An example of interfacial waves generated by a rotational force field

A. B. Zwart - A. D. Sneyd

University of Waikato, Hamilton, New Zealand

Abstract
We began to investigate analytically the perturbations in the aluminium/cryolite interface of an Hall-Heroult cell caused by the presence of a moving carbon dioxide gas bubble distribution on the anode under surface. Perturbation of the electric current about such bubbles generates a moving rotational force distribution which results in small lengthscale waves in the aluminium/cryolite interface. A number of simple analytic models were solved by Fourier series expansion and the results from these models suggest that waves generated by this mechanism in an actual cell are negligible. However, several of the models displayed a system of forced waves propagating away from the model boundaries, which seems unusual considering the global nature of the applied force distribution. We thus turn our attention to these waves in a more theoretical emphasis, and present a description of the waves behaviour. We consider a further model which can be solved asymptotically via Fourier transform and the method of stationary phase. This solution enables us to explain some of the waves behaviour, and to find an expression for the velocity of the wavefront as it moves away from the boundary. Figs 3, Refs 3.