Effects of the chaotic behavior of a superposition of waves in the flux across a channel

Abstract

Several numerical experiments were carried out to study the effects of chaotic behavior on the net tracer flux across a channel. The flow is given by a superposition of two propagating waves. The domain was set up so that a mode-I wave would fit on it, and the perturbation was a mode-4 wave. The experiments were carried out using a grid model with a second-order upwind differencing scheme. Simple Newtonian diffusion was used, and the velocities were calculated from a stream-function satisfying no normal flow boundary conditions. The experiments showed a small increase in the flux does appear due to the chaotic behavior, but this effect is only around 5% when the flux is compared to the one obtained from a pure 1-mode wave system. In contrast there is a difference of around 20% when the pure mode- 1 wave is compared to the pure mode-4 wave, the first one being more transportive. The chaotic behavior of the system is described in detail and a Lagrangian experiment was carried out as well to examine the motion of the particles and to explore a different approach to describing the dispersion of a tracer.