Germain Rousseaux

Observation of negative-frequency waves in a water tank: a classical analogue to the Hawking effect?

The conversion of positive-frequency waves into negative-frequency waves at the event horizon is the mechanism at the heart of the Hawking radiation of black holes. In black-hole analogues, horizons are formed for waves propagating in a medium against the current when and where the flow exceeds the wave velocity. We report on the first direct observation of negative-frequency waves converted from positive-frequency waves in a moving medium. The measured degree of mode conversion is significantly higher than that expected from the theory.

Horizon effects with surface waves on moving water

Surface waves on a stationary flow of water are considered in a linear model that includes the surface tension of the fluid. The resulting gravity-capillary waves experience a rich array of horizon effects when propagating against the flow. In some cases, three horizons (points where the group velocity of the wave reverses) exist for waves with a single laboratory frequency. Some of these effects are familiar in fluid mechanics under the name of wave blocking, but other aspects, in particular waves with negative co-moving frequency and the Hawking effect, were overlooked until surface waves were investigated as examples of analogue gravity (Schutzhold R and Unruh W G 2002 Phys. Rev. D 66 044019). A comprehensive presentation of the various horizon effects for gravity-capillary waves is given, with emphasis on the deep water/ short wavelength case kh1, where many analytical results can be derived. A similarity of the state space of the waves to that of a thermodynamic system is pointed out.

Lorenz or Coulomb in Galilean electromagnetism

Galilean electromagnetism was discovered thirty years ago by Levy-Leblond and Le Bellac. However, these authors only explored the consequences for the fields and not for the potentials. Following De Montigny et al., we show that the Coulomb gauge condition is the magnetic limit of the Lorenz gauge condition whereas the Lorenz gauge condition applies in the electric limit of Levy-Leblond and Le Bellac. Contrary to De Montigny et al., who used Galilean tensor calculus, we use orders of magnitude based on physical motivations in our derivation.

On some applications of Galilean electrodynamics of moving bodies

We discuss the seminal article by Le Bellac and Levy-Leblond in which they identified two Galilean limits (called “electric” and “magnetic” limits) of electromagnetism and their implications. Recent work has shed new light on the choice of gauge conditions in classical electromagnetism. We show that the recourse to potentials is compelling in order to demonstrate the existence of both (electric and magnetic) limits. We revisit some nonrelativistic systems and related experiments, in the light of these limits, in quantum mechanics, superconductivity, and the electrodynamics of continuous media. Much of the current technology where waves are not taken into account can be described in a coherent fashion by the two limits of Galilean electromagnetism instead of an inconsistent mixture of these limits.

Observation of noise correlated by the Hawking effect in a water tank

We measured the power spectrum and two-point correlation function for the randomly fluctuating free surface on the downstream side of a stationary flow with a maximum Froude number F_{max}≈0.85 reached above a localized obstacle. On such a flow the scattering of incident long wavelength modes is analogous to that responsible for black hole radiation (the Hawking effect). Our measurements of the noise show a clear correlation between pairs of modes of opposite energies. We also measure the scattering coefficients by applying the same analysis of correlations to waves produced by a wave maker.

On the electrodynamics of moving bodies at low velocities

We discuss an article by Le Bellac and Levy-Leblond in which they have identified two Galilean limits of electromagnetism (1973 Nuovo Cimento B 14 217–33). We use their results to point out some confusion in the literature, and in the teaching of special relativity and electromagnetism. For instance, it is not widely recognized that there exist two well-defined non-relativistic limits, so that researchers and teachers are likely to utilize an incoherent mixture of both. Recent works have shed new light on the choice of gauge conditions in classical electromagnetism. We retrieve the results of Le Bellac and Levy-Leblond first by examining orders of magnitudes and then with a Lorentz-like manifestly covariant approach to Galilean covariance based on a five-dimensional Minkowski manifold. We emphasize the Riemann–Lorenz approach based on the vector and scalar potentials as opposed to the Heaviside–Hertz formulation in terms of electromagnetic fields.

Viscous fingering in packed chromatographic columns: Non-linear dynamics

Viscous fingering (VF) is a hydrodynamic instability that occurs in a chromatographic column when a less viscous fluid displaces another more viscous one. This instability is detrimental to separation techniques as it leads to distorted peaks and peak broadening. Nonlinear interactions between developing fingers lead to complex dynamics investigated in the present study by means of numerical simulations based on a simple model for miscible VF of finite samples. We review the properties of nonlinear VF and discuss the quantitative measures that can be applied both on such numerical as well as on experimental data to gain insight into the influence of the parameters of the problem on the nonlinear properties of the fingers and on the broadening of output peaks.

Experimental study of dispersion and miscible viscous fingering of initially circular samples in Hele-Shaw cells

Experimental studies are conducted to analyze dispersion and miscible viscous fingering of initially circular samples of a given solution displaced linearly at constant speed U by another solution in horizontal Hele-Shaw cells (two glass plates separated by a thin gap). In the stable case of a dyed water sample having the same viscosity as that of displacing nondyed water, we analyze the transition between dispersive and advective transport of the passive scalar displaced linearly. At low displacement speed and after a certain time, the length of the sample increases as a square root of time allowing to compute the value of a dispersion coefficient. At larger injection speed, the displacement remains advective for the duration of the experiment, with a length of the sample increasing linearly in time. A parametric study allows to gain insight into the switch from one regime to another as a function of the gap width of the cell. In the unstable case of viscous glycerol samples displaced by dyed water, the ...

On the electrodynamics of Minkowski at low velocities

The Galilean constitutive equations for the electrodynamics of moving media are derived for the first time. They explain all the historic and modern experiments which were interpreted so far in a relativistic framework assuming the constant light celerity principle. Here, we show the latter to be sufficient but not necessary.

The C̆erenkov Effect Revisited: From Swimming Ducks to Zero Modes in Gravitational Analogues

We present an interdisciplinary review of the generalized Cerenkov emission of radiation from uniformly moving sources in the different contexts of classical electromagnetism, superfluid hydrodynamics, and classical hydrodynamics. The details of each specific physical systems enter our theory via the dispersion law of the excitations. A geometrical recipe to obtain the emission patterns in both real and wave-vector space from the geometrical shape of the dispersion law is discussed and applied to a number of cases of current experimental interest. Some consequences of these emission processes onto the stability of condensed-matter analogues of gravitational systems are finally illustrated.