Title: A NON-HYDROSTATIC UNSTRUCTURED-GRID FINITE-VOLUME COASTAL OCEAN MODEL SYSTEM (FVCOM-NH): DEVELOPMENT, VALIDATION AND APPLICATIONS

By: Zhigang Lai
Advisor: Changsheng Chen

Abstract: This dissertation research represents a systematic approach toward developing a modeling tool to investigate non-hydrostatic fluid dynamics and associated effects in real oceans. The research integrates algorithm and code development, validation tests and real applications.

In order to solve non-hydrostatic dynamics within current existing model framework, the full vertical momentum equation is maintained in the governing equations and the global pressure is decomposed into the hydrostatic and non-hydrostatic components. The non-hydrostatic pressure is determined from a pressure Poisson equation using a fractional-step formulation, whereby the hydrostatic part is computed explicitly from the free surface elevation and density field. The final velocity is obtained under assumption of its incompressibility from the projection of the intermediate result. This algorithm was implemented using an unstructured-grid, finite-volume approach, which assures local volume conservation and a second-order accurate spatial discretization. Modern efficient computational technologies have been incorporated into the non-hydrostatic version FVCOM (hereafter as FVCOM-NH) including MPI-based parallelization and the use of a scalable, sparse matrix solver library (PETSc) combined with a high-performance pre-conditioner library (Hypre). This allows FVCOM-NH to run efficiently in a multi-processor environment, a necessity for tackling the large problem sizes associated with non-hydrostatic flows.

FVCOM-NH has been thoroughly validated using four idealized non-hydrostatic problems. These include a linearized barotropic problem (standing surface wave over flat bathymetry), a nonlinear barotropic problem (surface solitary waves in flat and sloping-bottom channels) and two cases with non-uniform density, the well-known lock-exchange problem and a more realistic test consisting of the propagation of an internal solitary wave and subsequent breaking on a steep slope. The validations are conducted by comparing numerical solutions of FVCOM-NH with analytic solutions, high-order approximation numerical simulations and lab experiment observations. The results demonstrate well the robustness and accuracy of FVCOM-NH.

FVCOM-NH has been applied to the study of the large-amplitude, high-frequency nonlinear internal waves observed in Massachusetts Bay using a two-dimensional framework with no along-isobath variation. The model-derived internal wave characteristics are in excellent agreement with those observations from the internal wave field in an in-site experiment in 1998 (Butman et al, 2006). The model-guided experiments suggest that the internal wave over the Bank is generated by the interaction of tidal currents with steep bottom topography through a process of forming an initial density front on the western flank near ebb-flood transition; steeping of the front as density depression develops in early flood phase on the bay-side slope; and disintegrating of the density depression to a wave train. The earth's rotation tends to transfer the cross-banktidal kinetic energy into the along-bank direction and thus reduces the intensity of the density front at ebb-flood transition and density depression in flood period. The internal wave packet propagates as a leading edge feature of internal tidal waves, and the faster phase speed of the high-frequency internal waves in Mass Bay is caused by the earth's rotation. Ignoring bottom friction significantly enlarges the cross-bank scale of the density front, produces larger vertical density displacement, and weaker dissipation during the wave's shoaling. The Mellor-Yamada level 2.5 turbulence closure models tend to cause an over-damping of the high-frequency internal waves. The model results support the internal wave theory proposed by Lee and Beardsley (1974) but disagree with the mechanism proposed by Maxworthy (1979).