Numerical Simulation of Nonlinear Internal Solitary Wave Interactions with Submarine Topographic Features
Approximately 120 computer simulations were conducted to evaluate how a mode-1-type internal wave would interaction with a variety of submarine topographic (physiographic) obstacles likely to be found in a marine setting. A total of seven obstacle geometries were selected for evaluation - shelf, slope-shelf, extended slope, short-slope, reverse-shelf, a single (isolated) rectangular obstacle, and a single triangular obstacle. Internal waves of `depression' as well as `elevation' were formed using a two-layered, stratified numerical model based on the Navier-Stokes and continuity equations. The governing equations assumed Boussinesq conditions. Output data from the FORTRAN-based computer code were post-processed using MATLAB-based computer programs that calculated internal wave amplitudes and energies. These data were compared to published data associated with experimental wave tank studies and found generally to be in good agreement. Data from the numerical simulation trials were also used to generate figures illustrating various hydrodynamic features (pycnocline, streamlines, and velocity vectors) of an internal wave as it forms as well as when it interacts with different types of obstacle geometries. The types of features and processes observed included the formation of Kelvin-Helmholtz or K-H-like vortices and various stages of the classically-recognized wave-breaking progression ("wash-down," "breaking," "bore," and "surge"). When considering a stratified fluid system, it was confirmed that internal wave characteristics are influenced in large measure by the relative depths of the two fluids defining the system as well as the effects of viscous decay (damping). It was also confirmed that the nature of the interaction between an internal wave and a topographic obstacle is influenced by the magnitude of either the nonlinear parameter or the blocking parameter. The numerical simulation trials also allowed for the interrogation of the modeling domain to determine the nature of the stability conditions (static vs. dynamic) in time and space. In this regard, evaluation of both the Richardson number and the normalized density gradient provided additional insights into the hydrodynamics of the system when topographic obstacles are present. Three instability states were evaluated: K-H, buoyant, and static.This research contributes to a basic understanding of internal wave phenomena and includes some general conclusions regarding the effects of obstacle geometry on internal wave behavior and properties.
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