotes the gravitational acceleration of the Earth at the water surface and h is the height of the channel.) For incident waves moving against the flow it would be impossible to cross such a horizon, and in the sense that the system is the analogue of a white-hole horizon, the time reversal of a black-hole horizon. (In the engineering and fluid mechanics literature this effect is typically referred to as “wave blocking”.)

Remarkably, in 2007 Rousseaux et al. [532Jump To The Next Citation Point] reported the first direct observation of negative-frequency waves, converted from positive-frequency waves in a moving medium, albeit the degree of mode conversion appears to be significantly higher than that expected from theory. The same group has now set up a more compact experiment based on the hydraulic jump, wherein measurements of the “Froude cones” convincingly demonstrate the presence of a surface-wave white hole [334Jump To The Next Citation Point], (as described in Sections 4.1.3 and 4.1.4 and possibly implicit in the results of Badulin et al. [17Jump To The Next Citation Point]).

A related experiment, with a smaller water basin, performed under the auspices of the gravitation theory group (Physics) and the fluid mechanics group (Civil Engineering) at the University of British Columbia, has recently (August 2010) reported the detection of stimulated Hawking emission [682Jump To The Next Citation Point]. This stimulated Hawking emission is a classical effect that (via the usual discussion in terms of Einstein A and B coefficients) is rather closely related to spontaneous quantum Hawking emission. A central result of the Weinfurtner et al. group is that the relevant Bogoliubov coefficients have been experimentally measured and are observed to satisfy the expected Boltzmann relation

2 { } |β|- = exp − -2πω--- . (312 ) |α|2 gH∕cH
More details of the experimental setup can be found in [682Jump To The Next Citation Point], and additional details will soon be available in planned follow-up articles.
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