Application of eddy viscosity closure models for the M 2 tide and tidal currents in the Yellow Sea and the East China Sea

Abstract

A three-dimensional mode-splitting, σ-coordinate barotropic finite-difference model, with subgrid scale diffusion represented using a range of eddy viscosity closure models, is used to examine M 2 tidal elevation and currents in the Yellow Sea and the East China Sea. Four eddy viscosity formulations are considered: q 2- q 2 l turbulence energy model (Blumberg and Mellor, 1987), Prandtl mixing length model, Davies and Furnes’ (1980) simple flow-related model with mixing length which includes the bottom boundary layer thickness, and a time and space invariant eddy viscosity with 650 cm 2/s. The bottom friction at the sea bed is given in a quadratic form using a constant bottom friction coefficient, c f and near-bottom velocities. A series of M 2 tide model runs were carried out and optimal values of c f were determined through the comparison with tidal elevation amplitudes and phases at 203 stations. From these comparisons it is shown that the M 2 tidal charts computed with a range of eddy viscosity formulations are in good agreement with each other when optimal values of c f are chosen; comparing with M 2 tidal current amplitudes and phases at 15 stations, it is shown that tidal current distributions and its profiles are in reasonably good agreement with winter-time observations in the central part of the Yellow Sea; relatively poor results are obtained near the Chinese coast where non-tidal effects such as abrupt changes in tidal current phase in the vertical due to large freshwater discharge are pronounced. It is noted that the bottom friction coefficient has a major influence on tidal elevation and tidal currents and optimal values of bottom friction coefficient are closely related to the near-bottom eddy viscosity. The considered eddy viscosity closure models appear to work well for tidal problem when the bottom friction parameter is optimized. Results indicate that for a barotropic tide the Prandtl mixing length model which can account of the boundary layer thickness could be an useful alternative to a highly complex q 2- q 2 l model.