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Baylor Fox-Kemper

Abstract

Multiple-gyre ocean models have a weaker mean subtropical circulation than single-gyre calculations with the same viscosity and subtropical forcing. Traditionally, this reduction in circulation is attributed to an intergyre eddy vorticity flux that cancels some of the wind input, part of which does not require a Lagrangian mass exchange (theory of dissipative meandering). Herein the intergyre eddy vorticity flux is shown to be a controlling factor in barotropic models at high Reynolds number only with exactly antisymmetric gyres and slip boundary conditions. Almost no intergyre flux occurs when no-slip boundary conditions are used, yet the subtropical gyre is still significantly weaker in multiple-gyre calculations. Sinuous modes of instability present only in multiple gyres are shown here to vastly increase the eddy vorticity transport efficiency. This increase in efficiency reduces the mean circulation necessary for equilibrium. With slip boundary conditions, the intergyre eddy transport is possibly much larger. However, with wind forcing relevant for the ocean—two unequal gyres—a mean flow flux of vorticity rather than an eddy flux between the regions of opposing wind forcing is increasingly important with increasing Reynolds number. A physical rationalization of the differing results is provided by diagnosis of the equilibrium vorticity budget and eddy transport efficiency. Calculations varying 1) boundary conditions, 2) sources and sinks of vorticity, 3) eddy transport efficiency, and 4) the degree of symmetry of the gyres are discussed.

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Baylor Fox-Kemper and Raffaele Ferrari

Abstract

The authors propose a parameterization for restratification by mixed layer eddies that develop from baroclinic instabilities of ocean fronts. The parameterization is cast as an overturning streamfunction that is proportional to the product of horizontal buoyancy gradient, mixed layer depth, and inertial period. The parameterization has remarkable skill for an extremely wide range of mixed layer depths, rotation rates, and vertical and horizontal stratifications. In this paper a coarse resolution prognostic model of the parameterization is compared with submesoscale mixed layer eddy resolving simulations. The parameterization proves accurate in predicting changes to the buoyancy. The climate implications of the proposed parameterization are estimated by applying the restratification scaling to observations: the mixed layer depth is estimated from climatology, and the buoyancy gradients are from satellite altimetry. The vertical fluxes are comparable to monthly mean air–sea fluxes in large areas of the ocean and suggest that restratification by mixed layer eddies is a leading order process in the upper ocean. Critical regions for ocean–atmosphere interaction, such as deep, intermediate, and mode water formation sites, are particularly affected.

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Baylor Fox-Kemper and Raffaele Ferrari

Abstract

The time-mean effects of eddies are studied in a model based on the Parsons–Veronis–Huang–Flierl models of the wind-driven gyre. Much of the analysis used for the steady solutions carries over if the model is cast in terms of the thickness-weighted mean velocity, because then mass transport is nondivergent in the absence of diabatic forcing. The model exemplifies the use of residual mean theory to simplify analysis.

A result of the analysis is a boundary layer width in the case of a rapid upper-layer flow and weak lower-layer flow. This boundary layer width is comparable to an eddy mixing length when the typical eddy velocity is taken to be the long Rossby wave phase speed.

Further analysis of the model illustrates important aspects of eddy behavior, model sensitivity to eddy fluxes, and model sensitivity to frictional parameters.

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Qing Li and Baylor Fox-Kemper

Abstract

Large-eddy simulations (LESs) with various constant wind, wave, and surface destabilizing surface buoyancy flux forcing are conducted, with a focus on assessing the impact of Langmuir turbulence on the entrainment buoyancy flux at the base of the ocean surface boundary layer. An estimate of the entrainment buoyancy flux scaling is made to best fit the LES results. The presence of Stokes drift forcing and the resulting Langmuir turbulence enhances the entrainment rate significantly under weak surface destabilizing buoyancy flux conditions, that is, weakly convective turbulence. In contrast, Langmuir turbulence effects are moderate when convective turbulence is dominant and appear to be additive rather than multiplicative to the convection-induced mixing. The parameterized unresolved velocity scale in the K-profile parameterization (KPP) is modified to adhere to the new scaling law of the entrainment buoyancy flux and account for the effects of Langmuir turbulence. This modification is targeted on common situations in a climate model where either Langmuir turbulence or convection is important and may overestimate the entrainment when both are weak. Nevertheless, the modified KPP is tested in a global climate model and generally outperforms those tested in previous studies. Improvements in the simulated mixed layer depth are found, especially in the Southern Ocean in austral summer.

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Haijin Cao, Baylor Fox-Kemper, and Zhiyou Jing

Abstract

The submesoscale energy budget is complex and remains understood only in region-by-region analyses. Based on a series of nested numerical simulations, this study investigated the submesoscale energy budget and flux in the upper ocean of the Kuroshio Extension, including some innovations for examining submesoscale energy budgets in general. The highest-resolution simulation on a ~500-m grid resolves a variety of submesoscale instabilities allowing an energetic analysis in the submesoscale range. The frequency–wavenumber spectra of vertical vorticity variance (i.e., enstrophy) and horizontal divergence variance were used to identify the scales of submesoscale flows as distinct from those of inertia–gravity waves but dominating horizontal divergence variance. Next, the energy transfers between the background scales and the submesoscale were examined. The submesoscale kinetic and potential energy (SMKE and SMPE) were mainly contained in the mixed layer and energized through both barotropic (shear production) and baroclinic (buoyancy production) routes. Averaged over the upper 50 m of ROMS2, the baroclinic transfers amounted to approximately 75% of the sources for the SMKE (3.42 × 10−9 W kg−1) versus the remaining 25% (1.12 × 10−9 W kg−1) via barotropic downscale KE transfers. The KE field was greatly strengthened by energy sources through the boundary—this flux is larger than the mesoscale-to-submesoscale transfers in this region. Spectral energy production, importantly, reveals upscale KE transfers at larger submesoscales and downscale KE transfers at smaller submesoscales (i.e., a transition from inverse to forward KE cascade). This study seeks to extend our understanding of the energy cycle to the submesoscale and highlight the forward KE cascade induced by upper-ocean submesoscale activities in the research domain.

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Katherine McCaffrey, Baylor Fox-Kemper, and Gael Forget

Abstract

The Argo profiling float network has repeatedly sampled much of the World Ocean. This study uses Argo temperature and salinity data to form the tracer structure function of ocean variability at the macroscale (10–1000 km, mesoscale and above). Here, second-order temperature and salinity structure functions over horizontal separations are calculated along either pressure or potential density surfaces, which allows analysis of both active and passive tracer structure functions. Using Argo data, a map of global variance is created from the climatological average and each datum. When turbulence is homogeneous, the structure function slope from Argo can be related to the wavenumber spectrum slope in ocean temperature or salinity variability. This first application of structure function techniques to Argo data gives physically meaningful results based on bootstrapped confidence intervals, showing geographical dependence of the structure functions with slopes near ⅔ on average, independent of depth.

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Baylor Fox-Kemper, Raffaele Ferrari, and Joseph Pedlosky

Abstract

The decomposition of an eddy flux into a divergent flux component and a rotational flux component is not unique in a bounded or singly periodic domain. Therefore, assertions made under the assumption of uniqueness, implicit or explicit, may be meaningless. Nondivergent, irrotational perturbations are allowed to any decomposition that may affect naive interpretation of the flux field. These perturbations are restricted, however, so that unique diagnostics can be formed from the flux field.

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Samantha Stevenson, Baylor Fox-Kemper, and Markus Jochum

Abstract

The influence of atmospheric CO2 concentration on the El Niño–Southern Oscillation (ENSO) is explored using 800-yr integrations of the NCAR Community Climate System Model, version 3.5 (CCSM3.5), with CO2 stabilized at the a.d. 1850, 1990, and 2050 levels. Model mean state changes with increased CO2 include preferential SST warming in the eastern equatorial Pacific, a weakening of the equatorial trade winds, increased vertical ocean stratification, and a reduction in the atmospheric Hadley and oceanic subtropical overturning circulations. The annual cycle of SST strengthens with CO2, likely related to unstable air–sea interactions triggered by an increased Northern Hemisphere land–sea temperature contrast. The mean trade wind structure changes asymmetrically about the equator, with increased convergence in the Northern Hemisphere and divergence in the Southern Hemisphere leading to corresponding deepening and shoaling of the thermocline. The proportion of eastern versus central Pacific–type El Niño events increases with CO2, but the significance of the changes is relatively low; ENSO amplitude also increases with CO2, although the change is insignificant at periods longer than 4 yr. The 2–4-yr ENSO response shows an enhancement in equatorial Kelvin wave variability, suggesting that stochastic triggering of El Niño events may be favored with higher CO2. However, the seasonal cycle–ENSO interaction is also modified by the asymmetric climatological changes, and forcing by the Southern Hemisphere becomes more important with higher CO2. Finally, higher-resolution CCSM4 control simulations show that ENSO weakens with CO2 given a sufficiently long integration time. The cause for the difference in ENSO climate sensitivity is not immediately obvious but may potentially be related to changes in westerly wind bursts or other sources of high-frequency wind stress variability.

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Baylor Fox-Kemper, Raffaele Ferrari, and Robert Hallberg

Abstract

Ageostrophic baroclinic instabilities develop within the surface mixed layer of the ocean at horizontal fronts and efficiently restratify the upper ocean. In this paper a parameterization for the restratification driven by finite-amplitude baroclinic instabilities of the mixed layer is proposed in terms of an overturning streamfunction that tilts isopycnals from the vertical to the horizontal. The streamfunction is proportional to the product of the horizontal density gradient, the mixed layer depth squared, and the inertial period. Hence restratification proceeds faster at strong fronts in deep mixed layers with a weak latitude dependence. In this paper the parameterization is theoretically motivated, confirmed to perform well for a wide range of mixed layer depths, rotation rates, and vertical and horizontal stratifications. It is shown to be superior to alternative extant parameterizations of baroclinic instability for the problem of mixed layer restratification. Two companion papers discuss the numerical implementation and the climate impacts of this parameterization.

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Giulio Boccaletti, Raffaele Ferrari, and Baylor Fox-Kemper

Abstract

The restratification of the oceanic surface mixed layer that results from lateral gradients in the surface density field is studied. The lateral gradients are shown to be unstable to ageostrophic baroclinic instabilities and slump from the horizontal to the vertical. These instabilities, which are referred to as mixed layer instabilities (MLIs), differ from instabilities in the ocean interior because of the weak surface stratification. Spatial scales are O(1–10) km, and growth time scales are on the order of a day. Linear stability analysis and fully nonlinear simulations are used to study MLIs and their impact on mixed layer restratification. The main result is that MLIs are a leading-order process in the ML heat budget acting to constantly restratify the surface ocean. Climate and regional ocean models do not resolve the scales associated with MLIs and are likely to underestimate the rate of ML restratification and consequently suffer from a bias in sea surface temperatures and ML depths. In a forthcoming paper, the authors discuss a parameterization scheme to include the effect of MLIs in ocean models.

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