Understanding the pathways of floating material at the surface ocean is important to improve our knowledge on surface circulation and for its ecological and environmental impacts. Virtual particle simulations are a common method to simulate the dispersion of floating material. To advect the particles, velocities from ocean models are often used. Yet, the contribution of different ocean dynamics (at different temporal and spatial scales) to the net Lagrangian transport remains unclear. Here we focus on tidal forcing, only included in recent models, and so our research question is: What is the effect of tidal forcing on virtual particle dispersion at the ocean surface? By comparing a twin simulation with and without tidal forcing, we conclude that tides play an important role in horizontal Lagrangian dynamics. We focus on the Açores Islands region, and we find that surface particles travel a longer cumulative distance and a lower total distance with than without tidal forcing and a higher variability in surface particle accumulation patterns is present with tidal forcing.  The differences found in the surface particle accumulation patterns can be more than a 40\% increase/decrease. This has important implications for virtual particle simulations, showing that more than tidal currents need to be considered.  A deeper understanding of the dynamics behind these tidal forcing impacts is necessary, but our outcomes can already help improve Lagrangian simulations. This is particularly relevant for simulations done to understand the connectivity of marine species and for marine pollution applications.

During the past 25 years, altimetric observations of the ocean surface from space have been mapped to provide two dimensional sea surface height (SSH) fields which are crucial for scientific research and operational applications. The SSH fields can be reconstructed from conventional altimetric data using temporal and spatial interpolation. For instance, the standard DUACS products are created with an optimal interpolation method which is effective for both low temporal and low spatial resolution. However, the upcoming next-generation SWOT mission will provide very high spatial resolution but with low temporal resolution. The present paper makes the case that this temporal-spatial discrepancy induces the need for new advanced mapping techniques involving information on the ocean dynamics. An algorithm is introduced, dubbed the BFN-QG, that uses a simple data assimilation method, the back-and-forth nudging, to interpolate altimetric data while respecting quasigeostrophic dynamics. The BFN-QG is tested in an observing system simulation experiments and compared to the DUACS products. The experiments consider as reference the high-resolution numerical model simulation NATL60 from which are produced realistic data: four conventional altimetric nadirs and SWOT data. In a combined nadirs and SWOT scenario, the BFN-QG substantially improves the mapping by reducing the root-mean-square errors and increasing the spectral effective resolution by 40km. Also, the BFN-QG method can be adapted to combine large-scale corrections from nadirs data and small-scale corrections from SWOT data so as to reduce the impact of SWOT correlated noises and still provide accurate SSH maps.

The thickness-weighted average (TWA) framework, which treats the residual-mean flow as the prognostic variable, provides a clear theoretical formulation of the eddy feedback onto the residual-mean flow. The averaging operator involved in the TWA framework, although in theory being an ensemble mean, in practice has often been approximated by a temporal mean. Here, we analyze an ensemble of North Atlantic simulations at mesoscale-permitting resolution (1/12$^\circ$). We therefore recognize means and eddies in terms of ensemble means and fluctuations about those means. The ensemble dimension being orthogonal to the temporal and spatial dimensions negates the necessity for an arbitrary temporal or spatial scale in defining the eddies. Eddy-mean flow feedbacks are encapsulated in the Eliassen-Palm (E-P) flux tensor and its convergence indicates that eddy momentum fluxes dominate in the separated Gulf Stream. The eddies contribute to the zonal meandering of the Gulf Stream and a northward migration of it in the meridional direction. Downstream of the separated Gulf Stream in the North Atlantic Current region, the interfacial form stress convergence becomes leading order in the E-P flux convergence.

Fine-scale motions ($<$100 km) contribute significantly to the exchanges and dissipation of kinetic energy in the upper ocean. However, knowledge of ocean kinetic energy at fine-scales (in terms of density and transfers) is currently limited due to the lack of sufficient observational datasets at these scales. The sea-surface height measurements of the upcoming SWOT altimeter mission should provide information on kinetic energy exchanges in the upper ocean down to 10-15 km. Numerical ocean models, able to describe ocean dynamics down to $\sim$10 km, have been developed in anticipation of the SWOT mission. In this study, we use two state-of-the-art, realistic, North Atlantic simulations, with horizontal resolutions $ \sim $ 1.5 km, to investigate the distribution and exchanges of kinetic energy at fine-scales in the open ocean. Our results show that the distribution of kinetic energy at fine-scales approximately follows the predictions of quasi-geostrophic dynamics in summertime but is somewhat consistent with submesoscale fronts-dominated regimes in wintertime. The kinetic energy spectral fluxes are found to exhibit both inverse and forward cascade over the top 1000 m, with a maximum inverse cascade close to the average energy-containing scale. The forward cascade is confined to the ocean surface and shows a strong seasonality, both in magnitude and range of scales affected. Our analysis further indicates that high-frequency motions ($<$1day) play a key role in the forward cascade and that the estimates of the spectral fluxes based on geostrophic velocities fail to capture some quantitative aspects of kinetic energy exchanges across scales.

An important characteristic of geophysically turbulent flows is the transfer of energy between scales. It is expected that balanced flows pass energy from smaller to larger scales as part of the well-known upscale cascade while submesoscale and smaller scale flows can transfer energy eventually to smaller, dissipative scales. Much effort has been put into quantifying these transfers, but a complicating factor in realistic settings is that the underlying flows are often strongly spatially heterogeneous and anisotropic. Furthermore, the flows may be embedded in irregularly shaped domains that can be multiply connected. As a result, straightforward approaches like computing Fourier spatial spectra of nonlinear terms suffer from a number of conceptual issues. In this paper, we endeavor to compute cross-scale energy transfers in general settings, allowing for arbitrary flow structure, anisotropy and inhomogeneity. We employ a Green's function approach to the kinetic energy equation to relate kinetic energy at a point to its Lagrangian history. A spatial filtering of the resulting equation naturally decomposes kinetic energy into length scale dependent contributions and describes how the transfer of energy between those scales takes place. The method is applied to a numerical simulation of vortex merger, resulting in the demonstration of the expected upscale energy cascade. Somewhat novel results are that the energy transfers are dominated by pressure work, rather than kinetic energy exchange, and dissipation is a noticeable influence on the larger scale energy budgets.

Understanding processes associated with eddy-mean flow interactions helps our interpretation of ocean energetics, and guides the development of parameterizations. Here, we focus on the non-local nature of Kinetic Energy (KE) transfers between mean and turbulent reservoirs. Transfers are interpreted as non-local when the energy extraction from the mean flow does not locally sustain energy production of the turbulent flow, or vice versa. The novelty of our approach is to use ensemble statistics to define the mean and the turbulent flow. Based on KE budget considerations, we first rationalize the eddy-mean separation in the ensemble framework, and discuss the interpretation of a mean flow driven by the prescribed (surface and boundary) forcing and a turbulent flow u’ driven by non-linear dynamics sensitive to initial conditions. We then analyze 120-day long, 20-member ensemble simulations of the Western Mediterranean basin run at 1/60 resolution. Our main contribution is to recognize the prominent contribution of the cross energy term .u_h’ to explain non-local energy transfers. This provides a strong constraint on the horizontal organization of eddy-mean flow KE transfers since this term vanishes identically for perturbations (u_h’) orthogonal to the mean flow (). We also highlight the prominent contribution of vertical turbulent fluxes for energy transfers within the surface mixed layer. Analyzing the scale dependence of these non-local energy transfers supports the local approximation usually made in the development of meso-scale, energy-aware parameterizations for non-eddying models, but points out to the necessity of accounting for these non-local effects in the meso-to-submeso scale range.

The future Surface Water and Ocean Topography (SWOT) mission will soon provide Sea Surface Height (SSH) measurements resolving scales of a few tens of kilometers. Over a large fraction of the globe, the SSH signal at these scales is essentially a superposition of a component due to balanced motions (BM) and another component due to internal tides (IT). Several oceanographic applications require the separation of these components and their mapping on regular grids. For that purpose, the paper introduces an alternating minimization algorithm that iteratively implements two data assimilation techniques, each specific to the mapping of one component: a quasi-geostrophic model with Back-and-Forth Nudging for BM, and a linear shallow-water model with 4-Dimensional Variational (4DVar) assimilation for IT. The algorithm is tested with Observation System Simulation Experiments (OSSE) where the truth is provided by a primitive-equation ocean model in an idealized configuration simulating a turbulent jet and a mode-one IT. The algorithm reconstructs almost 80\% of the variance of BM and IT, the remaining 20\% being mostly due to dynamics that cannot be described by the simple models used. Importantly, in addition to the reconstruction of stationary IT, the amplitude and phase of nonstationary IT are reconstructed. Although idealized, this study represents a step forward towards the disentanglement of BM and IT signals from real SWOT data.

Ocean circulation is dominated by turbulent geostrophic eddy fields with typical scales ranging from 10 km to 300 km. At mesoscales (> 50 km), the size of eddy structures varies regionally following the Rossby radius of deformation. The variability of the scale of smaller eddies is not well known due to the limitations in existing numerical simulations and satellite capability. But it is well established that oceanic flows (< 50km) generally exhibit strong seasonality. In this study, we present a basin-scale analysis of coherent structures down to 10\,km in the North Atlantic Ocean using two submesoscale-permitting ocean models, a NEMO-based North Atlantic simulation with a horizontal resolution of 1/60 (NATL60) and an HYCOM-based Atlantic simulation with a horizontal resolution of 1/50 (HYCOM50). We investigate the spatial and temporal variability of the scale of eddy structures with a particular focus on eddies with scales of 10 to 100\,km, and examine the impact of the seasonality of submesoscale energy on the seasonality and distribution of coherent structures in the North Atlantic. Our results show an overall good agreement between the two models in terms of surface wavenumber spectra and seasonal variability. The key findings of the paper are that (i) the mean size of ocean eddies show strong seasonality; (ii) this seasonality is associated with an increased population of submesoscale eddies (10\,–\,50\,km) in winter; and (iii) the net release of available potential energy associated with mixed layer instability is responsible for the emergence of the increased population of submesoscale eddies in wintertime.