You are hereWavemaker 2.0: Simulation and Identification of Second-Order Waves

# Wavemaker 2.0: Simulation and Identification of Second-Order Waves

WAVEMAKER is a FORTRAN subroutine to simulate random non-Gaussian ocean wave histories. It generates a first-order (Gaussian) wave process with an arbitrary power spectrum, and applies nonlinear corrections based on second-order hydrodynamics. Inputs to the routine include the first-order spectrum, the water depth, and a set of locations in the along-wave direction at which wave elevation histories are desired. It may thus provide useful input to estimate loads on spatially distributed ocean structures and ships.

The WAVEMAKER package also includes a separate driver program, which facilitates input/output and generates several analytical spectra l models. Its input is specified in command-line format, similar to that of the TFPOP program for hydrodynamic post-processing also developed in the Stanford RMS program. An example problem is included to demonstrate the use of WAVEMAKER and its driver.

In terms of methodology, WAVEMAKER first uses standard frequency domain methods to generate first-order Gaussian histories at each location. For each of these, WAVEMAKER then evaluates the full set of second-order corrections according to hydrodynamic theory. Thus the first-order wave process, with *N* components at frequencies *ω _{n}* gives rise to a total of

*N*corrections, spread over all sum frequencies

^{2}*ω*+

_{n}*ω*, and to another

_{m}*N*corrections over all difference frequencies

^{2}*ω*-

_{n}*ω*.

_{m}

WAVEMAKER also includes the ability to identify the underlying first-order Gaussian history from a given observed time history. This feature is particularly attractive for use in situations where the second-order nonlinearity in the waves is built-in into the structural response calculations. To avoid double-counting therefore, the input waves should be filtered to remove any second-order nonlinearity. WAVEMAKER takes in an input wave history and identifies its first- and second-order wave components. This identification, an inverse feature to simulation, is based on a Newton-Raphson scheme to solve *N* simultaneous nonlinear equations to identify the first-order waves which, when run through the second-order wave predictor,

matches the observed waves.