Two Variations on Normal Modes: Sloshing in Free Containers & Bragg Resonance
Dr Andrzej Herczynski (Department of Physics, Boston College, USA)
Tuesday 7th August, 2012 13:00-14:00 Mathematics Building, room 325
Standing waves in a container partially filled with water and free to move horizontally inevitably cause the vessel to accelerate. A variety of rectilinear motions can arise depending on the initial conditions. In the simplest case, the container oscillates about a fixed position, out-of-phase with the liquid within. This counter-synchronous sloshing is investigated using linearized potential flow theory for vessel shapes amenable to analytical solutions. Experimental results for rectangular boxes, cylinders, etc., are compared to the theoretical predictions. A separate study concerns forced wave motion in a rectangular container of sinusoidal bottom partially filled with water. The theory of Howard and Yu predicts the existence of resonant normal modes—called Bragg resonance—wherein the amplitude grows exponentially, either from one end of the channel to the other or from the center out in each direction, depending on the endwall phases of the corrugated floor. Experiments confirm these predictions.