Topological Effects of a Vorticity Filament on the Coherent Backscattering Cone

In this Letter, we report on the effects of a vorticity filament on the coherent backscattering cone. Using ultrasonic waves in a strongly reverberating cavity, we experimentally show that the discrete number of loops of acoustic paths around a pointlike vortex located at the center of the cavity drives the cancellation and the potential rebirth of the coherent backscattering enhancement. The vorticity filament behaves, then, as a topological anomaly for wave propagation that provides some new insight between reciprocity and weak localization.

Figure 1

Intensity of the acoustic wave emitted and received by $T_1$ as a function of time. Two specular reflections are visible. The black vertical lines correspond to the propagation times of the wave for the distances indicated. The gray domain corresponds to a typical time window over which the CBC is measured. Inset: The experimental setup.

Figure 2

Phase shift for the transmitted signal between $T_1$ and $T_2$ induced by a vorticity filament measured as a function of the rotation speed of the motor (color coded) at a given pump flow ($0.06\mathrm{L}{\mathrm{s}}^{-1}$). The measurements are fitted to Eq. (1) to extract the vorticity parameter $\alpha$ of the vortex (solid lines). Inset (a): The fitted vorticity parameter $\alpha$ for the data plotted in the main figure as a function of the rotation speed of the upper circular plate. Inset (b): Phase shift for the transmitted signal between $T_1$ and $T_2$ induced by a solid rotation (i.e., pump turned off).

Figure 3

Coherent backscattering cones measured with solid rotation (left, no pump), and measured with a vorticity filament (right, pump imposing a flow of $45\mathrm{mL}{\mathrm{s}}^{-1}$). Similar rotation speeds (color coded) were used without and with the pump. The darkest curves on both sides show the same measurements realized without any flow. Inset: Normalized enhancement factor $E_{\mathsf{N}}$ of the backscattering cones measured with solid rotation ($+$) and with a vorticity filament ($\times$), as a function of the rotation speed of the upper plate.

Figure 4

(a) Enhancement factor of the coherent backscattering cone as a function of the vorticity parameter $\alpha$ for different travel times. Each color corresponds to a travel time, and the corresponding theoretical curve is plotted in the same color. For the sake of clarity, the three plots have been translated by $\alpha =0.01$. Inset: Plot of the average loop number $\beta$ with respect to travel time. (b) Predictions of the theory on a larger vorticity parameter range exhibiting a rebirth of the CBC for $\alpha =0.5$.