Global Bifurcation of Shilnikov Type in a Double-Gyre Ocean Model

Nadiga, Balasubramanya T.; Luce, Benjamin P.

doi:10.1175/1520-0485(2001)031<2669:gbosti>2.0.co;2

Cited by 53 publications

(37 citation statements)

References 31 publications

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“…Kondrashov et al (2004) also discussed this role more recently for transitions between the realistic NH regimes of the Marshall and Molteni (1993) three-layer QG model. Hetero-and homoclinic orbits were shown to play an important role in the interannual and interdecadal LFV of the midlatitude ocean's wind-driven circulation (Meacham 2000;Chang et al 2001;Nadiga and Luce 2001;Simmonet et al 2003a,b). Crommelin (2002Crommelin ( , 2003 explored in detail the role of such orbits in a low-order and an intermediate-order model of the extratropical atmosphere, respectively; the former had 10, the latter 231 variables.…”

Section: Transition To Chaosmentioning

confidence: 99%

Bimodal Behavior in the Zonal Mean Flow of a Baroclinic β-Channel Model

Kravtsov

Robertson

Ghil

2005

Journal of the Atmospheric Sciences

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The dynamical origin of midlatitude zonal-jet variability is examined in a thermally forced, quasi-geostrophic, two-layer channel model on a β-plane. The model's behavior is studied as a function of the bottom-friction strength.Two distinct zonal-flow states exist at realistic, low and intermediate values of the bottom drag; these two states are maintained by the eddies and differ mainly in terms of the meridional position of their climatological jets. The system's low-frequency evolution is characterized by irregular transitions between the two states.For a given branch of model solutions, the leading stationary and propagating empirical orthogonal functions are related to eigenmodes of the model's dynamical operator, linearized about the climatological state on this branch. Nonlinear interactions between these modes are instrumental in determining their relative energy level. In particular, the stationary modes' self-interaction is shown to vanish. Thus, these modes do not exchange energy with the mean flow and, consequently, dominate the lowest-frequency behavior in the model. The leading stationary mode resembles with the observed annular mode in the Southern Hemisphere.The bimodality is due to nonlinear interactions between nearly equivalent-barotropic, stationary and propagating modes, while the synoptic eddies play a modest role in determining the relative persistence of the two states. The role of synoptic eddies is very substantial only at unrealistically high values of the bottom drag, where they give rise to ultra-low-frequency variability by modifying the jet in a way that reinforces generation of the eddy field. This type of behavior is related to the presence of a homoclinic orbit in the model's phase space and is not apparent for more realistic, lower values of the bottom drag. 1 . IntroductionIn this paper, we study the origin of the zonally symmetric component of extratropical atmospheric variability. Midlatitude atmospheric behavior is characterized by a variety of spatial and temporal scales. Major weather phenomena are associated with fast baroclinic waves, whose breaking forms synoptic eddies; the spatial structures of these baroclinic phenomena vary with height, and their time scales are on the order of a week and shorter. In contrast, the midlatitude low-frequency variability (LFV), whose time scale is longer than that of synoptic eddies, is predominantly equivalent barotropic (Wallace 1983). The annular modes consist of meridional displacements of the zonally averaged zonal jet.The next EOF of the zonal-mean flow in both hemispheres is associated with irregular weakening and strengthening of the jet (Lorenz and Hartmann 2001, 2003). These modes have been also obtained in idealized numerical models (Robinson 1991(Robinson , 1996(Robinson , 2000Yu and Hartmann 1993; 2 Feldstein and Lee 1996;Lee and Feldstein 1996;Koo and Ghil 2002;Kravtsov et al. 2003).The mechanisms that govern this behavior are not fully understood: observational and theoretical results give rise to controvers...

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Section: Transition To Chaosmentioning

confidence: 99%

Bimodal Behavior in the Zonal Mean Flow of a Baroclinic β-Channel Model

Kravtsov

Robertson

Ghil

2005

Journal of the Atmospheric Sciences

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“…One of the intensively studied ideas is that the ocean variability can be understood in terms of early bifurcations of the forced and dissipative dynamical systems (Cessi and Ierley 1995;Ierley and Sheremet 1995;Speich et al 1995;Jiang et al 1995;Sheremet et al 1997;Dijkstra and Katsman 1997;Meacham and Berloff 1997a,b;Berloff andMeacham 1997, 1998;Meacham 2000;Nadiga and Luce 2001;Primeau 2002;Simonnet et al 2003a). In this approach, it is argued that the ocean is steered by the underlying, unstable low-dimensional attractors such as fixed points (steady), limit cycles (periodic), tori (quasiperiodic), strange attractors (chaotic states), and homoclinic orbits.…”

Section: B Backgroundmentioning

confidence: 99%

The Turbulent Oscillator: A Mechanism of Low-Frequency Variability of the Wind-Driven Ocean Gyres

Berloff

Hogg

Dewar

2007

Journal of Physical Oceanography

110

136

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Intrinsic low-frequency variability is studied in the idealized, quasigeostrophic, midlatitude, wind-driven ocean gyres operating at large Reynolds number. A robust decadal variability mode driven by the transient mesoscale eddies is found and analyzed. The variability is a turbulent phenomenon, which is driven by the competition between the eddy rectification process and the potential vorticity anomalies induced by changes of the intergyre transport.

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“…Chang et al (2001), Nadiga and Luce (2001) and Simonnet et al (2005) showed that a homoclinic bifurcation appears at a slightly higher value of σ . This global bifurcation in turn generates very low-frequency, interdecadal oscillations.…”

Section: B Deremble Et Al: Multiple Equilibria and Oscillatory Modementioning

confidence: 96%

Multiple equilibria and oscillatory modes in a mid-latitude ocean-forced atmospheric model

Deremble

Simonnet²,

Ghil

2012

Nonlin. Processes Geophys.

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Abstract. Atmospheric response to a mid-latitude sea surface temperature (SST) front is studied, while emphasizing low-frequency modes induced by the presence of such a front. An idealized atmospheric quasi-geostrophic (QG) model is forced by the SST field of an idealized oceanic QG model. First, the equilibria of the oceanic model and the associated SST fronts are computed. Next, these equilibria are used to force the atmospheric model and compute its equilibria when varying the strength of the oceanic forcing.Low-frequency modes of atmospheric variability are identified and associated with successive Hopf bifurcations. The origin of these Hopf bifurcations is studied in detail, and connected to barotropic instability. Finally, a link is established between the model's time integrations and the previously obtained equilibria.

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Global Bifurcation of Shilnikov Type in a Double-Gyre Ocean Model

Cited by 53 publications

References 31 publications

Bimodal Behavior in the Zonal Mean Flow of a Baroclinic β-Channel Model

Bimodal Behavior in the Zonal Mean Flow of a Baroclinic β-Channel Model

The Turbulent Oscillator: A Mechanism of Low-Frequency Variability of the Wind-Driven Ocean Gyres

Multiple equilibria and oscillatory modes in a mid-latitude ocean-forced atmospheric model

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