Longitudinal mixing in the upper reaches of the Bay of Fundy

Abstract

A time-dependent, one-dimensional, advection-diffusion equation is used to predict the salinity distribution in the vertically well mixed upper regions of the Bay of Fundy. It is shown that the longitudinal diffusion coefficient must increase in a seaward direction from the head of the bay to give a good agreement between the model and observations, and a simple parameterization of the coefficient is sought in terms of the product of appropriate length and velocity scales. A coefficient equal to b1U0l0 where b1 is a constant, U0 the amplitude of the tidal current and l0 the tidal excursion, is tried but does not give this increase and produces a poor description of the salinity distribution. However, a diffusion coefficient of the form cu*h, where c is a constant, u* the r.m.s. friction velocity from the tidal current averaged over the M2 tide, h, is the water depth and the overbar denotes a cross-sectional average, does give the required increasing value and allows a good agreement between the model and observations for c=200. This form of parameterization is the same as that for shear dispersion except that the coefficient c is in order of magnitude too large. It is suggested, instead, that the diffusion process results from the interaction of tidal residual eddies with the oscillatory tidal flow, a mechanism described by Zimmerman (1976) and capable of producing large diffusion coefficients. Preliminary estimates show that the construction of a tidal power barrage across Minas Basin would considerably reduce the salinity in the headpond of the barrage but have little effect seaward. A sinusoidally varying freshwater input to the estuary is shown to have a significant effect on the salinity distribution only for periods of oscillation exceeding a month, while variations in the longitudinal diffusion coefficient due to an apogee-perigee tidal cycle have little effect on the salinity distribution.