Wave Boundary Conditions
Accurately representing wave boundary conditions is fundamental to simulating coastal and offshore engineering problems. Whether modeling wave forces on a structure, wave break performance, wave overtopping of a seawall, wave-induced scour around a foundation, or the performance of a wave energy converter, the wave boundary condition determines the quality of everything downstream.
FLOW-3D and FLOW-3D HYDRO support a comprehensive set of wave generation methods covering regular and irregular waves across the full range of water depths, from deep water offshore to shallow coastal and nearshore environments. Waves are generated directly at mesh block boundaries and propagate through the computational. The defined wave profile at the boundary can also be applied as an initial condition to the computational domain.
Wave forces acting on a coastal walkway and flood wall, with hydrodynamic force on the wall object exported directly for structural analysis.
Wave Types
Linear Waves
Linear waves have a sinusoidal surface profile with small amplitude relative to the wavelength and water depth. They are generated using Airy linear wave theory and are appropriate for open-ocean conditions where wave steepness is low. An irregular wave can also be defined by superposing up to 1000 linear component waves with independent frequencies, amplitudes, and phase shifts, allowing arbitrary wave spectra to be represented without using a standard spectral formulation.
Stokes Waves
Stokes waves are nonlinear periodic waves appropriate for deep and intermediate water depths. They have sharper crests and flatter troughs than linear waves of the same height and period. Two generation methods are available: Fenton’s Fourier series method and Fenton’s fifth-order theory.
Cnoidal Waves
Cnoidal waves are nonlinear periodic waves appropriate for shallow and intermediate water depths. They are more peaked and asymmetric than Stokes waves of equivalent energy and are generated using Fenton’s Fourier series method. Fenton’s method is valid across the full range of periodic wave types from deep to shallow water.
Solitary Waves
A solitary wave is a single, non-periodic wave that exists entirely above the undisturbed water level. It is the limiting form of a cnoidal wave as wavelength approaches infinity and is relevant for modeling tsunami-like events, dam breaks, and large impulsive wave loading on coastal structures. Solitary waves are generated using McCowan’s theory.
Irregular Waves
FLOW-3D and FLOW-3D HYDRO generate irregular waves using the Pierson-Moskowitz spectrum, which describes fully developed windy seas, or the JONSWAP spectrum, which accounts for fetch-limited growth in coastal and semi-enclosed environments. A user-defined spectrum can also be imported from an external file for site-specific sea state representation.
Wave Generation Options
Wave conditions in FLOW-3D and FLOW-3D HYDRO can be specified:
- As a boundary condition at any of the four horizontal mesh block faces (X min, X max, Y min, Y max), where the wave enters the domain and propagates inward
- As an initial condition throughout the fluid domain, which initializes the wave field everywhere simultaneously and avoids the transient startup period needed for waves generated at a boundary to fill the domain
- With a superimposed steady current at the wave boundary, allowing combined wave-current conditions to be represented
Wave Applicability Chart
Selecting the appropriate wave theory for a given set of conditions depends on the wave height, wave period, and water depth. FLOW-3D and FLOW-3D HYDRO include a wave applicability chart based on established coastal engineering guidance to help users identify the correct wave generator for their application. Fenton’s Fourier series method is valid across the full range of periodic wave conditions and is the recommended default for all regular wave types.
Applications
Waves Boundary Conditions are used in FLOW-3D and FLOW-3D HYDRO for:
- Wave force and overtopping analysis for coastal protection structures, seawalls, and breakwaters
- Wave transmission and reflection across breakwater structures
- Wave-structure interaction for offshore platforms, gravity-based structures, and subsea foundations
- Wave energy converter design and performance assessment
- Tsunami and extreme wave loading on coastal infrastructure
- Nearshore wave transformation including shoaling, refraction, and breaking over complex bathymetry
- Wave-induced scour and sediment transport around coastal and offshore structures
- Harbor resonance and wave penetration analysis
- Wave interaction with floating and moored structures, in combination with the moving object and mooring lines models
Wave attenuation by a living shoreline reef structure, showing flow depth and a 65% reduction in wave height after passing through the WAD® reef elements.