Abstract Baroclinic eddy restratification strongly influences the ocean’s general circulation and tracer budgets, and has been routinely parameterized via the Gent–McWilliams (GM) scheme in coarse-resolution ocean climate models. These parameterizations have been improved via refinements of the GM eddy transfer coefficient using eddy-resolving simulations and theoretical developments. However, previous efforts have focused primarily on the open ocean, and the applicability of existing GM parameterization approaches to continental slopes remains to be addressed. In this study, we use a suite of eddy-resolving, process-oriented simulations to test scaling relationships between eddy buoyancy diffusivity, mean flow properties, and topographic geometries in simulations of baroclinic turbulence over continental slopes. We focus on the case of retrograde (i.e., opposing the direction of topographic wave propagation) winds, a configuration that arises commonly around the margins of the subtropical gyres. Three types of scalings are examined, namely, the GEOMETRIC framework developed by Marshall et al. (2012), a new ”Cross-Front” (CF) scaling derived via dimensional arguments, and the mixing length theory (MLT)-based scalings tested recently by Jansen et al. (2015) over a flat ocean bed. The present study emphasizes the crucial role of the local slope parameter, defined as the ratio between the topographic slope and the depth-averaged isopycnal slope, in controlling the nonlinear eddy buoyancy fluxes. Both the GEOMETRIC framework and the CF scaling can reproduce the depth-averaged eddy buoyancy transfer across alongshore-uniform continental slopes, for suitably chosen constant prefactors. Generalization of these scalings across both continental slope and open ocean environments requires the introduction of prefactors that depend on the local slope parameter via empirically derived analytical functions. In contrast, the MLT-based scalings fail to quantify the eddy buoyancy transfer across alongshore-uniform continental slopes when constant prefactors are adopted, but can reproduce the cross-slope eddy flux when the prefactors are adapted via empirical functions of the local slope parameter. Application of these scalings in prognostic ocean simulations also depends on an accurate representation of standing eddies associated with the topographic corrugations of the continental slope. These findings offer a basis for extending existing approaches to parameterizing transient eddies, and call for future efforts to parameterize standing eddies in coarse-resolution ocean climate models.

中文翻译：

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逆行风下跨大陆坡的涡流浮力传递的标度

摘要 斜压涡流再分层强烈影响海洋的一般环流和示踪剂预算，并且已通过粗分辨率海洋气候模型中的根特-麦克威廉姆斯 (GM) 方案进行常规参数化。通过使用涡流解析模拟和理论发展对 GM 涡流传递系数进行改进，这些参数化得到了改进。然而，以前的努力主要集中在公海，现有的 GM 参数化方法对大陆坡的适用性仍有待解决。在这项研究中，我们使用一套涡旋分辨、面向过程的模拟来测试在大陆坡上斜压湍流模拟中涡流浮力扩散系数、平均流动特性和地形几何形状之间的比例关系。我们关注逆行（即与地形波传播方向相反）风的情况，这种配置通常出现在亚热带环流的边缘。检查了三种类型的缩放，即由 Marshall 等人开发的 GEOMETRIC 框架。(2012)、通过维度参数得出的新“Cross-Front”(CF) 标度，以及最近由 Jansen 等人测试的基于混合长度理论 (MLT) 的标度。(2015) 在平坦的海床上。本研究强调局部坡度参数（定义为地形坡度与深度平均等密度坡度之间的比率）在控制非线性涡流浮力通量方面的关键作用。GEOMETRIC 框架和 CF 标度都可以重现沿海岸均匀大陆坡的深度平均涡流浮力传递，for suitably chosen constant prefactors. 这些尺度在大陆坡和公海环境中的推广需要通过经验派生的分析函数引入依赖于当地坡度参数的前置因素。相比之下，当采用恒定前置因子时，基于 MLT 的标度无法量化沿海岸均匀大陆坡的涡流浮力传递，但当前置因子通过局部坡度参数的经验函数进行调整时，可以重现跨坡涡通量。这些比例在预测海洋模拟中的应用还取决于与大陆坡地形波纹相关的直立涡流的准确表示。这些发现为扩展现有方法来参数化瞬态涡流提供了基础，