Petroleum Patch Transport in Marine and Coastal Zones

Abstract

The transport of pollutants is an important issue in a variety of natural systems. This study deals with distributive mixing of petroleum patches in tidal flows. A good approximation of such flows was suggested by Zimmerman [1]. He deviated from earlier attempts at modeling tidal flows by means of turbulence theory and adopted the idea of chaotic advection, first put forward by Aref [2]. In this pioneering paper it was shown that chaotic mixing of a passive tracer (which in our case will be the petroleum patch) may occur even in deceptively simple flow systems. Zimmerman [1] realized that the macroscale flow in a tidal sea is not much more complicated than chaotic advection model and so should lead to similar phenomena. In particular, he suggested that the many fine striations often observed in scalar dispersal were due to chaotic motion driven by the macroscale, rather than microscale turbulent mixing. By numerical simulations he demonstrated that the patterns formed by dispersed passive particles were very similar to field observations. In the recently published tutorial paper Aref [3] described numerous applications of chaotic advection in fluid mechanics, in general, and in geophysical and geological flows, in particular. It was shown in many other works [4–6] how important it is to identify the parameters and conditions that lead to widespread chaotic advection. In the course of flow evolution an initially designated interface of any petroleum patch may become extremely convoluted, and it appears difficult to follow pattern structures in full detail.