Sroka, S.G., 2016. Internal Tides Near Steep Topographies. SM Thesis, Massachusetts Institute of Technology, Mechanical Engineering, September 2016.
The primary contributions of this thesis include the first stages of development of a 2D, finitevolume,
non-hydrostatic, sigma-coordinate code and beginning to apply the Dynamically Orthogonal
field equations to study the sensitivity of internal tides to perturbations in the density field. First, we
ensure that the 2D Finite Volume (2DFV) code that we use can accurately capture non-hydrostatic
internal tides since these dynamics have not yet been carefully evaluated for accuracy in this framework.
We find that, for low-aspect ratio topographies, the -coordinate mesh in the 2DFV code
produces numerical artifacts near the bathymetry. To ameliorate these staircasing effects, and to
develop the framework towards a moving mesh with free-surface dynamics, we have begun to implement
a non-hydrostatic sigma-coordinate framework which significantly improves the representation
of the internal tides for low-aspect ratio topographies. Finally we investigate the applicability of
stochastic density perturbations in an internal tide field. We utilize the Dynamically Orthogonal
field equations for this investigation because they achieve substantial model order reduction over
ensemble Monte-Carlo methods.