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Register a new userA barotropic model of eddy saturation
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Authors
Navid C. Constantinou
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Eddy saturation refers to a regime in which the total volume transport of an oceanic current is insensitive to the wind stress strength. Baroclinicity is currently believed to be key to the development of an eddy-saturated state. In this paper, it is shown that eddy saturation can also occur in a purely barotropic flow over topography, without baroclinicity. Thus, eddy saturation is a fundamental property of barotropic dynamics above topography. It is demonstrated that the main factor controlling the appearance or not of eddy-saturated states in the barotropic setting is the structure of geostrophic contours, that is the contours of $f/H$ of the ratio of the Coriolis parameter to the oceans depth. Eddy-saturated states occur when the geostrophic contours are open, that is when the geostrophic contours span the whole zonal extent of the domain. This minimal requirement for eddy-saturated states is demonstrated using numerical integrations of a single-layer quasi-geostrophic flow over two different topographies characterized by either open or closed geostrophic contours with parameter values loosely inspired by the Southern Ocean. In this setting, transient eddies are produced through a barotropic-topographic instability that occurs due tot the interaction of the large-scale zonal flow with the topography. Through the study of this barotropic-topographic instability insight is gained on how eddy-saturated states are established.
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Eddy saturation is the regime in which the total time-mean volume transport of an oceanic current is relatively insensitive to the wind stress forcing and is often invoked as a dynamical description of Southern Ocean circulation. We revisit the problem of eddy saturation using a primitive-equations model in an idealized channel setup with bathymetry. We apply only mechanical wind stress forcing; there is no diapycnal mixing or surface buoyancy forcing. Our main aim is to assess the relative importance of two mechanisms for producing eddy saturated states: (i) the commonly invoked baroclinic mechanism that involves the competition of sloping isopycnals and restratification by production of baroclinic eddies, and (ii) the barotropic mechanism, that involves production of eddies through lateral shear instabilities or through the interaction of the barotropic current with bathymetric features. Our results suggest that the barotropic flow-component plays a crucial role in determining the total volume transport.
Eddy saturation describes the nonlinear mechanism in geophysical flows whereby, when average conditions are considered, direct forcing of the zonal flow increases the eddy kinetic energy, while the energy associated with the zonal flow does not increase. Here we present a minimal baroclinic model that exhibits complete eddy saturation. Starting from Phillips classical quasi-geostrophic two-level model on the beta channel of the mid-latitudes, we derive a reduced order model comprising of six ordinary differential equations including parameterised eddies. This model features two physically realisable steady state solutions, one a purely zonal flow and one where, additionally, finite eddy motions are present. As the baroclinic forcing in the form of diabatic heating is increased, the zonal solution loses stability and the eddy solution becomes attracting. After this bifurcation, the zonal components of the solution are independent of the baroclinic forcing, and the excess of heat in the low latitudes is efficiently transported northwards by finite eddies, in the spirit of baroclinic adjustment.
In this study the influence of stratification on surface tidal elevations in a two-layer analytical model is examined. The model assumes linearized, non-rotating, shallow-water dynamics in one dimension with astronomical forcing and allows for arbitrary topography. Using a natural modal separation, both large scale (barotropic) and small scale (baroclinic) components of the surface tidal elevation are shown to be comparably affected by stratification. It is also shown that the topography and basin boundaries affect the sensitivity of the barotropic surface tide to stratification significantly. This paper, therefore, provides a framework to understand how the presence of stratification impacts barotropic as well as baroclinic tides, and how climatic perturbations to oceanic stratification contribute to secular variations in tides. Results from a realistic-domain global numerical two-layer tide model are briefly examined and found to be qualitatively consistent with the analytical model results.
We use dynamical systems approach and Lagrangian tools to study surface transport and mixing of water masses in a selected coastal region of the Japan Sea with moving mesoscale eddies associated with the Primorskoye Current. Lagrangian trajectories are computed for a large number of particles in an interpolated velocity field generated by a numerical regional multi-layer eddy-resolving circulation model. We compute finite-time Lyapunov exponents for a comparatively long period of time by the method developed and plot the Lyapunov synoptic map quantifying surface transport and mixing in that region. This map uncovers the striking flow structures along the coast with a mesoscale eddy street and repelling material lines. We propose new Lagrangian diagnostic tools --- the time of exit of particles off a selected box, the number of changes of the sign of zonal and meridional velocities --- to study transport and mixing by a pair of strongly interacting eddies often visible at sea-surface temperature satellite images in that region. We develop a technique to track evolution of clusters of particles, streaklines and material lines. The Lagrangian tools used allow us to reveal mesoscale eddies and their structure, to track different phases of the coastal flow, to find inhomogeneous character of transport and mixing on mesoscales and submesoscales and to quantify mixing by the values of exit times and the number of times particles wind around the eddys center.
Zonal jets in a barotropic setup emerge out of homogeneous turbulence through a flow-forming instability of the homogeneous turbulent state (`zonostrophic instability) which occurs as the turbulence intensity increases. This has been demonstrated using the statistical state dynamics (SSD) framework with a closure at second order. Furthermore, it was shown that for small supercriticality the flow-forming instability follows Ginzburg-Landau (G-L) dynamics. Here, the SSD framework is used to study the equilibration of this flow-forming instability for small supercriticality. First, we compare the predictions of the weakly nonlinear G-L dynamics to the fully nonlinear SSD dynamics closed at second order for a wide ranges of parameters. A new branch of jet equilibria is revealed that is not contiguously connected with the G-L branch. This new branch at weak supercriticalities involves jets with larger amplitude compared to the ones of the G-L branch. Furthermore, this new branch continues even for subcritical values with respect to the linear flow-forming instability. Thus, a new nonlinear flow-forming instability out of homogeneous turbulence is revealed. Second, we investigate how both the linear flow-forming instability and the novel nonlinear flow-forming instability are equilibrated. We identify the physical processes underlying the jet equilibration as well as the types of eddies that contribute in each process. Third, we propose a modification of the diffusion coefficient of the G-L dynamics that is able to capture the asymmetric evolution for weak jets at scales other than the marginal scale (side-band instabilities) for the linear flow-forming instability.
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