Nonlinear Equilibration of Baroclinic Instability: The Growth Rate Balance Model

Radko, Timour; Flanagan, Jason D.

doi:10.1175/jpo-d-13-0248.1

Cited by 17 publications

(14 citation statements)

References 77 publications

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“…Until that time, there remains an urgent need for accurate representation/parameterization of mesoscale processes. The work presented in this study generalizes the theory of Radko et al () to make it more applicable to developing a new subgrid‐scale model for these large‐scale systems. In addition to the pragmatic task of parameterizing mesoscale eddies for the purpose of climate modeling, even more rewarding and intellectually challenging is the task of explaining the dynamics and transport characteristics of mesoscale eddies from first principles.…”

Section: Introductionmentioning

confidence: 57%

“…We simulate equations to using a dealiased pseudo‐spectral method in which integration in time is performed using a fourth‐order Runge‐Kutta scheme. The numerics generalize those of Radko et al () to include the effects of sloping bottom and flows with a general orientation. We performed a series of simulations with 256 Fourier modes in both x and y with a total extent of 100 radii of deformation in each direction.…”

Section: Numerical Modelmentioning

confidence: 95%

“…A cross‐stream thermal gradient maintains thermal wind balance, which serves as the energy source for the instability. This study attempts to explain the saturation of the baroclinic instability by invoking growth rate balance theory (Radko & Smith, ; Radko et al, ). Our model is based on an intuitive assumption that baroclinic instability grows until a secondary instability (such as the production of barotropic jets) begins to disrupt the initial instability.…”

Section: Introductionmentioning

confidence: 99%

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Effects of Topography and Orientation on the Nonlinear Equilibration of Baroclinic Instability

2019

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This study attempts to identify the equilibration mechanisms of baroclinic instability and investigate the effects of the orientation of the background flow and topography on eddy-induced transport. The analysis is based on growth rate balance theory, which assumes that nonlinear equilibration occurs when the growth rate of the primary baroclinic instability becomes comparable to that of the secondary instabilities of amplifying modes. Two-layer quasi-geostrophic numerical simulations are performed and compared to growth rate balance theory in order to analytically predict the cross-stream fluxes of potential vorticity. The model performs remarkably well in predicting the effects of variation in zonal topographic slope and background flow orientation. We find that meridional topographic slopes affect the baroclinic instability in an inherently nonlinear way. A predictive model based on conservation of potential vorticity is developed for the optimal slope that maximizes the transport characteristics of the baroclinic instability. Plain Language SummaryThe ocean is full of vortices on the scale of 10-100 km which play a major role in dispersing heat, salt, nutrients, and pollutants. However, the precise equilibration mechanisms controlling the production of these vortices remain a mystery. Physically, this process begins with the creation of north-south oriented streams which themselves result in a secondary stream formation oriented in an east-west direction. A new theory has found that when the north-south streams balance the east-west streams, the system achieves an equilibrium that allows us to characterize the heat transport by vortices through this system, which is critical to understanding global climate. Some key parts of this mystery are the effects of the ocean floor topography and the direction of the current on the production of these vortices. The proposed theory predicts the fluxes of heat as a function of ocean floor slopes and current direction. Key Points:• A semianalytical theory predicts eddy-induced transport in baroclinically unstable ocean regions • Effects of zonal topographic slope and orientation of the basic flow compare well to growth rate balance theory • We present a predictive model that determines the meridional slope that maximizes cross-stream flux of potential vorticity Supporting Information:• Supporting Information S1

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Section: Introductionmentioning

confidence: 57%

Section: Numerical Modelmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

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Effects of Topography and Orientation on the Nonlinear Equilibration of Baroclinic Instability

2019

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“…There are also eddy diffusivity theories for horizontally homogeneous flows [16], but their applicability to inhomogeneous flows is unclear. Another idea for deriving an eddy diffusivity closure is that a fully developed equilibrium state of the baroclinic turbulence is characterized by the comparable growth rates of primary and secondary instabilities of the large-scale flow patterns [17]. Finally, various spectral homogeneous-turbulence diffusivity approaches (e.g., [18]) base derivation of scale-dependent eddy diffusivity on the existence of a universal turbulent energy spectrum and on the mixing-length arguments; therefore, they do not apply to oceanic mesoscale eddies that are spatially inhomogeneous and exhibit no universal spectra.…”

Section: Introductionmentioning

confidence: 99%

Dynamically Consistent Parameterization of Mesoscale Eddies—Part II: Eddy Fluxes and Diffusivity from Transient Impulses

Berloff

2016

Fluids

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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.

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“…Although the linear mechanism of baroclinic instability is well understood, its nonlinear properties in a saturated state are still a subject of investigation. A recent study by Radko et al [2014] offers a theoretical model which allows one to predict certain properties of the variability generated by baroclinic instability. The theory is based on an assumption that instability saturates when the growth rates of the primary instability (meridional jets, noodles) and the secondary instability (zonal jets) are comparable.…”

Section: Introductionmentioning

confidence: 99%

Zonal jets in equilibrating baroclinic instability on the polar beta‐plane: Experiments with altimetry

Matulka

Afanasyev

2015

JGR Oceans

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Results from the laboratory experiments on the evolution of baroclinically unstable flows generated in a rotating tank with topographic -effect are presented.We study zonal jets of alternating direction which occur in these flows. The primary system we model includes lighter fluid in the South and heavier fluid in the North with resulting slow meridional circulation and fast mean zonal motion. In a two-layer system the velocity shear between the layers results in baroclinic instability which equilibrates with time and, due to interaction with -effect generates zonal jets. This system is archetypal for various geophysical systems including the general circulation and jet streams in the Earth's atmosphere, the Antarctic Circumpolar Current or the areas in the vicinity of western boundary currents where baroclinic instability and multiple zonal jets are observed. The gradient of the surface elevation and the thickness of the upper layer are measured in the experiments using the Altimetric Imaging Velocimetry and the Optical Thickness Velocimetry techniques respectively. Barotropic and baroclinic velocity fields are then derived from the measured quantities. The results demonstrate that the zonal jets are driven by "eddy forcing" due to continuously created baroclinic perturbations. The flow is baroclinic to a significant degree and the jets are "surface intensified". The meridional wavelength of 3 the jets varies linearly with the baroclinic radius of deformation and is also in a good agreement with a modified Rhines scale. This suggests a linear dependence of the perturbation velocity in the equilibrated baroclinically unstable flow on the parameter.

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Nonlinear Equilibration of Baroclinic Instability: The Growth Rate Balance Model

Cited by 17 publications

References 77 publications

Effects of Topography and Orientation on the Nonlinear Equilibration of Baroclinic Instability

Effects of Topography and Orientation on the Nonlinear Equilibration of Baroclinic Instability

Dynamically Consistent Parameterization of Mesoscale Eddies—Part II: Eddy Fluxes and Diffusivity from Transient Impulses

Zonal jets in equilibrating baroclinic instability on the polar beta‐plane: Experiments with altimetry

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