Intratidal and low-pass filtered fluctuations of density stratification in eastern Long Island Sound are apparently produced by both hydraulic effects and tidally induced vertical mixing. In order to evaluate the effects of bathymetry, oscillating barotropic forcing and vertical mixing on density stratification and on the exchange between estuarine and oceanic waters, a series of numerical experiments over a simplified sill bathymetry are performed. Hydraulic effects over a sill decrease exchange by 25% relative to flat bottom. There is a fundamental change in the nature of the flow from weak to strong barotropic forcing: during weak tidal forcing, sill exchange can be subject to hydraulic control and the intratidal stratification is determined by internal wave motion on the pycnocline; during strong forcing, the density field is determined by the gradient advection of the predominant barotropic tide, the hydraulic control is broken, and exchange is determined by the tidal prism. Vertical mixing tends to decrease exchange and to break the hydraulic control.