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Mei-Man Lee

Abstract

In understanding how errors decay in twin experiments, previous studies have shown that it can be due to bottom friction or geostrophic adjustment. However, there are quantities, such as passive tracers, that may not be recovered by either of these mechanisms. This study seeks a mechanism that can cause errors to decay in the absence of bottom friction or geostrophic adjustment.

Consider the particular case of an isopycnic layer where the velocity is perfectly known but the layer thickness is not. It will be argued that the errors in layer thickness decay by processes similar to that of tracer homogenization. Based on the fact that the homogenization is achieved by an initial rapid shear dispersion, it is hypothesized that the error decay is initially by shear dispersion. This hypothesis is tested using idealized twin experiments based on an eddy-resolving isopycnic channel model. A series of experiments with different diffusivities supports the idea that the initial decay timescale approximates to the shear dispersion timescale.

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Mei-Man Lee

Abstract

This study looks at the behavior of fluid particles/parcels that move along isopycnic surfaces. The aim is to show that the diffusive process of mixing by eddies causes such particles to move toward regions of greater isopycnic layer thickness or, equivalently, weaker stratification.

This is illustrated using a wind-driven eddy-resolving isopycnic layer model in a zonal channel configuration. Particles and tracers are integrated to demonstrate that their centers of mass move up the layer thickness gradient. In particular, a field of uniformly distributed particles is seen to move toward regions of large layer thickness, so the distribution of particles becomes asymmetric. The asymmetry is most obvious when the gradient of layer thickness is large in comparison to the volume of the layer. In the ocean, in the absence of other influences such as advection and varying diffusivity, one might expect isopycnic floats released in the upper thermocline to show a similar asymmetric behavior.

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A. J. George Nurser and Mei-Man Lee

Abstract

In , the “vertical” transport streamfunction was defined as resulting from isopycnic averaging at constant height in the same way that the meridional streamfunction results from averaging at constant latitude. Part II here discusses the relationship between these two isopycnic streamfunctions and the Eulerian residual streamfunction that arises from the transformed Eulerian mean (TEM). It is known that the meridional isopycnic streamfunction can be approximated by a Taylor expansion to give an Eulerian residual streamfunction involving the horizontal eddy flux. This Taylor expansion approximation works well in the interior, removing the spurious mixing associated with the simple Eulerian-averaged streamfunction. However, it fails near the surface where isopycnals outcrop to the surface. It can be shown in a similar way that the vertical isopycnic streamfunction can formally be approximated by a residual streamfunction involving the vertical eddy flux. However, if horizontal isopycnal displacements are large, this approximation fails even in the ocean interior. Inspired by the two different residual streamfunctions, a more general form of TEM formulation is explored. It is shown that the different TEM residual streamfunctions arise from decomposing the eddy flux into a component along isopycnals, which leads to advective flow, and a remaining diffusive component, which is oriented either vertically or horizontally. In theory the diffusive flux can be oriented in any direction, although in practice the orientation should be such that neither the advective flow nor the diffusive flux cross any boundary (surface, sidewalls, and bottom). However, it is not clear how to merge the continuously changing orientation in a physically meaningful way. A variety of approaches are discussed.

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A. J. George Nurser and Mei-Man Lee

Abstract

Simple Eulerian averaging of velocities, density, and tracers at constant position is the most natural way of averaging. However, Eulerian averaging gives incorrect watermass distributions and properties as well as spurious diabatic circulations such as the Deacon cell. Instead of averaging at constant height, averaging along isopycnals removes such fictitious mixing and diabatic circulations. Such isopycnal averaging is normally performed at constant latitude, that is, averaging along isopynals as they heave up and down. As a result, height information is lost and the sea surface becomes much warmer (or lighter) than with simple Eulerian averaging. In fact, averaging can be performed along arbitrarily aligned surfaces. This study considers a particular case in which isopycnal averaging is performed at constant height. Thus, this new isopycnal averaging follows isopycnals as they meander horizontally at constant z. Height information is now retained at the cost of losing latitudinal information. The advantage of this averaging is that it avoids the problem of giving a surface that is too warm. Associated with this new isopycnal averaging, a “vertical” transport streamfunction in (ρ, z) space can be defined, in analogy to the conventional meridional overturning streamfunction in (y, ρ) space. Here in Part I, this constant-height isopycnal averaging is explained and illustrated in an idealized zonal channel model. In Part II the relationship between the two different isopycnal averagings and the Eulerian mean eddy flux divergence is explored.

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Mei-Man Lee and A. J. George Nurser

Abstract

Subduction—the transport of fluid across the base of mixed layer—exchanges water masses and tracers between the ocean surface and interior. Eddies can affect subduction in a variety of ways. First, eddies shoal the mixed layer by restratifying water columns through baroclinic instabilities. Second, eddies induce an isopycnic transport that leads to the entrainment of warm waters and subduction of cold waters, which effectively counters the wind-driven overturning circulation. In this study, the authors use an idealized model to examine these two mechanisms by which eddies influence subduction and to discuss how eddy subduction may be better approximated using the concept of vertical transport streamfunction than the conventional meridional transport streamfunction.

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Mei-Man Lee, Andrew C. Coward, and A. J. George Nurser

Abstract

Recent idealized studies have shown that both explicit horizontal diffusion and the implicit diffusion associated with the advection scheme in high-resolution z-coordinate models may drive unrealistically high rates of diapycnal mixing. The aim here is to see whether the diapycnal mixing associated with the advection scheme in a global eddy-permitting (¼° by ¼°) z-level model is sufficiently strong to corrupt the thermohaline circulation. This paper diagnoses the diapycnal fluxes by using the ideas of water mass transformation.

In the Southern Ocean, the model deep and bottom waters drift rapidly away from the Levitus climatology, with dense isopycnals moving downward at rates of up to 35 m yr−1. The strong upward flux (up to 50 Sv) through the dense isopycnals cannot be explained by the incorrect surface forcing (as a result of poor surface fluxes and no ice model) as most of the anomalous diapycnal fluxes are occurring in the deep ocean far from surface forcing. Hence, the excessive diapycnal flux is driven by diffusion in the model, both explicit and implicit.

The “effective” diapycnic diffusivity driven by the numerical diffusion (associated with the horizontal advection scheme) is found to be the same order, 1–10 cm2 s−1, as that driven by the explicit horizontal diffusion. For strong vertical velocities (∼20 m day−1) as in models forced by high frequency winds, the vertical advection scheme also gives similar effective diffusivities. These effective diffusivities are considerably greater than suggested by observations. To alleviate these problems, it is suggested that eddy-resolving z-level climate models will require 1) less diffusive horizontal advection schemes and 2) better vertical resolution throughout much of the water column.

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David P. Marshall, Richard G. Williams, and Mei-Man Lee

Abstract

The dynamical control of the eddy-induced transport is investigated in a series of idealized eddy-resolving experiments. When there is an active eddy field, the eddy-induced transport is found to correlate with isopycnic gradients of potential vorticity, rather than gradients of layer thickness. For any unforced layers, the eddy transfer leads to a homogenization of potential vorticity and a vanishing of the eddy-induced transport in the final steady state.

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Mei-Man Lee, A. J. George Nurser, Andrew C. Coward, and Beverly A. de Cuevas

Abstract

This study uses tracer experiments in a global eddy-resolving ocean model to examine two diagnostic methods for inferring effective eddy isopycnic diffusivity from point release tracers. The first method is based on the growth rate of the area occupied by the tracers (the equivalent variance). During the period when tracer dispersion is dominated by stirring, the equivalent variance is found to increase at a rate between the second power law (for a pure shearing flow regime) and the exponential law (for a pure stretching flow regime). The second method is based on the length of the tracer contours. In the framework of equivalent radius, the two methods of inferring eddy diffusivity can be understood as two different averagings over the tracer patch. Over a shorter period of tracer dispersion the two methods give different eddy diffusivities, and only over a longer time when tracer dispersion approaches the final stage of diffusion do they give a similar value of diffusivity. A new diagnostic quantity called stirring efficiency is introduced to indicate different flow regimes by measuring the efficiency of stirring against mixing. The new diagnostic quantity has the advantage that it can be calculated directly from the gradients of tracer distribution without needing to estimate strain rate or background diffusivity.

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Mei-Man Lee, A. J. George Nurser, I. Stevens, and Jean-Baptiste Sallée

Abstract

This study examines the subduction of the Subantarctic Mode Water in the Indian Ocean in an ocean–atmosphere coupled model in which the ocean component is eddy permitting. The purpose is to assess how sensitive the simulated mode water is to the horizontal resolution in the ocean by comparing with a coarse-resolution ocean coupled model. Subduction of water mass is principally set by the depth of the winter mixed layer. It is found that the path of the Agulhas Current system in the model with an eddy-permitting ocean is different from that with a coarse-resolution ocean. This results in a greater surface heat loss over the Agulhas Return Current and a deeper winter mixed layer downstream in the eddy-permitting ocean coupled model. The winter mixed layer depth in the eddy-permitting ocean compares well to the observations, whereas the winter mixed layer depth in the coarse-resolution ocean coupled model is too shallow and has the wrong spatial structure. To quantify the impacts of different winter mixed depths on the subduction, a way to diagnose local subduction is proposed that includes eddy subduction. It shows that the subduction in the eddy-permitting model is closer to the observations in terms of the magnitudes and the locations. Eddies in the eddy-permitting ocean are found to 1) increase stratification and thus oppose the densification by northward Ekman flow and 2) increase subduction locally. These effects of eddies are not well reproduced by the eddy parameterization in the coarse-resolution ocean coupled model.

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Mei-Man Lee, A. J. George Nurser, A. C. Coward, and B. A. de Cuevas

Abstract

There are two distinct mechanisms by which eddies provide systematic transport of tracer on isopycnals: the advective transport, associated with the slumping of isopycnals, and the diffusive transport, associated with down-gradient diffusion. Depending on the large-scale tracer distribution, eddy advective transport has either the same direction as or opposite direction to eddy diffusive transport. As a consequence, eddy advection and eddy diffusion can reinforce each other for some tracers but oppose each other for other tracers. Using scaling analysis, it is argued that the relative directions of eddy advective and diffusive transports can be determined simply from the relative slopes of tracers and isopycnals. An eddy-resolving (1/12°) global ocean model is used to illustrate the two eddy transport mechanisms for temperature and salinity in the Southern Ocean. Applications to other tracers, such as oxygen, are discussed. The diagnosed eddy diffusivity for temperature (and salinity) is found to be considerably different from the eddy diffusivity for eddy advective transport velocity.

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