It is well known that discrete advection schemes can induce spurious numerical mixing in numerical models. In the present study, an offline method is applied to several idealized lock-exchange simulations and a realistic model simulation of BYECS (Bohai Sea, Yellow Sea, and East China Sea) to estimate the magnitude of numerical mixing. Numerical mixing is defined as the tracer variance dissipation rate induced by the discretization of advection schemes, and the offline method is achieved through diagnosing the residual of the tracer variance balance equation in terms of model output data. The offline method is demonstrated to be appropriate to estimate the volume (or depth) and temporally averaged numerical mixing when the model output data capture typical flow timescales. In both of the lock-exchange and BYECS simulations, the spatial distributions of numerical and explicit physical mixing of salinity correspond to the distributions of horizontal and vertical salinity gradients, respectively. In the lock-exchange simulations, explicit physical mixing depresses the magnitude of numerical mixing through reducing the horizontal salinity gradients at the heading fronts. In the BYECS simulations, numerical mixing of salinity inside the Changjiang River plume region is stronger during spring tides than neap tides.

众所周知，离散对流方案会在数值模型中引起虚假的数值混合。在本研究中，将离线方法应用于几种理想的锁交换模拟和BYECS（渤海，黄海和东海）的现实模型模拟，以估计数值混合的幅度。数值混合被定义为由对流方案离散化引起的示踪方差耗散率，并且脱机方法是通过根据模型输出数据诊断示踪方差平衡方程的残差来实现的。当模型输出数据捕获典型流量时标时，离线方法证明适合估计体积（或深度）和时间平均的数值混合。在锁交换和BYECS模拟中，盐度数值和显式物理混合的空间分布分别对应于水平和垂直盐度梯度的分布。在锁定交换模拟中，显式物理混合通过减小航向前沿的水平盐度梯度来降低数值混合的幅度。在BYECS模拟中，春季潮汐期间长江羽流区域内盐度的数值混合比潮汐潮汐更强。