KdV Equation Model in Open Cylindrical Channel under Precession

Abstract

A new model for Korteweg and de-Vries equation (KdV) is derived. The system under study is an open channel consisting of two concentric cylinders, rotating about their vertical axis, which is tilted by slope {\tau} from the inertial vertical z, in uniform rate {\Omega}_1={\tau}{\Omega}, and the whole tank is elevated over other table rotating at rate {\Omega}. Under these conditions, a set of Kelvin waves is formed on the free surface depending on the angle of tilt, characterized by the slope {\tau}, volume of water, and rotation rate. The resonant mode in the system appears in the form of a single Kelvin solitary wave, whose amplitude satisfies the Korteweg-de Vries equation with forced term. The equation was derived following classical perturbation methods, the additional term made the equation a non-integrable one, that cannot be solved without the help of numerical methods. Invoking the simple finite difference scheme method, it was found that the numerical results are in a good agreement with the experiment.