Date of Award

Winter 2023

Project Type


Program or Major


Degree Name

Doctor of Philosophy

First Advisor

Thomas Lippmann

Second Advisor

James Pringle

Third Advisor

Diane Foster


Tidally induced pressure gradients in sea level drive mean estuarine tidal currents that can have horizontal spatial variability across a bounded channel or inlet. Strong cross-channel gradients in along-channel mean velocity set up extremums in the background potential vorticity that can support instabilities of tidal currents flowing through narrow, bounded estuarine channels and tidal inlets. In addition, conservation of potential vorticity including frictional terms, results in intensification of along-channel tidal currents over shallow lateral shelves. In the first part of this dissertation (Chapter 2), the dispersion equation of barotropic instabilities of tidal currents is analytically solved for simple bathymetry defined by idealized and variable channel geometries that include lateral shelves. The solution is third-order and the cross-channel velocity structure, bathymetry, and geometry can be altered to approximate typical natural inlet geometries allowing for a range of scenarios to be examined. The resulting fastest growing unstable modes have wavelengths of O(10^2 m), periods of O(10^2 - 10^3 s), and growth rates of O(10^-3 - 10^-2 s^-1) with phase speeds approximately one third of the maximum velocity, consistent with instabilities of longshore currents studied in the nearshore (Bowen and Holman, 1989; Dodd and Thornton, 1990). In the second part of this dissertation (Chapter 3), the presence of instabilities of tidal currents is observed from a spatially lagged along-channel array consisting of seven current meters and pressure sensors deployed in the Hampton-Seabrook Inlet, NH for one week encompassing the spring tides in May 2021. Using iterative maximum likelihood estimators, wavenumber-frequency spectra are estimated during 3-4 hour time periods with approximately steady currents on both the flood and ebb tides. Dominant wavenumbers (± 0.002 - 0.02 m^-1) of the low frequency motions (0.0006 - 0.01 s^-1) with corresponding wavelengths (± 314.2 – 3141.6 m) and periods (628.3 – 10472 s) are resolved and consistent with motions estimated in Chapter 2. The lack of breaking wave group modulations within the inlet and the presence of the seaward (shoreward) propagating instabilities on the ebb (flood) flow indicate that the presence of the instabilities can be attributed to the shear of the tidal current. In the third part of the dissertation (Chapter 4), a numerical hydrodynamic model (ROMS) is used to better understand the forcing mechanisms driving intensification of velocity over the shallow lateral shelf in the Piscataqua River observed from ADCP transects obtained in 2015 during both the flood and ebb of the spring tide. Results show that the along-channel flow is intensified (convergence of streamlines) over the lateral shelf under high Reynolds number conditions, where the inertial forces dominate over the frictional and viscous forces, during both quasi-steady flooding and ebbing currents. Given the cross-channel structure of the velocity, the water circulates up onto the shelf by the conservation of potential vorticity. Due to the shallower depth over the shelf, the velocities increase due to conservation of volume, which leads to even stronger horizontal shear in the mean along-channel tidal currents. The spatial and temporal variability in mean tidal currents (consistent with instabilities of the flow) results from the background potential vorticity that mixes momentum horizontally across the channel and smooths the cross-channel velocity structure; thus, the potential vorticity balance leads to both velocity intensification over the shelf and unstable motions. Changes to the mean flow structure and mixing by instabilities have implications for estuarine dynamics such as the fate and transport of organic and inorganic matter, navigational safety, and tidal energy resource assessment.