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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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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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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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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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M. Jeroen Molemaker and Henk A. Dijkstra

Abstract

Geostrophic eddies in a stratified liquid are susceptible to baroclinic instabilities. In this paper, the authors consider these instabilities when such an eddy is simultaneously cooled homogeneously from above. As a linear stability analysis shows, the developing convection modifies the background stratification, the stability boundaries, and the patterns of the dominant modes. The coupling between the effects of convection and the large-scale flow development of the eddy is studied through high-resolution numerical simulations, using both nonhydrostatic and hydrostatic models. In the latter models, several forms of convective adjustment are used to model convection. Both types of models confirm the development of the dominant modes and indicate that their nonlinear interaction leads to localized intense convection. By comparing nonhydrostatic and hydrostatic simulations of the flow development carefully, it is shown that convective adjustment may lead to erroneous small-scale variability. A simple alternative formulation of convective adjustment is able to give a substantial improvement.

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Anna von der Heydt and Henk A. Dijkstra

Abstract

Multidecadal SST variability is studied in idealized one- and two-ocean-basin configurations, using simulations with the Modular Ocean Model. The authors demonstrate that the multidecadal variability on the global “conveyor type” circulation is localized in the North Atlantic Ocean. Interbasin exchange processes determine the locations where regions of deep-water formation occur and induce a localization of SST multidecadal anomalies in the Atlantic. The physics of this localization is subsequently investigated by considering more equatorially symmetric background flows in two-basin and one-basin configurations. A cross-equatorial flow in the Atlantic induces the localization of the multidecadal variability in the North Atlantic. By using the mechanism of multidecadal variability as proposed in 2002 by Te Raa and Dijkstra in a single-hemispheric configuration, the physics of these localization processes can be explained.

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Henk A. Dijkstra and Anna von der Heydt

Abstract

In a companion paper, the authors have shown that in an idealized Atlantic–Pacific Ocean configuration with a conveyor-type overturning circulation, localized multidecadal variability occurs in the Atlantic. Results suggest that the multidecadal variability originates from the instability of the three-dimensional thermohaline circulation and that the physics of the spatial patterns of the SST anomalies can be understood from a study of an Atlantic-only configuration. Specific internal (multidecadal) modes, which obtain a positive growth factor depending on the background thermohaline flow, are associated with the instability. In this paper, the spectral origin of these internal modes is studied using eigensolution continuation techniques. As in the single-hemispheric case, multidecadal modes arise through mergers of so-called SST modes. In the double-hemispheric case studied here, there actually are two types of multidecadal modes that lead to oscillatory behavior. Depending on the background conditions, one of these oscillatory flows is preferred.

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Maurice J. Schmeits and Henk A. Dijkstra

Abstract

Using nonseasonal altimeter data and SST observations of the North Atlantic, and more specifically the Gulf Stream region, dominant patterns of variability are determined using multivariate time series analyses. A statistically significant propagating mode of variability with a timescale close to 9 months is found, the latter timescale corresponding to dominant variability found in earlier studies. In addition, output from a high resolution simulation of the Parallel Ocean Climate Model (POCM) is analyzed, which also displays variability on a timescale of 9 months, although not statistically significant at the 95% confidence level. The vertical structure of this 9-month mode turns out to be approximately equivalent barotropic. Following the idea that this mode is due to internal ocean dynamics, steady flow patterns and their instabilities are determined within a barotropic ocean model of the North Atlantic using techniques of numerical bifurcation theory. Within this model, there appear to be two different mean flow paths of the Gulf Stream, both of which become unstable to oscillatory modes. For reasonable values of the parameters, an oscillatory instability having a timescale of 9 months is found. The connection between results from the bifurcation analysis, from the analysis of the observations, and from the analysis of the POCM output is explored in more detail and leads to the conjecture that the 9-month variability is related to a barotropic instability of the wind-driven gyres.

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