Numerical modeling of tides in the Great Bay Estuarine System: dynamical balance and spring–neap residual modulation

The Great Bay Estuarine System, in New Hampshire, USA, has been the focus area for an attempt to develop a robust finite element method model for estuarine hydrodynamics. Past studies used a nonlinear, time stepping, kinematic model with limited success (Ip et al. Advances in fluid mechanics III, WIT, Southampton (2000) 569; Bilgili et al. J. Geophys. Res. – Oceans 107 (2002); Ertu¨ rk et al. Estuar. Coast. Shelf Sci. 47 (1998) 119). We add dynamic physics (that is, local accelerations) for deep-water areas and keep kinematic physics (that is, without local and advective accelerations), with the inclusion of a porous medium beneath the open channel, for shallow and dewatering areas. The choice of which physics set to apply is made on an elemental depth dependent basis. The addition of the local acceleration terms for deep-water areas is seen to greatly improve accuracy in matching of tidal phasing over previous studies. Simulations involving M2/M4/M6 tidal constituents result in strong agreement to observed data from the 1975 Great Bay field program (Ertu¨ rk et al. Estuar. Coast. Shelf Sci. 17 (1983) 297), in terms of both tidal heights and cross-section averaged velocities. Comparisons with 10 tidal elevation observation stations and four cross-section averaged current transects show good agreement, displaying average normalized root mean square misfit values of 0.08 and 0.25, respectively. Study of the simulated momentum balance shows the size of the contributions from acceleration terms to be on the order of a third the size of the contributions from the pressure gradient and bottom stress terms. Although relatively small, they are observed to peak at the crucial time of tidal reversal. Application of the model for long-term simulation using an M2/N2/S2 forcing shows the ability to realistically capture the spring–neap cycle. The tidally rectified flow is generally described as a constant spatial pattern with overall amplitude modulation following the spring–neap cycle.