Edward S. Gross

A semi‐implicit method for vertical transport in multidimensional models

A one-dimensional scalar transport method which is appropriate for simulations over a wide range of Courant number is described. Von Neumann stability and matrix invertibility are guaranteed for all Courant numbers and the method has less diffusive and dispersive error than simpler implicit methods. It is implemented for vertical scalar transport in a three-dimensional hydrodynamic model, with horizontal transport discretized explicitly. The method is applied and compared with simpler semi-implicit methods in several test cases and used for a simulation of scalar transport in an estuary.

Time scales in Galveston Bay: An unsteady estuary

Estuarine time scales including the turnover, particle e-folding time, the age (calculated with a passive tracer), and residence time (calculated with Lagrangian particles) were computed using a three-dimensional hydrodynamic model of Galveston Bay, a low-flow, partially stratified estuary. Time scales were computed during a time period when river flow varied by several orders of magnitude and all time scales therefore exhibited significant temporal variability because of the unsteadiness of the system. The spatial distributions of age and residence time were qualitatively similar and increased from 15 days in a shipping channel to >45 days in the upper estuary. Volume-averaged age and residence time decreased during high-flow conditions. Bulk time scales, including the freshwater and salinity turnover times, were far more variable due to the changing river discharge and salt flux through the estuary mouth. A criterion for calculating a suitable averaging time is discussed to satisfy a steady state assumption and to estimate a more representative bulk time scale. When scaled with a freshwater advective time, all time scales were approximately equal to the advective time scale during high-flow conditions and many times higher during low-flow conditions. The mean age, Lagrangian residence, and flushing times exhibited a relationship that was weakly dependent on the freshwater advective time scale demonstrating predictability even in an unsteady, realistic estuary.

Using an isohaline flux analysis to predict the salt content in an unsteady estuary

AbstractAn estuary is classified as unsteady when the salinity adjustment time is longer than the forcing time scale. Predicting salt content or salt intrusion length using scaling arguments based on a steady-state relationship between flow and salinity is inaccurate in these systems. We have used a time-dependent salinity box-model based on an unsteady Knudsen balance to demonstrate the effects of river flow, inward total exchange flow (tidal plus steady), and the salinity difference between inflow and outflow on the salt balance. A key component of the box-model is a relationship we present linking the normalized difference between inflowing and outflowing salinity at the mouth and the mean salinity content. We show that the normalized salinity difference is proportional to the mean salinty squared based on theoretical arguments from the literature. We demonstrate the validity of the box-model by hindcasting five years of mean salinity in Galveston Bay (estimated from coarse observations) in response to...