On rectification of randomly forced flows

Author Posting. © Sears Foundation for Marine Research, 2005. This article is posted here by permission of Sears Foundation for Marine Research for personal use, not for redistribution. The definitive version was published in Journal of Marine Research 63 (2005): 497-527, doi:10.1357/0022240054307894.Nonlinear rectification of the ocean circulation driven by random forcing, which simulates the effect of unresolved eddies, is studied in an idealized closed basin. The results are based on the analysis of randomly forced solutions and linear eigenmodes. Depending on the forcing strength, two rectification regimes are found: zonal jets and isolated gyres. It is shown that both regimes are due to nonlinear interactions of resonant basin modes. In the zonal-jet regime, these interactions involve complex interplay between resonant baroclinic modes and some secondary modes. Both Rhines' scaling for zonal jets and prediction of gyres based on the maximum entropy argument are not confirmed

Random-forcing model of the mesoscale oceanic eddies

Author Posting. © Cambridge University Press, 2005. This article is posted here by permission of Cambridge University Press for personal use, not for redistribution. The definitive version was published in Journal of Fluid Mechanics 529 (2005): 71-95, doi:10.1017/S0022112005003393.The role of mesoscale oceanic eddies in driving large-scale currents is studied in an eddy-resolving midlatitude double-gyre ocean model. The reference solution is decomposed into large-scale and eddy components in a way which is dynamically consistent with a non-eddy-resolving ocean model. That is, the non-eddy-resolving solution driven by this eddy-forcing history, calculated on the basis of this decomposition, correctly approximates the original flow. The main effect of the eddy forcing on the large-scale flow is to enhance the eastward-jet extension of the subtropical western boundary current. This is an anti-diffusive process, which cannot be represented in terms of turbulent diffusion. It is shown that the eddy-forcing history can be approximated as a space–time correlated, random-forcing process in such a way that the non-eddy-resolving solution correctly approximates the reference solution. Thus, the random-forcing model can potentially replace the diffusion model, which is commonly used to parameterize eddy effects on the large-scale currents. The eddy-forcing statistics are treated as spatially inhomogeneous but stationary, and the dynamical roles of space–time correlations and spatial inhomogeneities are systematically explored. The integral correlation time, oscillations of the space correlations, and inhomogeneity of the variance are found to be particularly important for the flow response.Funding for this research was provided by NSF grants OCE 0091836 and OCE 03-44094, by the Royal Society Fellowship, and by WHOI grants 27100056 and 52990035

The dynamics of an equivalent-barotropic model of the wind-driven circulation

Various steady and time-dependent regimes of a quasi-geostrophic 1.5 layer model of an oceanic circulation driven by a steady wind stress are studied. After being discretized as a numerical model, the quasi-geostrophic equations of motion become a dynamical system with a large dimensional phase space. We find that, for a wide range of parameters, the large-time asymptotic regimes of the model correspond to low-dimensional attractors in this phase space. Motion on these attractors is significant in determining the intrinsic time scales of the system. In two sets of experiments, we explore the dependence of solutions on the viscosity coefficient and the deformation radius. Both experiments yielded a succession of solutions with different forms of time dependence including chaotic solutions. The transition to chaos in this model occurs through a modified classical Ruelle-Takens scenario. We computed some unstable steady regimes of the circulation and the associated fastest growing linear eigenmodes. The structure of the eigenmodes and the details of the energy conversion terms allow us to characterize the primary instability of the steady circulation. It is a complex instability of the western boundary intensification, the western gyre and the meander between the western and central gyres. The model exhibits ranges of parameters in which multiple, stable, time-dependent solutions exist. Further, we note that some bifurcations involve the appearance of variability at climatological time scales, purely as a result of the intrinsic dynamics of the wind-driven circulation

A Framework for Parameterizing Eddy Potential Vorticity Fluxes

A framework for parameterizing eddy potential vorticity fluxes is developed that is consistent with conservation of energy and momentum while retaining the symmetries of the original eddy flux. The framework involves rewriting the residual-mean eddy force, or equivalently the eddy potential vorticity flux, as the divergence of an eddy stress tensor. A norm of this tensor is bounded by the eddy energy, allowing the components of the stress tensor to be rewritten in terms of the eddy energy and nondimensional parameters describing the mean shape and orientation of the eddies. If a prognostic equation is solved for the eddy energy, the remaining unknowns are nondimensional and bounded in magnitude by unity. Moreover, these nondimensional geometric parameters have strong connections with classical stability theory. When applied to the Eady problem, it is shown that the new framework preserves the functional form of the Eady growth rate for linear instability. Moreover, in the limit in which Reynolds stresses are neglected, the framework reduces to a Gent and McWilliams type of eddy closure where the eddy diffusivity can be interpreted as the form proposed by Visbeck et al. Simulations of three-layer wind-driven gyres are used to diagnose the eddy shape and orientations in fully developed geostrophic turbulence. These fields are found to have large-scale structure that appears related to the structure of the mean flow. The eddy energy sets the magnitude of the eddy stress tensor and hence the eddy potential vorticity fluxes. Possible extensions of the framework to ensure potential vorticity is mixed on average are discussed. © 2012 American Meteorological Society

Properties and origins of the anisotropic eddy-induced transport in the North Atlantic

Author Posting. © American Meteorological Society, 2015. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 45 (2015): 778–791, doi:10.1175/JPO-D-14-0164.1.This study examines anisotropic transport properties of the eddying North Atlantic flow, using an idealized model of the double-gyre oceanic circulation and altimetry-derived velocities. The material transport by the time-dependent flow (quantified by the eddy diffusivity tensor) varies geographically and is anisotropic, that is, it has a well-defined direction of the maximum transport. One component of the time-dependent flow, zonally elongated large-scale transients, is particularly important for the anisotropy, as it corresponds to primarily zonal material transport and long correlation time scales. The importance of these large-scale zonal transients in the material distribution is further confirmed with simulations of idealized color dye tracers, which has implications for parameterizations of the eddy transport in non-eddy-resolving models.IK would like to acknowledge support through the NSF Grant OCE-1154923. IR was supported by the NSF OCE-1154641 and NASA Grant NNX14AH29G.2015-09-0

Ocean eddy dynamics in a coupled ocean-atmosphere model

Author Posting. © American Meteorological Society, 2007. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 37 (2007): 1103-1121, doi:10.1175/jpo3041.1.The role of mesoscale oceanic eddies is analyzed in a quasigeostrophic coupled ocean–atmosphere model operating at a large Reynolds number. The model dynamics are characterized by decadal variability that involves nonlinear adjustment of the ocean to coherent north–south shifts of the atmosphere. The oceanic eddy effects are diagnosed by the dynamical decomposition method adapted for nonstationary external forcing. The main effects of the eddies are an enhancement of the oceanic eastward jet separating the subpolar and subtropical gyres and a weakening of the gyres. The flow-enhancing effect is due to nonlinear rectification driven by fluctuations of the eddy forcing. This is a nonlocal process involving generation of the eddies by the flow instabilities in the western boundary current and the upstream part of the eastward jet. The eddies are advected by the mean current to the east, where they backscatter into the rectified enhancement of the eastward jet. The gyre-weakening effect, which is due to the time-mean buoyancy component of the eddy forcing, is a result of the baroclinic instability of the westward return currents. The diagnosed eddy forcing is parameterized in a non-eddy-resolving ocean model, as a nonstationary random process, in which the corresponding parameters are derived from the control coupled simulation. The key parameter of the random process—its variance—is related to the large-scale flow baroclinicity index. It is shown that the coupled model with the non-eddy-resolving ocean component and the parameterized eddies correctly simulates climatology and low-frequency variability of the control eddy-resolving coupled solution.Funding for this work came from NSF Grants OCE 02-221066 and OCE 03-44094. Additional funding for PB was provided by the U.K. Royal Society Fellowship and by WHOI Grants 27100056 and 52990035

On dynamically consistent eddy fluxes

Author Posting. © The Author, 2004. This is the author's version of the work. It is posted here by permission of Elsevier B. V. for personal use, not for redistribution. The definitive version was published in Dynamics of Atmospheres and Oceans 38 (2005): 123-146, doi:10.1016/j.dynatmoce.2004.11.003.The role of mesoscale oceanic eddies in driving the large-scale currents is studied in an eddy-resolving, double-gyre ocean model. The new diagnostic method is proposed, which is based on dynamical decomposition of the flow into the large-scale and eddy components. The method yields the time history of the eddy forcing, which can be used as additional, external forcing in the corresponding non-eddy-resolving model of the gyres. The main strength of this approach is in its dynamical consistency: the non-eddy-resolving solution driven by the eddy forcing history correctly approximates the original large-scale flow component. It is shown that statistical decompositions, which are based on space-time filtering diagnostics, are dynamically inconsistent. The diagnostics algorithm is formulated and tested, and the diagnosed eddies are analysed, both statistically and dynamically. It is argued that the main dynamic role of the eddies is to maintain the eastward-jet extension of the subtropical western boundary current (WBC). This is done largely by both the time–mean isopycnal-thickness flux and the relative-vorticity eddy flux fluctuations. The fluctuations drive large-scale flow through the nonlinear rectification mechanism. The relative-vorticity flux contributes mostly to the eastward jet meandering. Finally, eddy fluxes driven by both the eddies and the large-scale flow are found to be important. The latter is typically neglected in the analysis, but here it corresponds to important large-scale feedback on the eddies.Funding for this research was provided by NSF grant OCE 00–91836, by the Royal Society Fellowship, and by WHOI grants 27100056 and 52990035

A mechanistic model of mid-latitude decadal climate variability

Author Posting. © Elsevier B.V., 2007. This is the author's version of the work. It is posted here by permission of Elsevier B.V. for personal use, not for redistribution. The definitive version was published in Physica D: Nonlinear Phenomena 237 (2008): 584-599, doi:10.1016/j.physd.2007.09.025.A simple heuristic model of coupled decadal ocean–atmosphere modes in middle latitudes is developed. Previous studies have treated atmospheric intrinsic variability as a linear stochastic process modified by a deterministic coupling to the ocean. The present paper takes an alternative view: based on observational, as well as process modeling results, it represents this variability in terms of irregular transitions between two anomalously persistent, high-latitude and low-latitude jet-stream states. Atmospheric behavior is thus governed by an equation analogous to that describing the trajectory of a particle in a double-well potential, subject to stochastic forcing. Oceanic adjustment to a positional shift in the atmospheric jet involves persistent circulation anomalies maintained by the action of baroclinic eddies; this process is parameterized in the model as a delayed oceanic response. The associated sea-surface temperature anomalies provide heat fluxes that affect atmospheric circulation by modifying the shape of the double-well potential. If the latter coupling is strong enough, the model’s spectrum exhibits a peak at a periodicity related to the ocean’s eddy-driven adjustment time. A nearly analytical approximation of the coupled model is used to study the sensitivity of this behavior to key model parameters.This research was supported by National Science Foundation grant OCE-02-221066 (all coauthors) and the Department of Energy grant DE-FG-03-01ER63260 (MG and SK)

North Atlantic climate variability in coupled models and data

© 2008 The Authors. This work is licensed under a Creative Commons Attribution License. The definitive version was published in Nonlinear Processes in Geophysics 15 (2008): 13-24, doi:10.5194/npg-15-13-2008We show that the observed zonally averaged jet in the Northern Hemisphere atmosphere exhibits two spatial patterns with broadband variability in the decadal and inter-decadal range; these patterns are consistent with an important role of local, mid-latitude ocean–atmosphere coupling. A key aspect of this behaviour is the fundamentally nonlinear bi-stability of the atmospheric jet's latitudinal position, which enables relatively small sea-surface temperature anomalies associated with ocean processes to affect the large-scale atmospheric winds. The wind anomalies induce, in turn, complex three-dimensional anomalies in the ocean's main thermocline; in particular, they may be responsible for recently reported cooling of the upper ocean. Both observed modes of variability, decadal and inter-decadal, have been found in our intermediate climate models. One mode resembles North Atlantic tri-polar sea-surface temperature (SST) patterns described elsewhere. The other mode, with mono-polar SST pattern, is novel; its key aspects include interaction of oceanic turbulence with the large-scale oceanic flow. To the extent these anomalies exist, the interpretation of observed climate variability in terms of natural and human-induced changes will be affected. Coupled mid-latitude ocean-atmosphere modes do, however, suggest some degree of predictability is possible.This research was supported by NSF grant OCE-02-221066, DOE grants DE-FG-03-01ER63260 and DE-FG02-02ER63413, as well as NASA grant NNG-06-AG66G-1 (MG & SK). PB has also been supported by the Newton Trust research grant, and SK - by the University of Wisconsin-Milwaukee Research Growth Initiative program 2006-2007

A highly nonlinear coupled mode of decadal variability in a mid-latitude ocean–atmosphere model

Author Posting. © Elsevier B.V., 2007. This is the author's version of the work. It is posted here by permission of Elsevier B.V. for personal use, not for redistribution. The definitive version was published in Dynamics of Atmospheres and Oceans 43 (2007): 123-150, doi:10.1016/j.dynatmoce.2006.08.001.This study examines mid-latitude climate variability in a model that couples turbulent oceanic and atmospheric flows through an active oceanic mixed layer. Intrinsic ocean dynamics of the inertial recirculation regions combines with nonlinear atmospheric sensitivity to sea-surface temperature (SST) anomalies to play a dominant role in the variability of the coupled system. Intrinsic low-frequency variability arises in the model atmosphere; when run in a stand-alone mode, it is characterized by irregular transitions between preferred high-latitude and less frequent low-latitude zonal-flow states. When the atmosphere is coupled to the ocean, the low-latitude state occurrences exhibit a statistically significant signal in a broad 5–15-year band. A similar signal is found in the time series of the model ocean’s energy in this coupled simulation. Accompanying uncoupled ocean-only and atmosphere-only integrations are characterized by a decrease in the decadal-band variability, relative to the coupled integration; their spectra are indistinguishable from a red spectrum. The time scale of the coupled interdecadal oscillation is set by the nonlinear adjustment of the ocean’s inertial recirculations to the high-latitude and low-latitude atmospheric forcing regimes. This adjustment involves, in turn, SST changes resulting in long-term ocean–atmosphere heat-flux anomalies that induce the atmospheric regime transitions.This research was supported by NSF grant OCE-02-221066 (all co-authors) and DOE grant DE-FG-03-01ER63260 (MG and SK)