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Oceanic motions with spatial scales of 200 m–20 km, called submesoscales, are ubiquitous in the upper ocean and serve as a key intermediary between larger-scale balanced dynamics and unbalanced turbulence. Here, we introduce the fluid dynamics of submesoscales and contrast them with motions at larger and smaller scales. We summarize the various ways in which submesoscales develop due to instabilities that extract potential or kinetic energy from larger-scale balanced currents; some instabilities have counterparts at larger scales, while others are distinct to the submesoscale regime. Submesoscales modify the density stratification in the upper ocean and redistribute energy between scales. These energy transfers are complex, having both up-scale and down-scale components. Submesoscale eddies and fronts also contribute to a spatially heterogeneous distribution of shear and restratification that leave an imprint on upper ocean turbulence. The impact of submesoscales on the Earth's climate remains an exciting research frontier.

This paper proposes methods for set-valued state estimation of nonlinear, discrete-time systems with nonlinear measurements. This is achieved by combining a novel construct called the input-output set, which approximates system dynamics and measurements, with the hybrid zonotope set representation that can efficiently represent nonconvex and disjoint sets. The methods leverage existing approaches for approximation of nonlinear functions including special ordered set approximations and neural networks. A numerical example demonstrates the proposed method with comparison to a convex approach., Comment: arXiv admin note: text overlap with arXiv:2304.06827

A signature of submesoscale flows in the upper ocean is skewness in the distribution of relative vorticity. Expected to result for high Rossby number flows, such skewness has implications for mixing, dissipation, and stratification within the upper ocean. An array of moorings deployed in the Northeast Atlantic for 1 year as part of the experiment of the Ocean Surface Mixing, Ocean Submesoscale Interaction Study (OSMOSIS) reveals that relative vorticity is positively skewed during winter even though the scale of the Rossby number is less than 0.5. Furthermore, this skewness is reduced to zero during spring and autumn. There is also evidence of modest seasonal variations in the gradient Rossby number. The proposed mechanism by which relative vorticity is skewed is that the ratio of lateral to vertical buoyancy gradients, as summarized by the inverse gradient Richardson number, restricts its range during winter but less so at other times of the year. These results support recent observations and model simulations suggesting that the upper ocean is host to a seasonal cycle in submesoscale turbulence.

The ocean moderates the Earth's climate due to its vast capacity to store and transport heat; the influence of the large-scale ocean circulation on changes in climate is considered in this chapter. The ocean experiences both buoyancy forcing (through heating/cooling and evaporation/precipitation) and wind forcing. Almost all ocean forcing occurs at the surface, but these changes are communicated throughout the entire depth of the ocean through the meridional overturning circulation (MOC). In a few localized regions, water become sufficiently dense to penetrate thousands of meters deep, where it spreads, providing a continuous source of deep dense water to the entire ocean. Dense water returns to the surface and thus closes the MOC, either through density modification due to diapycnal mixing or by upwelling along sloping isopycnals across the Southern Ocean. Determination of the relative contributions of these two processes in the MOC remains an active area of research. Observations obtained primarily from isotopic compositions in ocean sediments provide substantial evidence that the structure of the MOC has changed significantly in the past. Indeed, large and abrupt changes to the Earth's climate during the past 120,000 years can be linked to either a reorganization or a complete collapse of the MOC. Two of the more dramatic instances of abrupt change include Dansgaard-Oeschger events, abrupt warmings that could exceed 10°C over a period as short as a few decades, and Heinrich events, which are associated with massive freshwater fluxes due to rapid iceberg discharges into the North Atlantic. Numerical models of varying complexity that have captured these abrupt transitions all underscore that the MOC is a highly nonlinear system with feedback loops, multiple equilibria, and hysteresis effects. Prediction of future abrupt shifts in the MOC or “tipping points” remains uncertain. However, the inferred behavior of the MOC during glacial climates suggests that significant modifications to the present circulation are possible and that any change is likely to have a large effect on the Earth's climate.

The eddy heat flux generated by the statistically equilibrated baroclinic instability of a uniform, horizontal temperature gradient is studied using a two- mode quasigeostrophic model. An overview of the dependence of the eddy diffusivity of heat D[tau] on the planetary potential vorticity gradient [beta], the bottom friction [kappa], the deformation radius [lambda], the vertical shear of the large-scale flow 2U and the domain size L is provided at 70 numerical simulations with [beta]=0 (f-plane) and 110 simulations with [beta] != 0 ([beta]-plane). Strong, axisymmetric, well-separated baroclinic vortices dominate the equilibrated barotropic vorticity and temperature fields of f-plane turbulence. The heat flux arises from a systematic northward (southward) migration of anti-cyclonic (cyclonic) eddies with warm (cold) fluid trapped in the cores. Zonal jets form spontaneously on the [beta]-plane, and stationary, isotropic, jet-scale eddies align within the strong eastward-flowing regions of the jets. In both studies, the vortices and jets give rise to a strong anti-correlation between the barotropic vorticity [zeta] and the temperature field [tau]. The baroclinic mode is also an important contributor to dissipation by bottom friction and energizes the barotropic mode at scales larger than [lambda]. This in part explains why previous parameterizations for the eddy heat flux based on Kolmogorovian cascade theories are found to be unreliable. In a separate study, temperature and salinity profiles obtained with expendable conductivity, temperature and depth (XCTD) probes within Drake Passage, Southern Ocean are used to analyze the turbulent diapycnal eddy diffusivity [kappa][rho] to a depth of 1000 meters. The Polar Front separates two dynamically different regions with strong, surface-intensified mixing north of the Front. South of the Polar Front mixing is weaker and peaks at a depth of approximately 500 m, near the local temperature maximum. Peak values of [kappa][rho] are found to exceed 10^-3 m^2 s^-1. Wind-driven near-inertial waves, mesoscale eddies and thermohaline intrusions are discussed as possible factors contributing to observed mixing patterns