We have realized a stationary transcritical flow of water in a flume that possesses the analogue of a black hole horizon for long-wavelength surface waves. The horizon has been probed via the scattering of an incident co-current wave, which partially scatters into counter-current waves on either side of the horizon, yielding three outgoing waves (of which one is anomalous) rather than two in the absence of transcriticality. The measured scattering coefficients are in good agreement with the predictions of the non-dispersive theory, where the kinematical description in terms of an effective spacetime metric is exact. We also show the emergence of characteristic peaks in the two-point correlation function of free surface deformations, one of which indicates the presence of a horizon and in quantum settings would be used to demonstrate the presence of the thermal analogue Hawking effect.Recent years have witnessed an explosion of interest in Analogue Gravity [1]. This newly emergent field builds on Unruh's insight of 1981 [2] that, using the mathematical equivalence between wave propagation in curved spacetimes and in condensed matter systems, one can realize in the laboratory an analogue black hole and test Hawking's prediction that black holes emit radiation [3,4]. An analogue black hole is represented by an accelerating flow which at some point becomes transcritical. The point where the flow reaches the speed of sound is the (acoustic) horizon for sound waves, in analogy with the (event) horizon for light in a gravitational black hole. Because wave propagation close to the horizon is equivalent in the two cases, the Hawking effect, which is derived from purely kinematical considerations, should be present also in the analogue system. This effect has been the main driving force behind the Analogue Gravity program since its inception, with experimental studies in a wide range of physical systems, including photons in nonlinear optics [5,6], exciton-polaritons [7] and Bose-Einstein condensates [8,9].Surface waves on fluids are describable in this way, and there have been a number of experiments aimed at realizing and probing the analogue spacetimes [10][11][12][13][14][15][16]. Most, however, have focused on analogue white hole-like flows, which are time-reversed analogue black hole-like flows. While wave scattering on transcritical flows has been studied from a theoretical perspective [17,18], such flows have not yet been realized in experiment, not even of the white hole type. Moreover, white hole horizons are associated with the production of a stationary undulation [19,20] which complicates the effective spacetime and the scattering it induces.In this paper we report on the first-known scattering experiment of surface waves on a 1 + 1-dimensional analogue black hole, namely an effectively one-dimensional transcritical water flow inducing an effective spacetime metric with a black-hole horizon. We show how the waves available in each of the asymptotic regions indicate that a horizon is present. We also report on ...
The aerodynamics of the Stardust Sample Return Capsule are analyzed in the lowdensity, transitional ow regime using free-molecular, Direct Simulation Monte Carlo, Navier-Stokes, and Newtonian methods to provide inputs for constructing a transitional ow bridging relation. The accuracy of this bridging relation in reconstructing the aerodynamic coe cients given by the more exact methods is presented for a range of ight conditions and vehicle attitudes. There is good agreement b e t w een the various prediction methods, and a simple sine-squared bridging relation is shown to provide a reasonably good description of the axial force, normal force, and pitching moment o v er a range of Knudsen numbers from 0.001 to 10. The predictions show a static instability of the Stardust capsule in the free-molecular regime that persists well into the transitional ow. The addition of a thin disk to the base of the capsule is shown to remove this static instability. H o w ever, the extremely high entry velocity of 12.6 km s for the proposed trajectory introduces di cult design issues for incorporating this disk caused by the high aerothermal loads that occur even under relatively rare ed conditions.
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