SoulsbyKH

Methods for Calculating kh

The dispersion equation for surface gravity waves is $\omega ^{2}=gk~{\text{tanh}}(kh)$, where $\omega$ is the angular frequency of the wave ($2\pi /T$) where $T$ is period (s), $g$ is gravitational acceleration (m2 s-1), $h$ is water depth (m), and $k$ is wavenumber ($2\pi /\lambda$) where $\lambda$ is wavelength (m). $k$ is difficult to calculate because it is implicit. Wiberg and Sherwood (2008) reported on the speed and accuracy of several explicit and iterative methods for approximating $kh$. Two good methods are implemented in ROMS/CSTMS.

A fifth-order polynomial approximation attributed to Hunt (1979) by Dean and Dalrymple (1991), p72 is used when SSW_HUNT_KH is defined, and the Newton-Raphson method suggested by Soulsby (2005) is used when SSW_SOULSBY_KH is defined.

Note: The Soulsby option and these two CPP defs are only implemented in the version of SSW_BBL.h located in Sherwood's branch. Define one of these two options:

#define SSW_SOULSBY_KH
#undef SSW_HUNT_KH