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.
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On non-uniqueness of the mesoscale eddy diffusivity
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.
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- Award ID(s):
- 1849990
- NSF-PAR ID:
- 10329883
- Date Published:
- Journal Name:
- Journal of fluid mechanics
- Volume:
- 920
- Issue:
- A32
- ISSN:
- 1469-7645
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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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 We use an interannually forced version of the Parallel Ocean Program, configured to resolve mesoscale eddies, to close the global eddy potential energy (EPE) budget associated with temperature variability. By closing the EPE budget, we are able to properly investigate the role of diabatic processes in modulating mesoscale energetics in the context of other processes driving eddy–mean flow interactions. A Helmholtz decomposition of the eddy heat flux field into divergent and rotational components is applied to estimate the baroclinic conversion from mean to eddy potential energy. In doing so, an approximate two-way balance between the “divergent” baroclinic conversion and upgradient vertical eddy heat fluxes in the ocean interior is revealed, in accordance with baroclinic instability and the relaxation of isopycnal slopes. However, in the mixed layer, the EPE budget is greatly modulated by diabatic mixing, with air–sea interactions and interior diffusion playing comparable roles. Globally, this accounts for ∼60% of EPE converted to EKE (eddy kinetic energy), with the remainder being dissipated by air–sea interactions and interior mixing. A seasonal composite of baroclinic energy conversions shows that the strongest EPE to EKE conversion occurs during the summer in both hemispheres. The seasonally varying diabatic processes in the upper ocean are further shown to be closely linked to this EPE–EKE conversion seasonality, but with a lead. The peak energy dissipation through vertical mixing occurs ahead of the minimum EKE generation by 1–2 months.more » « less
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Abstract 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°). 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 can be interpreted to 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.
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Sensitivity of large eddy simulations of tropical cyclone to sub-grid scale mixing parameterization.The surface wind structure and vertical turbulent transport processes in the eyewall of hurricane Isabel (2003) are investigated using six large-eddy simulations (LESs) with different horizontal grid spacing and three-dimensional (3D) sub-grid scale (SGS) turbulent mixing models and a convection permitting simulation that uses a coarser grid spacing and one-dimensional vertical turbulent mixing scheme. The mean radius-height distribution of storm tangential wind and radial flow, vertical velocity structure, and turbulent kinetic energy and momentum fluxes in the boundary layer generated by LESs are consistent with those derived from historical dropsonde composites, Doppler radar, and aircraft measurements. Unlike the convection permitting simulation that produces storm wind fields lacking small-scale disturbances, all LESs are able to produce sub-kilometer and kilometer scale eddy circulations in the eyewall. The inter-LES differences generally reduce with the decrease of model grid spacing. At 100-m horizontal grid spacing, the vertical momentum fluxes induced by the model-resolved eddies and the associated eddy exchange coefficients in the eyewall simulated by the LESs with different 3D SGS mixing schemes are fairly consistent. Although with uncertainties, the decomposition in terms of eddy scales suggests that sub-kilometer eddies are mainly responsible for the vertical turbulent transport within the boundary layer (~1 km depth following the conventional definition) whereas eddies greater than 1 km become the dominant contributors to the vertical momentum transport above the boundary layer in the eyewall. The strong dependence of vertical turbulent transport on eddy scales suggests that the vertical turbulent mixing parameterization in mesoscale simulations of tropical cyclones is ultimately a scale-sensitive problem.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2021.472
