Bifurcation structure of a wind-driven shallow water model with layer-outcropping

François W Primeau,David Newman

doi:10.1016/j.ocemod.2006.10.003

Abstract

The steady state bifurcation structure of the double-gyre wind-driven ocean circulation is examined in a shallow water model where the upper layer is allowed to outcrop at the sea surface. In addition to the classical jet-up and jet-down multiple equilibria, we find a new regime in which one of the equilibrium solutions has a large outcropping region in the subpolar gyre. Time dependent simulations show that the outcropping solution equilibrates to a stable periodic orbit with a period of 8 months. Co-existing with the periodic solution is a stable steady state solution without outcropping. A numerical scheme that has the unique advantage of being differentiable while still allowing layers to outcrop at the sea surface is used for the analysis. In contrast, standard schemes for solving layered models with outcropping are non-differentiable and have an ill-defined Jacobian making them unsuitable for solution using Newton’s method. As such, our new scheme expands the applicability of numerical bifurcation techniques to an important class of ocean models whose bifurcation structure had hitherto remained unexplored.

Highlights

The wind-driven double-gyre ocean circulation is responsible for the transport of heat, mass and fresh water between low and high latitudes, and is important to climate variability
By applying a numerical scheme first proposed by Salmon (2002) to solve the shallow water equations, we have performed the first numerical bifurcation analysis of the double-gyre circulation in the case where layers outcrop at the surface
In one part of parameter space we recovered the multiple equilibria with the jet-up and jet-down solutions first found by Jiang et al (1995)

Summary

Introduction

The wind-driven double-gyre ocean circulation is responsible for the transport of heat, mass and fresh water between low and high latitudes, and is important to climate variability. An important feature of the mid-latitude ocean circulation – found both in observations and numerical simulations – is its lowfrequency variability. In observations decadal time scale variability has been documented by Qiu and Chen (2005) for the Kuroshio extension system and in models intrinsic decadal variability due to non-linear dynamics is common The mechanisms responsible for this variability are not fully understood. The motivation for this paper is to continue a line of study that applies bifurcation theory and dynamical-systems theory to a hierarchy of increasingly more realistic ocean models with the goal of better understanding the dynamics of this flow.

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Conclusion