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Quantitative analysis of numerically induced mixing in a coastal model application

机译：数值模拟混合在沿海模型应用中的定量分析

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摘要

In recent years, various attempts have been made to estimate the amount of numerical mixing in numerical ocean models due to discretisation errors of advection schemes. In this study, a high-resolution coastal model using the ocean circulation model GETM is applied to the Western Baltic Sea, which is characterised by energetic and episodic inflows of dense bottom waters originating from the Kattegat. The model is equipped with an easy-to-implement diagnostic method for obtaining the numerical mixing which has recently been suggested. In this diagnostic method, the physical mixing is defined as the mean tracer variance decay rate due to turbulent mixing. The numerical mixing due to discretisation errors of tracer advection schemes is defined as the decay rate between the advected square of the tracer variance and the square of the advected tracer, which can be directly compared to the physical variance decay. The source and location of numerical mixing is further investigated by comparing different advection schemes and analysing the amount of numerical mixing in each spatial dimension during the advection time step. The results show that, for the setup used, the numerically and physically induced mixing have the same orders of magnitude but with different vertical and horizontal distributions. As the main mechanism for high numerical mixing, vertical advection of tracers with strong vertical gradients has been identified. The main reason for high numerical mixing is due tornbottom-following coordinates when density gradients, especially for regions of steep slopes, are advected normal to isobaths. With the bottom-following coordinates used here, the horizontal gradients are reproduced by a spurious sawtooth-type profile where strong advection through, but not along, the vertical coordinate levels occurs. Additionally, the well known relation between strong tracer gradients and high velocities on the one and high numerical mixing on the other hand is approved quantitatively within this work.
机译：近年来，由于对流方案的离散化误差，已经进行了各种尝试来估计数值海洋模型中的数值混合量。在这项研究中，使用海洋环流模型GETM的高分辨率沿海模型被应用于西波罗的海，其特征是源自卡特加特海域的稠密底水的能量和间歇性流入。该模型配备了易于实现的诊断方法，用于获得最近提出的数值混合。在此诊断方法中，物理混合定义为由于湍流混合而导致的示踪剂平均方差衰减率。由示踪剂对流方案的离散化误差引起的数值混合定义为示踪剂方差平移平方和示踪剂平方平方之间的衰减率，可以将其与物理方差衰减直接比较。通过比较不同的对流方案并分析对流时间步长在每个空间维度上的数字混合量，进一步研究了数字混合的来源和位置。结果表明，对于所使用的设置，数值和物理诱导的混合具有相同的数量级，但垂直和水平分布不同。作为高数值混合的主要机制，已确定具有强垂直梯度的示踪剂的垂直对流。高度数值混合的主要原因是当密度梯度（尤其是陡坡区域）垂直于等压线平移时，由于底部跟随坐标的原因。通过在此处使用底部跟随坐标，可以通过伪锯齿形轮廓来再现水平梯度，在该轮廓上会发生强烈的对流，但不沿垂直坐标方向发生。另外，这项工作中定量地证实了强示踪剂梯度和高速度之间以及另一方面高数值混合之间的众所周知的关系。

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