Ocean–atmosphere dynamics and Rossby waves in fractal anisotropic media

Abstract

We study some basic problems arising in ocean–atmosphere dynamics including the ocean surface waves and Rossby waves based on the concept of product-like fractal measure introduced recently by Li and Ostoja-Starzewski in their formulation of anisotropic media. We have derived the fractal fluid equations and we have analyzed several fundamental problems related to earth’s ocean and Rossby waves. This study demonstrates the mutual effects of eastward-propagating stationary barotropic Rossby waves and westward-propagating stationary barotropic Rossby waves in the atmosphere which are in agreement with some recent studies and satellite observations. Numerical estimates of fractal dimensions were also given.