On nonlinearity in three-dimensional equatorial flows

Abstract

We examine an aspect of the modelling of the underlying fluid motion in the equatorial region of the ocean. In particular, we assess whether nonlinearity is inherently vital in capturing the three-dimensional upwelling and downwelling phenomena. A recent applied mathematical approach has successfully captured these processes through an application of asymptotic approximations to the Euler equation, resulting in a simplified yet nonlinear model. This note demonstrates that any linearisation of the fluid flow will fail to capture the emergence and persistence of similar large-scale coherent structures.

Keywords:

• Nonlinearity
• geophysical fluid dynamics
• non-traditional
• β -plane

2010 Mathematics Subject Classification:

• 37N10
• 76U05
• 76B70