THE INFLUENCE OF BED FRICTION AND VERTICAL EDDY VISCOSITY ON TIDAL PROPAGATION

Single-point solutions to the horizontal momentum equation (describing tidal propagation) are used to illustrate the influence of both botto m friction and vertical eddy viscosity. These influences determine whe ther a simplified vertically-averaged, two-dimensional model will adeq uately simulate tidal propagation, or where a fully three-dimensional model is required. The effective influences of these two terms is sens itive to both latitude and tidal frequency, in addition to current spe ed and water depth - thus complicating the a-priori selection of a 2-D or 3-D model. The present study shows that, for applications concerne d primarily with prediction of water levels and depth-integrated tidal fluxes, 2-D models are generally entirely adequate in water depths ex ceeding 50 m-a consequence of small frictional influence. However, exc eptions to this conclusion may arise at latitudes corresponding to the inertial frequencies, i.e. lambda>70 degrees for semi-diurnal constit uents and 27 degrees less than or equal to lambda less than or equal t o 30 degrees for diurnal constituents. Analytical solutions can be use d to augment 2-D model results providing reliable qualitative descript ions of variations in current profiles. However, for applications wher e detailed current profiles are important, including accurate represen tation of the near-bed velocity and associated erosional stress, 3-D m odels with detailed descriptions of turbulence structure are required. The use of 3-D models for shallow estuaries and bays should avoid the necessity of empirical adjustment to the dissipation processes that a re poorly represented by a quadratic-type law based on depth-averaged velocities. The above conclusions apply to the propagation of tides in the absence of pronounced effects of wind forcing or density gradient s. (C) 1997 Elsevier Science Ltd.