Hydrodynamic surface wave analogues for quantum mechanics and optics

quantum-dropIn a special joint session of the water waves programme and the quantum control programme, on Thursday afternoon, Paul Milewski talked about two examples where phenomena in free surface flows have analogues in quantumology and optics.  Water waves differ fundamentally from light waves because of the importance of dispersion and nonlinearity.  However, with pulsed lasers nonlinearity and dispersion can show up.  In this case a focussing nonlinear Schodinger equation can be derived as a model which is exactly the same as a deep water surface waves with moderate values of surface tension.  Experimental and numerical results were presented showing that the focussing is very similar in both cases. The second part of the talk was on the behaviour of a drop of fluid impacting a free surface.  Surprisingly, high speed photography shows that the drop may bounce before penetrating. Couder & Fort (2006) enhanced the experiment, by introducing a Faraday-like forcing at the appropriate frequency to the vessel, allowing the drop to remain on the surface seemingly indefinitely, including “walking” around the surface, and creating secondary waves. This experiment has now been generalized in several directions: free particle in a corral, more than one drop, and a hydrodynamic version of the two-slit experiment.  Paul then introduced a theoretical model for the phenomena based on a “virtual wave tank”.  The fluid was modelled as a linear viscous fluid, with a particle model for the drop. A bifurcation diagram was constructed which correlates well with the experiments.  Collaborators on this project are Zhan Wang (UCL), John Bush (MIT), Andre Nachbin (IMPA) and Carlos Galeano-Rios (IMPA). A video of the talk is available here.

This entry was posted in Uncategorized. Bookmark the permalink.