Viscous Effect on Solitary Kelvin Wave in Open Cylindrical Channel under Precession

Abstract

Viscous effect is introduced into the system of Navier–Stokes equations, that were derived to study the solitary Kelvin mode in an open cylindrical channel that precesses. Accordingly, three new weakly nonlinear models were derived: Korteweg–de Vries-Burgers, and two new Benjamin–Bona–Mahony-Burgers. The first was solved analytically by discussing the phase solution and numerically using an implicite finite difference method to track the solution with time under diffusion effect. The second two models were solved numerically only using the Quartic B-Spline collocation method. By manipulating the scaling the first model included only the gravity force effect, and the second included both gravity and Coriolis forces. The numerical method is tested experimentally by comparing the velocity solutions with ADV signal extracted from the ADV measurements under bore conditions, and the amplitude solution with the solitary kelvin mode.