A comparison of the nonlinear frictional characteristics of two‐dimensional and three‐dimensional models of a shallow tidal embayment

The nonlinear frictional behavior of two‐dimensional (2‐D) and three‐dimensional (3‐D) models are compared in this study of tides in the Bight of Abaco. The shallow depths and the existence of an extensive set of tidal elevation data (five astronomical and two overtide constituents at 25 stations) from Filloux and Snyder (1979) offer an excellent opportunity to compare the effects of different frictional formulations. In addition, previous modeling efforts in the bight have consistently overpredicted the M 6 and generally overdamped the O 1 , K 1 , and S 2 tides. The results indicate that although the 2‐D and 3‐D models may be calibrated to produce nearly identical responses for the dominant M 2 tide, there are systematic differences in the responses of the primary overrides. These differences are explained using analytical expansions of the friction terms and are shown to be due to differences in the terms that are nonlinear in velocity and in water level. The investigation concludes that the overgeneration of M 6 and the overdamping of secondary astronomical tides will occur in 3‐D models as well as 2‐D models. Although several causes for these problems were considered, improvement in these constituents could be achieved only by modifying the standard quadratic friction or flow‐dependent eddy viscosity relations to reduce the nonlinear frictional effect relative to the linear frictional effect. The required modifications suggest the presence of a constant background velocity, residual turbulence field, or possibly the need for a more advanced frictional closure.