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  • Author or Editor: Henk A. Dijkstra x
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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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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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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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Themistoklis P. Sapsis
and
Henk A. Dijkstra

Abstract

In this paper the authors study the interactions of additive noise and nonlinear dynamics in a quasigeostrophic model of the double-gyre wind-driven ocean circulation. The recently developed framework of dynamically orthogonal field theory is used to determine the statistics of the flows that arise through successive bifurcations of the system as the ratio of forcing to friction is increased. This study focuses on the understanding of the role of the spatial and temporal coherence of the noise in the wind stress forcing. When the wind stress noise is temporally white, the statistics of the stochastic double-gyre flow does not depend on the spatial structure and amplitude of the noise. This implies that a spatially inhomogeneous noise forcing in the wind stress field only has an effect on the dynamics of the flow when the noise is temporally colored. The latter kind of stochastic forcing may cause more complex or more coherent dynamics depending on its spatial correlation properties.

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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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Qiang Wang
,
Youmin Tang
, and
Henk A. Dijkstra

Abstract

A new optimization strategy is proposed to identify the sensitivities of simulations of atmospheric and oceanic models to uncertain parameters. The strategy is based on a nonlinear optimization method that is able to estimate the maximum values of specific parameter sensitivity measures; meanwhile, it takes into account interactions among uncertain parameters. It is tested using the Lorenz’63 model and an intermediate complexity 2.5-layer shallow-water model of the North Pacific Ocean. For the Lorenz’63 model, it is shown that the parameter sensitivities of the model results depend on the initial conditions. For the 2.5-layer shallow-water model used to simulate the Kuroshio large meander (KLM) south of Japan, the optimization strategy reveals that the prediction of the KLM path is insensitive to the uncertainties in the bottom friction coefficient, the interfacial friction coefficient, and the lateral friction coefficient. Rather, the KLM prediction is relatively sensitive to the uncertainties of the reduced gravity representing ocean stratification and the wind stress coefficient.

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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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Mu Mu
,
Liang Sun
, and
Henk A. Dijkstra

Abstract

Within a simple model context, the sensitivity and stability of the thermohaline circulation to finite-amplitude perturbations are studied. A new approach is used to tackle this nonlinear problem. The method is based on the computation of the so-called conditional nonlinear optimal perturbation (CNOP), which is a nonlinear generalization of the linear singular vector approach (LSV). It is shown that linearly stable thermohaline circulation states can become nonlinearly unstable, and the properties of the perturbations with optimal nonlinear growth are determined. An asymmetric nonlinear response to perturbations exists with respect to the sign of finite-amplitude freshwater perturbations, on both thermally dominated and salinity-dominated thermohaline flows. This asymmetry is due to the nonlinear interaction of the perturbations through advective processes.

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