Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · 2004 · 213 citations · 25 references
Natural SciencesOcean EngineeringOceanographyFluid DynamicsOcean ModelingOcean WavesLinear Wave TheoryNonlinear Wave DynamicsNumerical Ocean SimulationPropagation ModelingSurface Wave DynamicsWave PropagationNumerical Wave ModelingVelocity ProfilesWave Equation ModelsWave EquationsWave HydrodynamicsWave ModelWave Propagation ModelingWave Theory
The study derives two‑layer water‑wave equations by integrating the primitive equations across two arbitrary layers. Independent velocity profiles are defined for each layer, matched at the interface, yielding a three‑parameter system that is optimized and solved numerically, with the solver tested on one‑ and two‑dimensional cases. The optimized model accurately reproduces linear wave behavior up to kh≈6 and captures second‑order nonlinear effects to the same limit, with numerical results matching laboratory data.
A set of model equations for water–wave propagation is derived by piecewise integration of the primitive equations of motion through two arbitrary layers. Within each layer, an independent velocity profile is derived. With two separate velocity profiles, matched at the interface of the two layers, the resulting set of equations has three free parameters, allowing for an optimization with known analytical properties of water waves. The optimized model equations show good linear wave characteristics up to kh ≈ 6, while the second–order nonlinear behaviour is captured to kh ≈ 6 as well. A numerical algorithm for solving the model equations is developed and tested against one– and two–horizontal–dimension cases. Agreement with laboratory data is excellent.
25