Quoted from: https://github.com/NOAA-EMC/WW3/wiki/About-WW3 

WAVEWATCH III® is a community wave modeling framework that includes the latest scientific advancements in the field of wind-wave modeling and dynamics.

The core of the framework consists of the WAVEWATCH III® third-generation wave model (WAVE-height, WATer depth and Current Hindcasting), developed at NOAA/NCEP in the spirit of the WAM model (WAMDIG 1988, Komen et al, 1994), which evolved from WAVEWATCH (Delft: Tolman 1989, 1991a), and WAVEWATCH II (NASA Goddard: Tolman, 1992). WAVEWATCH III® differs from its predecessors in many important points such as governing equations, model structure, numerical methods and physical parameterizations.

WAVEWATCH III® solves the random phase spectral action density balance equation for wavenumber-direction spectra. The implicit assumption of this equation is that properties of medium (water depth and current) as well as the wave field itself vary on time and space scales that are much larger than the variation scales of a single wave. The model includes options for shallow-water (surf zone) applications, as well as wetting and drying of grid points. Propagation of a wave spectrum can be solved using regular (rectilinear or curvilinear) and unstructured (triangular) grids.

For more detailed information:

Physics

Numerics

Output Options

WW3 Manual References (As seen in the manual)

MetEd WAVEWATCH III Course (requires login)

Google Scholar

The WAVEWATCH III Development Group (As seen in the manual)