Publications
91 results found
Haigh M, Sun L, Shevchenko I, et al., 2020, Tracer-based estimates of eddy-induced diffusivities, Deep Sea Research Part I: Oceanographic Research Papers, Vol: 160, Pages: 1-8, ISSN: 0967-0637
This study provides estimates of the mean eddy-induced diffusivities of passive tracers in a three-layer, double-gyre quasigeostrophic (QG) simulation. A key aspect of this study is the use of a spatial filter to separate the flow and tracer fields into small-scale and large-scale components, and we compare results with those obtained using Reynolds temporal averaging. The eddy tracer flux is related to a rank-2 diffusivity tensor via the flux-gradient relation, which is solved for a pair of tracers with misaligned large-scale gradients. We concentrate on the symmetric part of the resulting diffusivity tensor which represents irreversible mixing processes. The eigenvalues of the symmetric tensor exhibit complicated behaviour, but a particularly dominant and robust feature is the positive/negative eigenvalue pairs, which physically represent filamentation of the tracer concentration. The large off-diagonal diffusivity tensor component is the primary contributor to the eigenvalue polarity, and since this is such a prevalent feature we argue that the (horizontal) eddy-induced diffusivity should always be treated as a full tensor. Diffusivity magnitudes are largest in the upper layer and in the eastward jet region, where the eddying flow is strongest. After removing the rotational part of the eddy tracer flux, typical mean diffusivities (eigenvalues) in the upper-layer are on the order of m2 s−1 in the jet region and m2 s−1 elsewhere. We also confirm that the time-mean of the diffusivity calculated from instantaneous fluxes is not the same as the diffusivity associated with the time-mean fluxes.
Kondrashov D, Ryzhov EA, Berloff P, 2020, Data-adaptive harmonic analysis of oceanic waves and turbulent flows, Chaos: an interdisciplinary journal of nonlinear science, Vol: 30, Pages: 1-12, ISSN: 1054-1500
We introduce new features of data-adaptive harmonic decomposition (DAHD) that are showcased to characterize spatiotemporal variability in high-dimensional datasets of complex and mutsicale oceanic flows, offering new perspectives and novel insights. First, we present a didactic example with synthetic data for identification of coherent oceanic waves embedded in high amplitude noise. Then, DAHD is applied to analyze turbulent oceanic flows simulated by the Regional Oceanic Modeling System and an eddy-resolving three-layer quasigeostrophic ocean model, where resulting spectra exhibit a thin line capturing nearly all the energy at a given temporal frequency and showing well-defined scaling behavior across frequencies. DAHD thus permits sparse representation of complex, multiscale, and chaotic dynamics by a relatively few data-inferred spatial patterns evolving with simple temporal dynamics, namely, oscillating harmonically in time at a given single frequency. The detection of this low-rank behavior is facilitated by an eigendecomposition of the Hermitian cross-spectral matrix and resulting eigenvectors that represent an orthonormal set of global spatiotemporal modes associated with a specific temporal frequency, which in turn allows to rank these modes by their captured energy and across frequencies, and allow accurate space-time reconstruction. Furthermore, by using a correlogram estimator of the Hermitian cross-spectral density matrix, DAHD is both closely related and distinctly different from the spectral proper orthogonal decomposition that relies on Welch’s periodogram as its estimator method.The turbulent oceanic flows consist of ubiquitous complex motions—jets, vortices, and waves—that co-exist on very different spatiotemporal scales but also without a clear scale separation, and it brings natural challenge to characterize the whole complexity across the scales. In particular, the study of temporal scales has got less attention than of spatial
Haigh M, Berloff P, 2020, Rossby waves and zonal momentum redistribution induced by localised forcing in the rotating shallow-water model, Journal of Fluid Mechanics, Vol: 885, Pages: A43-1-A43-26, ISSN: 0022-1120
The aim of this study is to understand the dynamics of Rossby waves induced by a localised and periodic ‘plunger’ forcing – imposed on a background flow – which is intended as an elementary representation of transient mesoscale eddy forcing in the ocean. We consider linearised dynamics and its quasi-nonlinear extension, and focus on the rotating shallow-water model. The plunger induces a spectrum of Rossby waves that drive zonal momentum flux convergence at the forced latitudes. This behaviour has a robust and significant dependence on the background flow, which we treat as zonal and uniform. We systematically analyse this dependence using two methods. First, we use the eddy geometry formulation, in which Reynolds stresses are expressed in terms of eddy elongation and eddy tilt parameters, and consider the relationship between eddy geometry and zonal momentum redistribution. Second, we implement decompositions of flow responses into linear dynamical eigenmodes and compare with expectations from linear Rossby wave theory. Both methods compliment each other and aid the understanding of zonal momentum redistribution and its dependence on uniform background flow. We find that this dependence is determined by two factors: (i) dispersion-constrained resonance with the plunger forcing and (ii) efficiency of nonlinear eddy self-interactions. These results significantly improve our understanding of shallow-water Rossby waves, and may also be applied towards the development of parameterisations of oceanic mesoscale eddies.
Stepanov DV, Ryzhov EA, Zagumennov AA, et al., 2020, Clustering of floating tracer due to mesoscale vortex and submesoscale fields, Geophysical Research Letters, Vol: 47, Pages: 1-10, ISSN: 0094-8276
American Geophysical Union. All Rights Reserved. Floating tracer clustering is studied in oceanic flows that combine both a field of coherent mesoscale vortices, as simulated by a regional, comprehensive, eddy-resolving general circulation model, and kinematic random submesoscale velocity fields. Both fields have rotational and divergent velocity components, and depending on their relative contributions, as well as on the local characteristics of the mesoscale vortices, we identified different clustering scenarios. We found that the mesoscale vortices do not prevent clustering but significantly modify its rate and spatial pattern. We also demonstrated that even weak surface-velocity divergence has to be taken into account to avoid significant errors in model predictions of the floating tracer patterns. Our approach combining dynamically constrained and random velocity fields, and the applied diagnostic methods, are proposed as standard tools for analyses and predictions of floating tracer distributions, in both observational data and general circulation models.
Berloff P, 2019, Clustering of floating tracers in weakly divergent velocity fields, Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, Vol: 100, Pages: 1-15, ISSN: 1539-3755
This work deals with buoyant tracers floating at the ocean surface, where the geostrophic velocitycomponent is 2D and rotational (non-divergent), and the ageostrophic component can containcomparable in size rotational and potential (divergent) contributions. We consider a randomkinematic flow model and study the process of clustering, that is, aggregation of the floatingtracer in localized spatial patches. In the large-time limit, and in the cases of strongly and weaklydivergent flows, the existing analytical theory predicts the process of exponential clustering, whichis the emergence of spatial singularities containing all the available tracer. Here, we confirm thisanalytical prediction, in numerical model solutions spanning different combinations of rotationaland potential surface velocity components, and report that exponential clustering persists evenin weakly divergent flows, however, at significantly slower rates. For a wide range of parameters,we analyzed not only the exponential clustering, but also the other type of tracer aggregation,referred to as fragmentation clustering, as well as the coarse-graining effects on clustering. For thepresented analyses we considered ensembles of Lagrangian particles, and introduced and appliedthe statistical topography methodology.
Berloff P, 2019, Rossby waves and momentum fluxes induced by transient localised forcing in the shallow-water model, Journal of Fluid Mechanics, ISSN: 0022-1120
The aim of this study is to understand the dynamics of eddies induced by a localised and periodic‘plunger’ forcing - imposed on a background flow - which is intended as an elementary representation oftransient mesoscale eddy forcing in the ocean. We consider linearised dynamics and its quasi-nonlinearextension, and focus on the rotating shallow-water model. The plunger induces a spectrum of Rossbywaves that drive zonal momentum flux convergence at the forced latitudes. This behaviour has arobust and significant dependence on the background flow, which we treat as zonal and uniform. Wesystematically analyse this dependence using two methods. First, we use the eddy geometry formulation, in which Reynolds stresses are expressed in terms of eddy elongation and eddy tilt parameters,and consider the relationship between eddy geometry and zonal momentum redistribution. Second,we implement decompositions of flow responses into linear dynamical eigenmodes and compare withexpectations from linear Rossby wave theory. Both methods compliment each other and aid the understanding of zonal momentum redistribution and its dependence on uniform background flow. Wefind that this dependence is determined by two factors: (1) dispersion-constrained resonance with theplunger forcing and (2) efficiency of nonlinear eddy self-interactions. These results significantly improveour understanding of shallow-water Rossby waves, and may also be applied towards the developmentof parameterisations of oceanic mesoscale eddies.
Ryzhov EA, Kondrashov D, Agarwal N, et al., 2019, On data-driven augmentation of low-resolution ocean model dynamics, Ocean Modelling, Vol: 142, ISSN: 1463-5003
The problem of augmenting low-resolution ocean circulation models with the information extracted from the data relevant to the unresolved subgrid processes is addressed. A highly nonlinear model of eddy-resolving oceanic circulation – quasigeostrophic wind-driven double gyres – is considered. The model solutions are characterized by a vigorous dynamic coupling between the resolved large-scale and small-scale (eddy) flow features. This solution provides the data for augmenting the low-resolution model with the same configuration. The eddy forcing field, which contains the essential information about coupling between the large and eddy scales, is obtained, modified, coarse-grained and added to augment the low-resolution model. The implemented modification involves novel data-adaptive harmonic decomposition analysis and dynamical constraining based on the low-resolution nonlinear advection operator. The resulting augmentation of the low-resolution model significantly improves the solution, including its time-mean circulation and low-frequency variability. This result also paves the way for a systematic data-driven emulation of unresolved and under-resolved scales of motion.
Berloff P, Khatri H, 2019, Tilted, drifting jets over a zonally sloped topography: Effects of vanishing eddy viscosity, Journal of Fluid Mechanics, Vol: 876, Pages: 939-961, ISSN: 0022-1120
Oceanic multiple jets are seen to possess spatiotemporal variability imposed by varyingbottom topography resulting in jets that can drift and merge. The dynamics of multiplejets over a topographic zonal slope is studied in a two-layer quasi-geostrophic model.The jets tilt from the zonal direction and drift meridionally. In addition to the tilted jets,other large-scale spatial patterns are observed, which are extracted using the principalcomponent analysis. The variances of these patterns are strongly influenced by the valuesof eddy viscosity and bottom friction parameters. The contribution of the tilted jets tothe full flow field decreases with decreasing friction and viscosity parameters, and purelyzonal large-scale modes, propagating in the meridional direction, populate the flow field.Linear stability analysis and two-dimensional kinetic-energy spectrum analysis suggestthat the zonal modes gain energy from ambient eddies as well as from the tilted jetsthrough nonlinear interactions. However, viscous dissipation and bottom friction tendto suppress the nonlinear interactions, which results in the inhibition of the upscaleenergy transfer from eddies to the zonal modes. These simulations suggest that, in thepresence of topography, alternating jet patterns may be sustained through interactionsamong various large-scale modes. This is different from the classical zonal jet formationarguments, in which direct eddy forcing maintains the jets.
Kamenkovich I, Berloff P, Rypina II, 2019, Anisotropic and inhomogeneous eddy-induced transport in flows with jets, Zonal Jets: Phenomenology, Genesis, and Physics, Pages: 437-449, ISBN: 9781107043886
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Berloff P, Kamenkovich I, 2019, Dynamics of baroclinic multiple zonal jets, Zonal Jets: Phenomenology, Genesis, and Physics, Pages: 292-306, ISBN: 9781107043886
Khatri H, Berloff P, 2018, Role of eddies in the maintenance of multiple jets embedded in eastward and westward baroclinic shears, Fluids, Vol: 3, ISSN: 2311-5521
Multiple zonal jets observed in many parts of the global ocean are often embedded in large-scale eastward and westward vertically sheared background flows. Properties of the jets and ambient eddies, as well as their dynamic interactions, are found to be different between eastward and westward shears. However, the impact of these differences on overall eddy dynamics remains poorly understood and is the main subject of this study. The roles of eddy relative vorticity and buoyancy fluxes in the maintenance of oceanic zonal jets are studied in a two-layer quasigeostrophic model. Both eastward and westward uniform, zonal vertically sheared cases are considered in the study. It is shown that, despite the differences in eddy structure and local characteristics, the fundamental dynamics are essentially the same in both cases: the relative-vorticity fluxes force the jets in the entire fluid column, and the eddy-buoyancy fluxes transfer momentum from the top to the bottom layer, where it is balanced by bottom friction. It is also observed that the jets gain more energy via Reynolds stress work in the layer having a positive gradient in the background potential vorticity, and this is qualitatively explained by a simple reasoning based on Rossby wave group velocity.
Haigh MC, Berloff PS, 2018, Potential vorticity redistribution by localised transient forcing in the shallow-water model, Journal of Fluid Mechanics, Vol: 852, Pages: 199-225, ISSN: 0022-1120
This study is motivated by the need to develop stochastic parameterisations for representing the effects of mesoscale oceanic eddies in non-eddy-resolving and eddy-permitting ocean circulation models. A necessary logical step on the way to such parameterisations is the understanding of flow responses to spatially stationary and localised, time-dependent ‘plunger’ forcings intended to represent transient eddy flux divergences. Specifically, this study develops an understanding of the plunger-induced convergence of potential vorticity (PV) fluxes using the linearised single-layer shallow-water model. Time-periodic solutions are obtained and the ‘footprint’, defined as the time-mean, quasi-linear PV flux convergence, quantifies the cumulative PV redistribution induced by the plunger. Using the footprint, the equivalent eddy flux (EEF) is defined such that it succinctly quantifies the extent of the PV redistribution, and its dependencies on the forcing latitude and the background flow are examined in detail. For a uniform background flow the EEF is positive for all forcing latitudes, corresponding to net-poleward PV flux convergence, as expected by current theory of -plane Rossby waves. The EEF also has a robust dependence on the direction and magnitude of a uniform background flow, which is a useful quality for the EEF to provide a basis for a parameterisation of eddy PV fluxes. We also examine the PV redistribution due to forcing on top of a Gaussian jet background flow and find that forcing proximity to the jet core is the primary factor in determining whether the jet is sharpened or broadened.
Khatri H, Berloff P, 2018, A mechanism for jet drift over topography, Journal of Fluid Mechanics, Vol: 845, Pages: 392-416, ISSN: 0022-1120
The dynamics of multiple alternating oceanic jets has been studied in the presence of a simple bottom topography with constant slope in the zonal direction. A baroclinic quasi-geostrophic model forced with a horizontally uniform and vertically sheared background flow generates mesoscale eddies and jets that are tilted from the zonal direction and drift with constant speed. The governing dynamical equations are rewritten in a tilted frame of reference moving with the jets, and the cross-jet time-mean profiles of the linear and nonlinear stress terms are analysed. Here, the linear stress terms are present because of the zonally asymmetric topography. It is demonstrated that the linear dynamics controls the drift mechanism. Also, it is found that the drifting jets are directly forced by the imposed vertical shear, whereas the eddies oppose the jets, although this is limited to continuously forced dissipative systems. This role of the eddies is opposite to the one in the classical baroclinic model of stationary, zonally symmetric multiple jets. This is expected to be more generic in the ocean, which is zonally asymmetric nearly everywhere.
Berloff P, 2018, Dynamically consistent parameterization of mesoscale eddies. Part III: deterministic approach., Ocean Modelling, Vol: 127, Pages: 15-15, ISSN: 1463-5003
This work continues development of dynamically consistent parameterizations for representing mesoscale eddy effects in non-eddy-resolving and eddy-permitting ocean circulation models and focuses on the classical double-gyre problem, in which the main dynamic eddy effects maintain eastward jet extension of the western boundary currents and its adjacent recirculation zones via eddy backscatter mechanism. Despite its fundamental importance, this mechanism remains poorly understood, and in this paper we, first, study it and, then, propose and test its novel parameterization.We start by decomposing the reference eddy-resolving flow solution into the large-scale and eddy components defined by spatial filtering, rather than by the Reynolds decomposition. Next, we find that the eastward jet and its recirculations are robustly present not only in the large-scale flow itself, but also in the rectified time-mean eddies, and in the transient rectified eddy component, which consists of highly anisotropic ribbons of the opposite-sign potential vorticity anomalies straddling the instantaneous eastward jet core and being responsible for its continuous amplification. The transient rectified component is separated from the flow by a novel remapping method. We hypothesize that the above three components of the eastward jet are ultimately driven by the small-scale transient eddy forcing via the eddy backscatter mechanism, rather than by the mean eddy forcing and large-scale nonlinearities. We verify this hypothesis by progressively turning down the backscatter and observing the induced flow anomalies.The backscatter analysis leads us to formulating the key eddy parameterization hypothesis: in an eddy-permitting model at least partially resolved eddy backscatter can be significantly amplified to improve the flow solution. Such amplification is a simple and novel eddy parameterization framework implemented here in terms of local, deterministic flow roughening controlled by single paramet
Kondrashov D, Chekroun MD, Berloff P, 2018, Multiscale Stuart-Landau emulators: application to wind-driven ocean gyres, Fluids, Vol: 3, ISSN: 2311-5521
The multiscale variability of the ocean circulation due to its nonlinear dynamics remains a big challenge for theoretical understanding and practical ocean modeling. This paper demonstrates how the data-adaptive harmonic (DAH) decomposition and inverse stochastic modeling techniques introduced in (Chekroun and Kondrashov, (2017), Chaos, 27), allow for reproducing with high fidelity the main statistical properties of multiscale variability in a coarse-grained eddy-resolving ocean flow. This fully-data-driven approach relies on extraction of frequency-ranked time-dependent coefficients describing the evolution of spatio-temporal DAH modes (DAHMs) in the oceanic flow data. In turn, the time series of these coefficients are efficiently modeled by a family of low-order stochastic differential equations (SDEs) stacked per frequency, involving a fixed set of predictor functions and a small number of model coefficients. These SDEs take the form of stochastic oscillators, identified as multilayer Stuart–Landau models (MSLMs), and their use is justified by relying on the theory of Ruelle–Pollicott resonances. The good modeling skills shown by the resulting DAH-MSLM emulators demonstrates the feasibility of using a network of stochastic oscillators for the modeling of geophysical turbulence. In a certain sense, the original quasiperiodic Landau view of turbulence, with the amendment of the inclusion of stochasticity, may be well suited to describe turbulence.
van Sebille E, Griffies SM, Abernathey R, et al., 2017, Lagrangian ocean analysis: fundamentals and practices, Ocean Modelling, Vol: 121, Pages: 49-75, ISSN: 1463-5003
Lagrangian analysis is a powerful way to analyse the output of ocean circulation models and other ocean velocity data such as from altimetry. In the Lagrangian approach, large sets of virtual particles are integrated within the three-dimensional, time-evolving velocity fields. Over several decades, a variety of tools and methods for this purpose have emerged. Here, we review the state of the art in the field of Lagrangian analysis of ocean velocity data, starting from a fundamental kinematic framework and with a focus on large-scale open ocean applications. Beyond the use of explicit velocity fields, we consider the influence of unresolved physics and dynamics on particle trajectories. We comprehensively list and discuss the tools currently available for tracking virtual particles. We then showcase some of the innovative applications of trajectory data, and conclude with some open questions and an outlook. The overall goal of this review paper is to reconcile some of the different techniques and methods in Lagrangian ocean analysis, while recognising the rich diversity of codes that have and continue to emerge, and the challenges of the coming age of petascale computing.
Shevchenko I, Berloff P, 2017, On the roles of baroclinic modes in eddy-resolving midlatitude ocean dynamics, Ocean Modelling, Vol: 111, Pages: 55-65, ISSN: 1463-5011
This work concerns how different baroclinic modes interact and influence solutions of the midlatitude oceandynamics described by the eddy-resolving quasi-geostrophic model of wind-driven gyres. We developedmulti-modal energetics analysis to illuminate dynamical roles of the vertical modes, carried out a systematicanalysis of modal energetics and found that the eddy-resolving dynamics of the eastward jet extension of thewestern boundary currents, such as the Gulf Stream or Kuroshio, is dominated by the barotropic, and thefirst and second baroclinic modes, which become more energized with smaller eddy viscosity. In the absenceof high baroclinic modes, the energy input from the wind is more efficiently focused onto the lower modes,therefore, the eddy backscatter maintaining the eastward jet and its adjacent recirculation zones is thestrongest and overestimated with respect to cases including higher baroclinic modes. In the presence of highbaroclinic modes, the eddy backscatter effect on the eastward jet is much weaker. Thus, the higher baroclinicmodes play effectively the inhibiting role in the backscatter, which is opposite to what has been previouslythought. The higher baroclinic modes are less energetic and have progressively decreasing effect on the flowdynamics; nevertheless, they still play important roles in inter-mode energy transfers (by injecting energyinto the region of the most intensive eddy forcing, in the neighborhood of the eastward jet) that have to betaken into account for correct representation of the backscatter and, thus, for determining the eastward jetextension.
Kamenkovich I, Berloff P, 2017, Role of Nonlinear Eddy Forcing in the Dynamics of Multiple Zonal Jets, Advances in Nonlinear Geosciences, Pages: 161-178, ISBN: 9783319588940
Turbulent oceanic and atmospheric flows are characterized by persistent nearly zonal alternating currents, referred to as multiple zonal jets. These jets emerge from self-organization of the flow, and are maintained by persistent action of transient fluctuations (“eddies”). The action of these eddies takes a form of internally generated eddy forcing that can either resist the jets or support them against dissipation and other processes. This review chapter is concerned with the role of the eddy forcing in the dynamics of the multiple zonal jets in the ocean, but the results are also applicable to atmospheric flows and some isolated jets in the ocean.
Chen C, Kamenkovich I, Berloff P, 2016, Eddy trains and striations in quasigeostrophic simulations and the ocean, Journal of Physical Oceanography, Vol: 46, Pages: 2807-2825, ISSN: 1520-0485
This study explores the relationship between coherent eddies and zonally elongated striations. The investigation involves an analysis of two baroclinic quasigeostrophic models of a zonal and double-gyre flow and a set of altimetry sea level anomaly data in the North Pacific. Striations are defined by either spatiotemporal filtering or empirical orthogonal functions (EOFs), with both approaches leading to consistent results. Coherent eddies, identified here by the modified Okubo–Weiss parameter, tend to propagate along well-defined paths, thus forming “eddy trains” that coincide with striations. The striations and eddy trains tend to drift away from the intergyre boundary at the same speed in both the model and observations. The EOF analysis further confirms that these striations in model simulations and altimetry are not an artifact of temporal averaging of random, spatially uncorrelated vortices. This study suggests instead that eddies organize into eddy trains, which manifest themselves as striations in low-pass filtered data and EOF modes.
Shevchenko I, Berloff P, 2016, Eddy Backscatter and Counter-Rotating Gyre Anomalies of Midlatitude Ocean Dynamics, Fluids, Vol: 1, ISSN: 2311-5521
This work concerns how two competing mechanisms – eddy backscatter and2 counter-rotating gyre anomalies – influence the midlatitude ocean dynamics, as described by3 the eddy-resolving quasi-geostrophic (QG) model of wind-driven gyres. We analysed dynamical4 balances and effects of different eddy forcing components, as well as their dependencies on5 increasing vertical resolution and decreasing eddy viscosity and found that the eastward jet6 and its adjacent recirculation zones are maintained mostly by the eddy forcing via the eddy7 backscatter mechanism, whereas the time-mean eddy-forcing component plays not only direct8 jet-supporting but also indirect jet-inhibiting role. The latter is achieved by inducing zonally9 elongated anticyclonic/cyclonic Counter-rotating Gyre Anomaly (CGA) in the subpolar/subtropical10 gyre. The indirect effect of CGAs on the eastward jet is found to be moderate relative to the dominant11 eddy backscatter mechanism. We also found that the higher is the vertical baroclinic mode, the12 weaker is its backscatter role and the stronger is its CGA-driving role. Although the barotropic and13 first baroclinic modes are the most efficient ones in maintaining the backscatter, the higher, up to the14 fifth baroclinic modes also have significant but reverse impact that reduces the backscatter
Berloff P, 2016, Dynamically Consistent Parameterization of Mesoscale Eddies-Part II: Eddy Fluxes and Diffusivity from Transient Impulses, Fluids, Vol: 1, ISSN: 2311-5521
This work continues development of the framework for dynamically consistent parameterization of mesoscale eddy effects in non-eddy-resolving ocean circulation models. Here, we refine and extend the previous results obtained for the double gyres and aim to account for the eddy backscatter mechanism that maintains eastward jet extension of the western boundary currents. We start by overcoming the local homogeneity assumption and by taking into account full large-scale circulation. We achieve this by considering linearized-dynamic responses to finite-time transient impulses. Feedback from these impulses on the large-scale circulation are referred to as footprints. We find that the local homogeneity assumption yields only quantitative errors in most of the gyres but breaks down in the eastward jet region, which is characterized by the most significant eddy effects. The approach taken provides new insights into the eddy/mean interactions and framework for parameterization of unresolved eddy effects. Footprints provide us with maps of potential vorticity anomalies expected to be induced by transient eddy forcing. This information is used to calculate the equivalent eddy potential vorticity fluxes and their divergences that partition the double-gyre circulation into distinct geographical regions with specific eddy effects. In particular, this allows approximation of the real eddy effects that maintain the eastward jet extension of the western boundary currents and its adjacent recirculation zones. Next, from footprints and their equivalent eddy fluxes and from underlying large-scale flow gradients, we calculate spatially inhomogeneous and anisotropic eddy diffusivity tensor. Its properties suggest that imposing parameterized source terms, that is, equivalent eddy flux divergences, is a better parameterization strategy than implementation of the eddy diffusion.
Shevchenko I, Berloff P, Guerrero-López D, et al., 2016, On low-frequency variability of the midlatitude ocean gyres, Journal of Fluid Mechanics, Vol: 795, Pages: 423-442, ISSN: 1469-7645
This paper studies the large-scale low-frequency variability of the wind-driven midlatitude ocean gyres and their western boundary currents, such as the Gulf Stream or Kuroshio, simulated with the eddy-resolving quasi-geostrophic model. We applied empirical orthogonal functions analysis to turbulent flow solutions and statistically extracted robust and significant large-scale decadal variability modes concentrated around the eastward jet extension of the western boundary currents. In order to interpret these statistical modes dynamically, we linearized the governing quasi-geostrophic equations around the time-mean circulation and solved for the corresponding full set of linear eigenmodes with their eigenfrequencies. We then projected the extracted decadal variability on the eigenmodes and found that this variability is a multimodal coherent pattern phenomenon rather than a single mode or a combination of several modes as in the flow regimes preceding developed turbulence.
Shevchenko IV, Berloff PS, 2015, Multi-layer quasi-geostrophic ocean dynamics in Eddy-resolving regimes, Ocean Modelling, Vol: 94, Pages: 1-14, ISSN: 1463-5011
The multi-layer quasi-geostrophic model of the wind-driven ocean gyres is numerically investigated using a combination of long-time runs (200 years) needed for accurate statistics, spatial resolutions (grid interval of less than one kilometer) needed for accurate representation of mesoscale eddies, and large Reynolds number (Re > 104) needed for more realistic flow regimes. We gradually increased the Reynolds number by lowering the eddy viscosity and analysed the corresponding changes of the large-scale circulation, energetics and eddy fluxes, with the goal to understand how the nonlinear eddy dynamics affects the large-scale ocean circulation, as more and more degrees of freedom become dynamically available. Three- and six-layer configurations of the model are considered in order to understand effects of higher baroclinic modes. A parameter sensitivity study is also carried out to show that the explored flow regime is robust.As Re increases, most properties of the flow show no signs of approaching an asymptote, and the following tendencies are found. The time-mean flow properties tend to an asymptote in the three-layer model but not in the six-layer one, suggesting that higher baroclinic modes are dynamically more active at larger Re. The eddy kinetic and potential energies grow faster in the six-layer case. The intensity of the eddy forcing (eddy flux divergence) increases with Re. The inter-gyre eddy potential vorticity flux is predominantly northward and up-gradient for all Re studied. A comparison of the three- and six-layer model solutions revealed an inhibitory influence of high baroclinic modes on the penetration length of the eastward jet extension of the western boundary currents and on the strength of the adjacent recirculation zones. In large-Re regimes, the population of eddies is mostly sustained by the eddy generation at the eastern end of the eastward jet rather than in its central section. Finally, by studying the numerical convergence of the sol
Kondrashov D, Berloff P, 2015, Stochastic modeling of decadal variability in ocean gyres, GEOPHYSICAL RESEARCH LETTERS, Vol: 42, Pages: 1543-1553, ISSN: 0094-8276
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Berloff P, 2015, Dynamically consistent parameterization of mesoscale eddies. Part I: Simple model, Ocean Modelling, Vol: 87, Pages: 1-19, ISSN: 1463-5003
This work aims at developing a framework for dynamically consistent parameterization of mesoscale eddy effects for use in non-eddy-resolving ocean circulation models. The proposed eddy parameterization framework is successfully tested on the classical, wind-driven double-gyre model, which is solved both with explicitly resolved vigorous eddy field and in the non-eddy-resolving configuration with the eddy parameterization replacing the eddy effects. The parameterization locally approximates transient eddy flux divergence by spatially localized and temporally periodic forcing, referred to as the plunger, and focuses on the linear-dynamics flow solution induced by it. The nonlinear self-interaction of this solution, referred to as the footprint, characterizes and quantifies the induced cumulative eddy forcing exerted on the large-scale flow. We find that spatial pattern and amplitude of the footprint strongly depend on the underlying large-scale and the corresponding relationships provide the basis for the eddy parameterization and its closure on the large-scale flow properties. Dependencies of the footprints on other important parameters of the problem are also systematically analyzed. The parameterization utilizes the local large-scale flow information, constructs and scales the corresponding footprints, and then sums them up over the gyres to produce the resulting eddy forcing field, which is interactively added to the model as an extra forcing. The parameterization framework is implemented in the simplest way, but it provides a systematic strategy for improving the implementation algorithm.
Kamenkovich I, Rypina II, Berloff P, 2015, Properties and Origins of the Anisotropic Eddy-Induced Transport in the North Atlantic, JOURNAL OF PHYSICAL OCEANOGRAPHY, Vol: 45, Pages: 778-791, ISSN: 0022-3670
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- Citations: 34
Chen C, Kamenkovich I, Berloff P, 2015, On the Dynamics of Flows Induced by Topographic Ridges, JOURNAL OF PHYSICAL OCEANOGRAPHY, Vol: 45, Pages: 927-940, ISSN: 0022-3670
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- Citations: 11
Berloff P, Kamenkovich I, 2013, On Spectral Analysis of Mesoscale Eddies. Part I: Linear Analysis, JOURNAL OF PHYSICAL OCEANOGRAPHY, Vol: 43, Pages: 2505-2527, ISSN: 0022-3670
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- Citations: 34
Berloff P, Kamenkovich I, 2013, On spectral analysis of mesoscale eddies. Part II: Nonlinear analysis., Journal of Physical Oceanography, Vol: n/a, ISSN: 0022-3670
Rypina II, Kamenkovich I, Berloff P, et al., 2012, Eddy-Induced Particle Dispersion in the Near-Surface North Atlantic, JOURNAL OF PHYSICAL OCEANOGRAPHY, Vol: 42, Pages: 2206-2228, ISSN: 0022-3670
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- Citations: 83
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