Coupled processes and the tropical climatology : part III : instabilities of the fully coupled climatology

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 phe- nomenon.In this paper,we consider the connection between both effects of coupling 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 simul- taneous 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 ap- pears 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 qual- itatively similar in this fully coupled problem compared to the ?ux-corrected problem,but the sensitivity of the ENSO mode to parameters and external variations is larger due to feedbacks in the climatology

Bimodal behavior of the Kuroshio and the Gulf Stream

For a long time, observations have been pointing out that the Kuroshio in the North Paciffc Ocean displays bimodal meandering behavior of the southern coast of Japan. For the Gulf Stream in the North Atlantic Ocean, weakly and strongly deffected 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 the 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

Imperfections of the thermohaline circulation: latitudinal asymmetry and preferred northern sinking

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 fresh- water 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 fresh-water 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

On the stability of a cold-core eddy in the presence of convection: hydrostatic versus non-hydrostatic modeling

Geostrophic eddies in a stratified liquid are susceptable to baroclinic instabilities.In this paper,we consider these instabilities when such an eddy is simultaneously cooled homoge- neously from above.As a linear stability analysis shows,the developing convection modi ?es the background stratification,the stability boundaries and the patterns of the dominant modes.The coupling between the effects of convection and the large scale fiow devel- opment of the eddy is studied through high resolution numerical simulations,using both non-hydrostatic and hydrostatic models.In the latter models,several forms of convective adjustment are used to model convection.Both type of models conform the development of the dominant modes and indicate that their nonlinear interaction leads to localized in- tense convection.By comparing non-hydrostatic 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

Imperfections of the North-Atlantic wind-driven ocean circulation: continental geometry and windstress shape

Multiple equilibria of the wind-driven gyres have been found in idealized quasi- geostrophic and shallow water models.In this paper we demonstrate that multiple equilibria persist within a reduced gravity shallow water model under quite realis- tic continental geometry and windstress orcing for the North-Atlantic.Multiple mean flow patterns of the Gulf Stream exist and differ with respect to their separation behavior along the North-American coast.The origin of these equilibria is investigated by determining the structure of steady solutions within a hierarchy of equivalent barotropic ocean models using continuation techniques.Within each model,the magnitude of lateral riction is used as a control parameter.It is shown that symmetry breaking, found in a quasi-geostrophic model for a rectan- gular ocean basin with idealized wind forcing is at the origin of two different mean states of the Gul Stream.The steady states ound become unstable only to a small number of oscillatory modes,which either have intermonthly or interannual periods.The modes of variability remain strongly related through the hierarchy of models indicating that their physics is not strongly dependent on the shape of the continents but is controlled by internal ocean dynamics

A bifurcation study of the three-dimensional thermohaline ocean circulation: the double-hemispheric case

Within a low-resolution primitive-equation model of the three-dimensional ocean circulation, a bifurcation analysis is performed of double-hemispheric basin flows. Main focus is on the connection between results for steady two-dimensional flows in a non-rotating basin and those for three-dimensional flows in a rotating basin. With the use of continuation methods, branches of steady states are followed in parameter space and their linear stability is monitored. There is a close qualitative similarity between the bifurcation structure of steady-state solutions of the two- and three dimensional flows. In both cases, symmetry-breaking pitchfork bifurcations are central in generating a multiple equilibria structure. The locations of these pitchfork bifurcations in parameter space can be characterized through a zero of the tendency of a particular energy functional. Although balances controlling the steady-state ?ows are quantitatively very di?erent, the zonally averaged patterns of the perturbations associated with symmetry-breaking are remarkably similar for two-dimensional and three-dimensional ?ows, and the energetics of the symmetry-breaking mechanism is in essence the same

Barotropic instabilities of the Agulhas Current system and their relation to ring formation

Recent work has shown that different steady retroflection regimes,a viscous and an inertial regime,exist for the Agulhas Current system in an idealized ge- ometry.In this paper,instabilities of these steady flows are considered by solving the linear stability problem numerically.Barotropic instabilities occur as so-called Hopf bifurcations in the viscous regime,with corresponding patterns related to Rossby basin modes.Depending on the value of the reduced gravity parameter, these instabilities may introduce intermonthly to interannual variability into the retroflection region.Finite amplitude development of these instabilities display "ring-like" localized anomaly patterns which travel around the tip of the continent. The results demonstrate that (i)the origin of the frequency of the ring formation is set by the physics of the large scale barotropic instabilities and (ii)the rectifi- cation processes due to these instabilities decrease the degree of retroflection of the mean state.The latter result suggests that the dominant mechanism of the retroflection is captured within the steady balances

Instability of the thermohaline ocean circulation on interdecadal time scales

The stability of three-dimensional thermally driven ocean flows in a single hemispheric sector basin is investigated using techniques of numerical bifur- cation theory.Under restoring conditions for the temperature,the flow is stable.However,when forced with the associated heat flux,an interdecadal oscillatory time scale instability appears.This occurs as a Hopf bifurcation when the horizontal mixing coeffcient 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 westwards 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 merid- ional 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 time scale of the oscillation

On the physics of the Agulhas Current: steady retroflection regimes

From previous model studies,it has become clear that several physical mech- anisms may be at work in the retroflection of the Agulhas current.Here,a sys- tematic study of steady barotropic flows connecting the Indian Ocean and South Atlantic Ocean in several idealized set-ups is performed.By solving directly for the steady circulation with continuation methods,the connection between differ- ent retroflection regimes can be monitored as external conditions,such as the wind forcing,bottom topography as well as parameters,for example the lateral friction and layer depth,are changed.To distinguish the different steady retroflecting flows,an objective measure of the degree of retroflection,a retroflection index R ,is introduced.By monitoring R along a branch of steady solutions,using the horizontal friction as control parameter,several steady retroflecting regimes are found.At large friction there exist stable steady states with viscously dominated retroflection.When friction is decreased,inertial effects become more dominant and eventually unstable steady states with strong retroflection characteristics ex- ist.Within this framework,different results from earlier studies can be reconciled

Application of continuation methods in physical oceanography

A specific example will be considered in which continuation methods are used to study fundamental problems in physical oceanography.The separation be- havior of the Gulf Stream in the North Atlantic is a long standing problem in dynamical oceanography,with state-of-the-art ocean models still having trouble to simulate to correct mean path.Bifurcation analysis in simplified models,as used here,points to one of difficulties involved:there may be two separation paths at the same forcing conditions.By studying the stability of steady North Atlantic ocean circulation patterns,also transitions to time-dependence are found which are linked to specific low frequency variability in the Gulf Stream region