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.
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