Date of Award

12-2019

Level of Access Assigned by Author

Open-Access Thesis

Degree Name

Master of Arts (MA)

Department

Mathematics

Advisor

Thomas Bellsky

Second Committee Member

Lauren Ross

Third Committee Member

Peter Stechlinski

Additional Committee Members

Robert Franzosa

Abstract

Estuaries are coastal bodies of water subjected to strong tidal influence and characterized by their morphology, tidal dynamics, topography, and stratification. Tidal flow is critically important to the water circulation, nutrient influx, and sediment transport in or out of an estuary. However, tidal asymmetry enhanced by estuary shape and nonlinear processes can lead to complications in estuarine flow. Analytical models are used to systematically study tidal flow within an estuary. Previous studies have derived analytical models of varying complexity and applied them to investigate tidal and residual flow. This thesis derives a three-dimensional analytical model with a perturbation expansion of the Navier-Stokes equations in the shallow water limit, modified from. The resulting zero-order solution is analyzed to provide insight into the tidal flow of the Damariscotta River estuary. The Damariscotta River is a tidally-dominated, well-mixed estuary located on the coast of Maine. Despite its importance to local aquaculture, few studies have been conducted within the estuary. This thesis is an exploratory study providing further understanding of the tidal flow dynamics of the Damariscotta River estuary.

The water level elevation and three-dimensional tidal flow velocity are presented, and sensitivity to changes in friction and width convergence are studied by altering their respective parameters, vertical eddy viscosity and width convergence factor. Water level elevation amplitude increases along-channel due to amplification from width convergence and, contrarily, along-channel velocity amplitude decreases along-channel due to friction, which suggests that width convergence dominates friction in determining water elevation, but friction has greater influence over velocity. This could be the result of the model assuming constant friction. Lateral velocities exhibited a two-cell structure with flow of the near-surface cell and the near-bottom cell in opposite directions. Results of the model compared well to previous studies within the estuary and to the Upper Ems estuary, which has similar dynamics as the Damariscotta estuary although important morphological distinctions should be noted. Tidal asymmetry and variable friction within the estuary were not studied in this thesis, as non-linear terms were dropped in governing equations and vertical eddy viscosity was assumed to be constant. Furthermore, the model considers the zero-order solution and is unable to study residual flow in the estuary. Future work should investigate tidal asymmetry and residual flow in the Damariscotta estuary, while considering a more complicated friction regime.

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