Resonantly Forced Waves and the Effect of Tank Geometry on the Free Surface

Abstract

This thesis examines the evolution of small-amplitude, resonantly forced fluid waves in a tank of finite extent. A rectangular and annular tank are considered, with the fluid in each tank subject to periodic lengthwise or radial forcing. The resonant forcing of fluid in a rectangular tank has been examined previously. How varying the geometry of the tank affects the evolution of the free surface is not yet fully understood. This work aims to contribute toward better understanding the interplay between geometric and resonant effects in axisymmetric geometries. Analytic and numerical results are used to examine the effects brought forth by varying the tank geometry. The responses in the rectangular and annular tanks can be qualitatively distinct. The inner radius of the annular tank is connected to the degree to which the underlying spectrum is commensurate, and this is shown to play a key role in determining how the results vary.