Bathymetric Influences on the Estuarine Equilibrium Length and Adjustment Time

Abstract

inear theories are extended to enable investigations of how exponentially convergent width and sloping bottom affect the sensitivity of estuarine equilibrium length and adjustment time. We focus on the response to river forcing and consider a regime dominated by gravitational circulation, but the results are generalizable. For a range of forcing and bathymetric profiles, the predicted equilibrium length and adjustment time compare favorably with numerical solutions from a width-averaged model. The main findings are that: (1) convergent width and sloping bottom reduce the sensitivity of equilibrium length to river forcing. The sensitivity is governed by a dimensionless parameter which measures the degree of width and depth changes sampled by the intrusion length. Hence, the sensitivity is not a constant in a system but varies with forcing: When discharge increases, a shortened estuary experiences less bathymetric changes over its intrusion. The sensitivity therefore increases progressively toward the conventional -1/3 power-law. An observational example of variable sensitivity from Delaware Bay is given. (2) width convergence and bottom slope help accelerate the adjustment process. It is shown that the linear adjustment time is set by the ratio of salt content variations to the discharge perturbation. Hence, under the same forcing, the adjustment time is controlled by the salt content variations which decrease monotonically with increasing convergence and slope. This means that, to achieve a given length change, a more strongly convergent and sloped system simply requires to move less salt, thereby needing a shorter adjustment time.