This study provides an interpretation of isopycnal eddy transport for mass and passive tracers in double-gyre eddy-resolving oceanic circulation. This paper focuses on a transport/diffusion tensor representation of the eddy tracer flux, and a companion paper will focus on advective eddy-induced tracer and mass transports. We use a spatial filter to separate the large and small scales, which leads to results distinct from those obtained via a temporal Reynolds eddy decomposition. To work towards a parameterisation, we relate the eddy tracer flux to the large-scale tracer gradient via the transport tensor $\mathit{K}$. The symmetric part of $\mathit{K}$ is the diffusion tensor, $\mathit{S}$, which parameterises diffusive fluxes and whose mixing properties are determined by the signs of its eigenvalues. The eigenvalues of $\mathit{S}$ are robustly of opposite sign (polar) and thus quantify filamentation of the tracer via both up- and down-gradient fluxes. Given the prevalence of polar eigenvalues – which are also obtained for Reynolds eddy fluxes – representing their associated effects should be a target of future eddy tracer transport closures. Given the inherent inhomogeneity and anisotropy of the eddy-induced transport, we argue that a full transport tensor is better suited to this task than scalar coefficients or diagonal tensors. The diffusion axis, which represents the direction of preferential mixing, tends to align with the large-scale velocity vector and contours of large-scale relative vorticity and layer thickness. Strong shears can inhibit this alignment. We show that the large-scale velocity gradient matrix may be suitable for parameterising the transport tensor, in particular at depth. Furthermore, since entries of $\mathit{K}$ and $\mathit{S}$ exhibit probabilistic distributions when conditioned on certain large-scale flow features, we suggest that a stochastic closure for the eddy transport would be most suitable.

这项研究为双环流涡旋解决海洋环流中质量和被动示踪剂的等密度涡流输运提供了解释。本文重点介绍涡流示踪剂通量的输运/扩散张量表示，另一篇配套论文将重点介绍平流涡诱导示踪剂和质量输运。我们使用空间滤波器来分离大尺度和小尺度，这导致结果与通过时间雷诺涡分解获得的结果不同。为了实现参数化，我们通过传输张量将涡流示踪剂通量与大规模示踪剂梯度联系起来$\mathit{钾}$. 的对称部分$\mathit{钾}$ 是扩散张量， $\mathit{秒}$，它参数化扩散通量，其混合特性由其特征值的符号决定。的特征值$\mathit{秒}$具有相反的符号（极性），因此通过向上和向下梯度通量量化示踪剂的丝状。鉴于极地特征值的普遍性——这也是为雷诺涡通量获得的——代表它们的相关效应应该是未来涡流示踪剂传输闭合的目标。鉴于涡致输运固有的不均匀性和各向异性，我们认为完整输运张量比标量系数或对角线张量更适合这项任务。代表优先混合方向的扩散轴倾向于与大尺度速度矢量以及大尺度相对涡度和层厚的等高线对齐。强剪切力可以抑制这种对齐。我们表明大规模速度梯度矩阵可能适用于参数化传输张量，特别是在深度。此外，由于条目$\mathit{钾}$ 和 $\mathit{秒}$ 当以某些大规模流动特征为条件时表现出概率分布，我们建议涡流传输的随机闭合将是最合适的。