# Simulation of Standing and Propagating Sea Waves with Three-Dimensional ARMA Model

Simulation of sea waves is a problem appearing in the framework of developing software-based ship motion modelling applications. These applications generally use linear wave theory to generate small-amplitude waves programmatically and determine impact of external excitations on a ship hull. Using linear wave theory is feasible for ocean waves, but is not accurate for shallow-water and storm waves. To cope with these shortcomings we introduce autoregressive moving-average (ARMA) model, which is widely known in oceanography, but rarely used for sea wave modelling. The new model allows to generate waves of arbitrary amplitudes, is accurate for both shallow and deep water, and its software implementation shows superior performance by relying on fast Fourier transform family of algorithms. Integral characteristics of wavy surface produced by ARMA model are verified against the ones of real sea surface. Despite all its advantages, ARMA model requires a new method to determine wave pressures, an instance of which is included in the chapter.

## Bibtex

@inbook{gankevich2018ocean, title={Simulation of Standing and Propagating Sea Waves with Three-Dimensional ARMA Model}, author={Ivan Gankevich and Alexander Degtyarev}, publisher={Springer}, howpublished={The Ocean in Motion: Circulation, Waves, Polar Oceanography}, year={2018}, month={01}, doi={10.1007/978-3-319-71934-4_18}, isbn={978-3-319-71934-4}, pages={249--278}, address={Cham}, editor={Velarde, Manuel G. and Tarakanov, Roman Yu. and Marchenko, Alexey V.}, type={inbook} }

Publication: The Ocean in Motion: Circulation, Waves, Polar Oceanography

Publisher: Springer