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Henk A. Dijkstra

Abstract

The spectral origin of the recently discovered multidecadal modes (MMs) and centennial modes (CMs) is explained. These modes appear in the linear stability analysis of thermohaline-driven flows in a single-hemispheric ocean basin. It is shown that both classes of modes arise through interaction of so-called sea surface temperature (SST) modes. These SST modes are damped and nonoscillatory for the unforced (motionless) flow. They become oscillatory under small thermal forcing through mode merging that is induced by the meridional overturning circulation. The type of merger responsible for each class of modes explains many features—for example, why CMs can be found in two-dimensional models whereas MMs cannot—of the patterns of the modes at realistic forcing strength.

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Wilbert Weijer and Henk A. Dijkstra

Abstract

For the first time, the (linear) stability of the global ocean circulation has been determined explicitly. In a low-resolution general circulation model, a steady state is computed directly by solving the elliptic boundary value problem. The stability of this solution is determined by solving the generalized eigenvalue problem. Although the steady global circulation is (linearly) stable, there are two interesting oscillatory modes among the least stable ones, with periods of about 3800 and 2300 yr. These modes are characterized by buoyancy anomalies that propagate through the ocean basins as they are advected by the global overturning circulation. The millennial timescale is set by the time it takes for anomalies to travel, at depth, from the North Atlantic to the North Pacific. Further analyses confirm that the advective feedback between the steady flow and buoyancy anomalies is an essential process in the propagation mechanism. The growth rate of the millennial modes is controlled by vertical mixing. It is argued that these internal ocean modes may be a relevant mechanism for global climate variability on millennial timescales.

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Eric Simonnet and Henk A. Dijkstra

Abstract

In idealized models that aim to understand the temporal variability of the wind-driven ocean circulation, low-frequency instabilities associated with so-called oscillatory gyre modes have been found. For the double-gyre case, the spectral origin of these modes as well as the physical mechanism of the instability is explained. In a barotropic quasigeostrophic model, the low-frequency modes arise spontaneously from the merging between two nonoscillatory eigenmodes. Of the latter two, one is called here the P-mode and is responsible for the existence of multiple steady states. The other is called the L-mode and it controls the intensity of the gyres. This merging turns out to be robust over a hierarchy of models and can even be found in a low-order truncated quasigeostrophic model. The latter model is used to determine the physical mechanism of the instability. The low-frequency oscillation results from the conjugate effects of shear- and symmetry-breaking instabilities and is free of Rossby wave dynamics.

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Henk A. Dijkstra and Wilbert Weijer

Abstract

A study of the stability of the global ocean circulation is performed within a coarse-resolution general circulation model. Using techniques of numerical bifurcation theory, steady states of the global ocean circulation are explicitly calculated as parameters are varied. Under a freshwater flux forcing that is diagnosed from a reference circulation with Levitus surface salinity fields, the global ocean circulation has no multiple equilibria. It is shown how this unique-state regime transforms into a regime with multiple equilibria as the pattern of the freshwater flux is changed in the northern North Atlantic Ocean. In the multiple-equilibria regime, there are two branches of stable steady solutions: one with a strong northern overturning in the Atlantic and one with hardly any northern overturning. Along the unstable branch that connects both stable solution branches (here for the first time computed for a global ocean model), the strength of the southern sinking in the South Atlantic changes substantially. The existence of the multiple-equilibria regime critically depends on the spatial pattern of the freshwater flux field and explains the hysteresis behavior as found in many previous modeling studies.

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Lianke A. te Raa and Henk A. Dijkstra

Abstract

In this paper, an explanation is proposed for the changes in the amplitude of multidecadal variability found in the GFDL climate model when different restoring salinity fields in the flux adjustments were considered. This explanation arises from a study of the stability of three-dimensional thermohaline flows in an idealized coupled ocean–atmosphere model. The shape of the freshwater flux affects the stability properties of the thermohaline flows, in particular the growth rate of a stable interdecadal mode. The physics of this change in decay rate is explained by analyzing the energy conversions in the flows. Under a stronger freshening of the northern North Atlantic, the interdecadal mode destabilizes, which can result in an increase of the amplitude of the multidecadal variability.

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Lianke A. te Raa and Henk A. Dijkstra

Abstract

The stability of three-dimensional thermally driven ocean flows in a single hemispheric sector basin is investigated using techniques of numerical bifurcation theory. Under restoring conditions for the temperature, the flow is stable. However, when forced with the associated heat flux, an interdecadal oscillatory timescale instability appears. This occurs as a Hopf bifurcation when the horizontal mixing coefficient of heat is decreased. The physical mechanism of the oscillation is described by analyzing the potential energy changes of the perturbation flow near the Hopf bifurcation. In the relatively slow phase of the oscillation, a temperature anomaly propagates westward near the northern boundary on a background temperature gradient, thereby changing the perturbation zonal temperature gradient, with corresponding changes in meridional overturning. This is followed by a relatively fast phase in which the zonal overturning reacts to a change in sign of the perturbation meridional temperature gradient. The different responses of zonal and meridional overturning cause a phase difference between the effect of temperature and vertical velocity anomalies on the buoyancy work anomaly, the latter dominating the changes in potential energy. This phase difference eventually controls the timescale of the oscillation.

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Henk A. Dijkstra and J. David Neelin

Abstract

Coupled processes between the equatorial ocean and atmosphere control the spatial structure of the annual-mean state in the Pacific region, in particular the warm pool–cold tongue structure. At the same time, coupled processes are known to be responsible for the variability about this mean state, in particular the El Niño–Southern Oscillation phenomenon. In this paper, the connection between both effects of coupling is considered by investigating the linear stability of fully coupled climatologies in an intermediate coupled model. The new element here is that when parameters—such as the coupling strength—are changed, the potential amplification of disturbances can be greatly influenced by a simultaneous modification of the mean state. This alters the stability properties of the coupled climatology, relative to the flux-corrected cases that have been previously studied. It appears possible to identify a regime in parameter space where ENSO-like unstable modes coincide with a reasonable warm pool–cold tongue structure. These unstable modes are mixed SST–ocean dynamics modes, that is, they arise through an interaction of oscillatory modes originating from ocean dynamics and oscillatory SST modes. These effects are qualitatively similar in this fully coupled problem compared to the flux-corrected problem, but the sensitivity of the ENSO mode to parameters and external variations is larger due to feedbacks in the climatology.

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Ziqing Zu, Mu Mu, and Henk A. Dijkstra

Abstract

Within a three-dimensional ocean circulation model, the nonlinear optimal initial perturbations (NOIP) of sea surface salinity (SSS) and sea surface temperature (SST) to excite variability in the Atlantic meridional overturning circulation (AMOC) were obtained under prescribed heat and freshwater flux boundary conditions, using the conditional nonlinear optimal perturbation (CNOP) method. After 10 years, the optimal SSS and SST perturbations lead to reductions of the AMOC by 3.6 and 2.5 Sv (1 Sv = 106 m3 s−1), respectively, followed by multidecadal oscillations with a period of about 50 years. During the first 30 years, nonlinear processes have an important influence on the AMOC strength: convection strengthens the AMOC during years 0–2, zonal density advection promotes the slowdown of the AMOC during years 7–20, and meridional density advection inhibits the slowdown of meridional velocities in the upper ocean during years 5–18. The linear optimal initial perturbation (LOIP) was also computed using the first singular vector (FSV) method. For SSS perturbations with an amplitude of 0.5 psu, the LOIP will cause an underestimation of the amplitude of the multidecadal AMOC variability by about 1 Sv, compared to that induced by the NOIP. This underestimation will become more significant as the amplitudes of SSS perturbations increase.

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Maurice J. Schmeits and Henk A. Dijkstra

Abstract

For a long time, observations have indicated that the Kuroshio in the North Pacific Ocean displays bimodal meandering behavior off the southern coast of Japan. For the Gulf Stream in the North Atlantic Ocean, weakly and strongly deflected paths near the coast of South Carolina have been observed. This suggests that bimodal behavior may occur in the Gulf Stream as well, although less pronounced than in the Kuroshio. Evidence from a high-resolution ocean general circulation model (OGCM) and intermediate complexity models is given to support the hypothesis that multiple mean paths of both the Kuroshio and the Gulf Stream are dynamically possible. These paths are found as multiple steady states in an intermediate complexity shallow-water model. In the OGCM, transitions between similar mean paths are found, with the patterns having similarity to the ones in observations as well. To study whether atmospheric noise can induce transitions between the multiple steady states, a stochastic component is added to the annual mean wind stress forcing in the intermediate complexity model and differences between the transition behavior in the Gulf Stream and Kuroshio are considered.

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Henk A. Dijkstra and J. David Neelin

Abstract

The present Atlantic thermohaline circulation is dominated by deep water formation in the north despite the fact that surface buoyancy forcing has relatively modest latitudinal asymmetry. Many studies have shown that even with buoyancy forcing that is symmetric about the equator, spontaneous symmetry breaking can produce a single overturning cell with intense sinking in the north. This occurs by salt advection at sufficiently large freshwater forcing. In this symmetry-breaking case, a southern-sinking solution and a symmetric solution are also possible. A simple coupled ocean–atmosphere model of the zonally averaged thermohaline circulation is used to examine the effect of latitudinal asymmetries in the boundary conditions. The greater continental area in the Northern Hemisphere, combined with the slight asymmetry in the observed freshwater flux, induce a strong preference for the northern-sinking solution. Examining the relation to the solution under symmetric conditions, the salt-advection mechanism still acts to enhance the overturning circulation of the northern-sinking branch, but multiple equilibria are much less likely to occur within the realistic parameter range. The most plausible shift between equilibria for paleoclimate applications would be between a strong northern-sinking branch and a weak northern-sinking branch that is an asymmetric version of the thermally driven solution. However, this is possible only in a very limited range of parameters. There is a substantial parameter range where the northern-sinking branch is unique. The role of the fractional region of air–sea interaction at each latitude is substantial in producing north–south asymmetry.

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