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, a-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 Fumes' (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, cf 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. (C) 1999 Elsevier Science Ltd. All rights reserved.