Application of the Green-Naghdi Theory of Fluid Sheets to Shallow-Water Wave Problems. Report 1. Model Development
COASTAL ENGINEERING RESEARCH CENTER VICKSBURG MS
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This report presents the mathematical formulation for the development of a numerical model that simulates wave transformation in shallow waters. The model is intended both for military and civil works projects involving propagation of time-dependent and nonlinear waves where existing models may either be inapplicable or use of simple analytic or numerical solutions is infeasible. The theory detailed in this report introduces a new-generation water wave model for shallow to moderate water depths where the seabed varies rapidly. The Green-Naghdi Level II theory, hereafter referred to simply as the GN theory, has been significantly modified in this research and a powerful, general-purpose numerical model, called GNWave, is developed for water wave problems. The theory and ensuing model incorporate some of the most important mathematical features of the water wave equations. These include non-approximating of the governing Eulers field equations and imposing the proper boundary conditions necessary for capturing the bulk physical characteristics of wave trains in the shallow- water regime. The GN approach, which is fundamentally different from the perturbation method based on developments in classical wave theory begun by Stokes and Boussinesq in the last century, can do this only because it does not introduce any simplifications of the velocity variation in the vertical direction across the fluid layers or sheets. Amphibiouslanding operations, Coastal processes, Hydraulic structures, Logistics-Over-The-Shore LOTS, Numerical simulation, Water surface profile, Wave-structure interaction, Wave theories.
- Physical and Dynamic Oceanography