The influence of bed friction and vertical eddy viscosity on tidal propagation

Abstract

Single-point solutions to the horizontal momentum equation (describing tidal propagation) are used to illustrate the influence of both bottom friction and vertical eddy viscosity. These influences determine whether a simplified vertically-averaged, two-dimensional model will adequately simulate tidal propagation, or where a fully three-dimensional model is required. The effective influences of these two terms is sensitive to both latitude and tidal frequency, in addition to current speed and water depth - thus complicating the a-priori selection of a 2-D or 3-D model. The present study shows that, for applications concerned primarily with prediction of water levels and depth-integrated tidal fluxes, 2-D models are generally entirely adequate in water depths exceeding 50 m—a consequence of small frictional influence. However, exceptions to this conclusion may arise at latitudes corresponding to the inertial frequencies, i.e. λ>70° for semi-diurnal constituents and 27°≤λ≤30° for diurnal constituents. Analytical solutions can be used to augment 2-D model results providing reliable qualitative descriptions of variations in current profiles. However, for applications where detailed current profiles are important, including accurate representation of the near-bed velocity and associated erosional stress, 3-D models 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 are 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 gradients. © 1997 Elsevier Science Ltd