Successive bifurcations in a shallow-water model applied to the wind-driven ocean circulation

Abstract

Abstract. Climate - the "coarse-gridded" state of the coupled ocean - atmosphere system - varies on many time and space scales. The challenge is to relate such variation to specific mechanisms and to produce verifiable quantitative explanations. In this paper, we study the oceanic component of the climate system and, in particular, the different circulation regimes of the mid-latitude win driven ocean on the interannual time scale. These circulations are dominated by two counterrotating, basis scale gyres: subtropical and subpolar. Numerical techniques of bifurcation theory are used to stud the multiplicity and stability of the steady-state solution of a wind-driven, double-gyre, reduced-gravity, shallow water model. Branches of stationary solutions and their linear stability are calculated systematically as parameter are varied. This is one of the first geophysical studies i which such techniques are applied to a dynamical system with tens of thousands of degrees of freedom. Multiple stationary solutions obtain as a result of nonlinear interactions between the two main recirculating cell (cyclonic and anticyclonic) of the large- scale double-gyre flow. These equilibria appear for realistic values of the forcing and dissipation parameters. They undergo Hop bifurcation and transition to aperiodic solutions eventually occurs. The periodic and chaotic behaviour is probably related to an increased number of vorticity cells interaction with each other. A preliminary comparison with observations of the Gulf Stream and Kuroshio Extensions suggests that the intern variability of our simulated mid-latitude ocean is a important factor in the observed interannual variability o these two current systems.

Sensitivity of a double-gyre ocean model to details of stochastic forcing

“…Cessi and Ierley (1995) conjecture that all equilibria are of significance in the description of the low-frequency variability of the wind-driven circulation, regardless of their stability. Comparable experiments with the primitive equations were performed by Speich et al (1995) and Jiang et al (1995). Despite the fact that the primitive equations do not satisfy quasi-geostrophic symmetry, they showed that the asymmetric equilibria come in pairs, in agreement with the quasi-geostrophic calculations.…”

“…Beside the role played by dissipative processes within the western boundary currents, the rich structure of multiple equilibria is becoming evident. Several authors show that, for a range of parameters, the double-gyre circulation possesses multiple steady states (e.g., Cessi and Ierley, 1995;Speich et al, 1995;Jiang et al, 1995;Primeau, 1998a,b;Scott and Straub, 1998). More precisely, these authors explicitly computed fixed point solutions for a broad range of parameters except Jiang et al (1995).…”

On a Wind-Driven, Double-Gyre, Quasi-Geostrophic Ocean Model: Numerical Simulations and Structural Analysis

“…These gyres have a typical horizontal scale of about one thousand kilometers. Several main features of the double-gyre ocean circulation have been identified by analyzing the observational data as well as by numerical simulations; see, for instance, Speich and Ghil [30], Jiang et al [12], and Speich et al [29]. First, these gyres are dominant and persistent; second, they represent typical seasonal and inter-annual oscillations of the large-scale ocean; third, they transfer potential energy.…”

“…Many published results are available on wind-driven ocean circulation; see, among others, Veronis [33], Pedlosky [22], Stommel [31], Charney [5], Haidvogel et al [9], Speich and Ghil [30], Jiang et al [12], Speich et al [29], Chassignet [6,7,21], Holland [10], Holland and Rhines [11], Berloff and Meacham [1,2], and Meacham and Berloff [20]. They used this model to study the formation of the western boundary currents in the North Pacific and the North Atlantic.…”

Coupled ocean-atmosphere model system for studies of interannual-to-decadal climate variability over the North Pacific Basin and precipitation over the Southwestern United States

“…This predictability is associated with ocean dynamics and its interaction with the atmosphere (Davis, 1976;Namias, 1979;Wallace and Jiang, 1987). Recent studies (Jacobs et al, 1994;Speich et al, 1995) suggest that the intrinsic variability of North Pacific major currents may modulate and interact with the sea surface temperature (SST) anomaly signals on a decadal time scale. This may give a background of the fluctuation of precipitation.…”