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Abstract Mesoscale eddies—irregular time‐dependent currents with lateral scales of 10–200 km—are ubiquitous in the World Ocean. They profoundly affect general circulation and actively redistribute oceanic heat, salt, biogeochemical tracers, and pollutants. The development of accurate parameterizations of eddy‐induced transport remains one of the most pressing challenges in physical oceanography. Commonly used mesoscale parameterizations assume that the relation between eddy‐induced fluxes and the large‐scale property gradients is local and instantaneous. The present communication challenges this premise. We consider a closure that incorporates a delay in the adjustment of eddy fluxes to changing ambient distribution of properties. This model is inspired by the century‐and‐a‐half‐old idea of Maxwell, who argued that molecular dispersion necessarily involves a finite relaxation period. In our study, this principle is reinterpreted in the context of the turbulent transport problem. A series of simulations reveal marked improvements in eddy parameterizations brought by the inclusion of Maxwell's effect. 

Abstract Stirring of water by mesoscale currents (“eddies”) leads to large‐scale transport of many important oceanic properties (“tracers”). These eddy‐induced transports can be related to the large‐scale tracer gradients, using the concept of turbulent diffusion. The concept is widely used to describe these transports in the real ocean and to represent them in climate models. This study focuses on the inherent complexity of the corresponding coefficient tensor (“K‐tensor”) and its components, defined here in all its spatio‐temporal complexity. Results demonstrate that this comprehensiveK‐tensor is space‐, time‐, direction‐ and tracer‐dependent. Using numerical simulations with both idealized and comprehensive models of the Atlantic circulation, we show that these properties lead to upgradient eddy fluxes and the potential importance of all tensor components. The uncovered complexity of the eddy transports calls for reconsideration of how they are estimated in practice, included in the general circulation models and theoretically interpreted. 

Abstract. Mixed-layer depth (MLD) exhibits significant variability, which is important for atmosphere–ocean exchanges of heat and atmospheric gases. The origins of the mesoscale MLD variability in the Southern Ocean are studied here in an idealised regional ocean–atmosphere model (ROAM). The main conclusion from the analysis of the upper-ocean buoyancy budget is that, while the atmospheric forcing and oceanic vertical mixing, on average, induce the mesoscale variability of MLD, the three-dimensional oceanic advection of buoyancy counteracts and partially balances these atmosphere-induced vertical processes. The relative importance of advection changes with both season and average MLD. From January to May, when the mixed layer is shallow, the atmospheric forcing and oceanic mixing are the most important processes, with the advection playing a secondary role. From June to December, when the mixed layer is deep, both atmospheric forcing and oceanic advection are equally important in driving the MLD variability. Importantly, buoyancy advection by mesoscale ocean current anomalies can lead to both local shoaling and deepening of the mixed layer. The role of the atmospheric forcing is then directly addressed by two sensitivity experiments in which the mesoscale variability is removed from the atmosphere–ocean heat and momentum fluxes. The findings confirm that mesoscale atmospheric forcing predominantly controls MLD variability in summer and that intrinsic oceanic variability and surface forcing are equally important in winter. As a result, MLD variance increases when mesoscale anomalies in atmospheric fluxes are removed in winter, and oceanic advection becomes a dominant player in the buoyancy budget. This study highlights the importance of oceanic advection and intrinsic ocean dynamics in driving mesoscale MLD variability and underscores the importance of MLD in modulating the effects of advection on upper-ocean dynamics. 

Abstract Lateral mesoscale eddy-induced tracer transport is traditionally represented in coarse-resolution models by the flux–gradient relation. In its most complete form, the relation assumes the eddy tracer flux as a product of the large-scale tracer concentration gradient and an eddy transport coefficient tensor. However, several recent studies reported that the tensor has significant spatiotemporal complexity and is not uniquely defined, that is, it is sensitive to the tracer distributions and to the presence of nondivergent (“rotational”) components of the eddy flux. These issues could lead to significant biases in the representation of the eddy-induced transport. Using a high-resolution tracer model of the Gulf Stream region, we examine the diffusive and advective properties of lateral eddy-induced transport of dynamically passive tracers, reevaluate the utility of the flux–gradient relation, and propose an alternative approach based on modeling the local eddy forcing by a combination of diffusion and generalized eddy-induced advection. Mesoscale eddies are defined by a scale-based spatial filtering, which leads to the importance of new eddy-induced terms, including eddy-mean covariances in the eddy fluxes. The results show that the biases in representing these terms are noticeably reduced by the new approach. A series of targeted simulations in the high-resolution model further demonstrates that the approach outperforms the flux–gradient model in reproducing the stirring and dispersing effect of eddies. Our study indicates potential to upgrade the traditional flux–gradient relation for representing the eddy-induced tracer transport. 

Abstract The Atlantic meridional overturning circulation (AMOC) plays a key role in climate due to uptake and redistribution of heat and carbon anomalies. This redistribution takes place along several main pathways that link the high-latitude North Atlantic with midlatitudes and the Southern Ocean and involves currents on a wide range of spatial scales. This numerical study examines the importance of mesoscale currents (“eddies”) in these AMOC pathways and associated time scales, using a highly efficient offline tracer model. The study uses two boundary impulse response (BIR) tracers, which can quantify the importance of the Atlantic tracer exchanges with the high-latitude atmosphere in the north and with the Southern Ocean in the south. The results demonstrate that mesoscale advection leads to an increase in the overall BIR inventory during the first 100 years and results in a more efficient and spatially uniform ventilation of the deep Atlantic. Mesoscale currents also facilitate meridional spreading of the BIR tracer and thus assist the large-scale advection. The results point toward the importance of spatial inhomogeneity and anisotropy of the eddy-induced mixing in several mixing “hotspots,” as revealed by an eddy diffusivity tensor. Conclusions can be expected to assist evaluations of eddy-permitting simulations that stop short of full resolution of mesoscale, as well as development of eddy parameterization schemes. 

Abstract We analyze the role of mesoscale heat advection in a mixed layer (ML) heat budget, using a regional high-resolution coupled model with realistic atmospheric forcing and an idealized ocean component. The model represents two regions in the Southern Ocean, one with strong ocean currents and the other with weak ocean currents. We conclude that heat advection by oceanic currents creates mesoscale anomalies in sea surface temperature (SST), while the atmospheric turbulent heat fluxes dampen these SST anomalies. This relationship depends on the spatial scale, the strength of the currents, and the mixed layer depth (MLD). At the oceanic mesoscale, there is a positive correlation between the advection and SST anomalies, especially when the currents are strong overall. For large-scale zonal anomalies, the ML-integrated advection determines the heating/cooling of the ML, while the SST anomalies tend to be larger in size than the advection and the spatial correlation between these two fields is weak. The effects of atmospheric forcing on the ocean are modulated by the MLD variability. The significance of Ekman advection and diabatic heating is secondary to geostrophic advection except in summer when the MLD is shallow. This study links heat advection, SST anomalies, and air–sea heat fluxes at ocean mesoscales, and emphasizes the overall dominance of intrinsic oceanic variability in mesoscale air–sea heat exchange in the Southern Ocean. 

Oceanic mesoscale currents (‘eddies’) can have significant effects on the distributions of passive tracers. The associated inhomogeneous and anisotropic eddy fluxes are traditionally parametrised using a transport tensor (K-tensor), which contains both diffusive and advective components. In this study, we analyse the eddy transport tensor in a quasigeostrophic double-gyre flow. First, the flow and passive tracer fields are decomposed into large- and small-scale (eddy) components by spatial filtering, and the resulting eddy forcing includes an eddy tracer flux representing advection by eddies and non-advective terms. Second, we use the flux-gradient relation between the eddy fluxes and the large-scale tracer gradient to estimate the associated K-tensors in their entire structural, spatial and temporal complexity, without making any additional assumptions or simplifications. The divergent components of the eddy tracer fluxes are extracted via the Helmholtz decomposition, which yields a divergent tensor. The remaining rotational flux does not affect the tracer evolution, but dominates the total tracer flux, affecting both its magnitude and spatial structure. However, in terms of estimating the eddy forcing, the transport tensor prevails over its divergent counterpart because of the significant numerical errors induced by the Helmholtz decomposition. Our analyses demonstrate that, in general, the K-tensor for the eddy forcing is not unique, that is, it is tracer-dependent. Our study raises serious questions on how to interpret and use various estimates of K-tensors obtained from either observations or eddy-resolving model solutions.