SoulsbyKH: Difference between revisions
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A stable and precise method for calculating the product of wavenumber x depth $kh$ in the linear gravity-wave dispersion equation is implemented in the version of SSW_BBL.h located in [https://www.myroms.org/projects/cstm/browser/branches/crs/cstm_trunk Sherwood's branch]. | A stable and precise method for calculating the product of wavenumber x depth $kh$ in the linear gravity-wave dispersion equation is implemented in the version of SSW_BBL.h located in [https://www.myroms.org/projects/cstm/browser/branches/crs/cstm_trunk Sherwood's branch]. | ||
The dispersion equation is $\omega^2 = gk$ tanh($kh$), where $\omega$ is the angular frequency of the wave ($2pi/T$) where $T$ is period (s), $g$ is gravitational acceleration {\text{m}}^2 {\text{s}}^{-1}, $h$ is water depth (m), and $k$ is wavenumber ($2pi/\lambda$) where $\lambda$ is wavelength (m). $k$ is difficult to calculate because it is implicit. | The dispersion equation is $\omega^2 = gk$ tanh($kh$), where $\omega$ is the angular frequency of the wave ($2pi/T$) where $T$ is period (s), $g$ is gravitational acceleration {\text{m}}^2 {\text{s}}^{-1}, $h$ is water depth (m), and $k$ is wavenumber ($2pi/\lambda$) where $\lambda$ is wavelength (m). $k$ is difficult to calculate because it is implicit. | ||
[[Bibliography#WibergP_2008a | Sherwood | [[Bibliography#WibergP_2008a | Wiberg and Sherwood (2008)]] reported on the speed and accuracy of several explicit and iterative methods for approximating $kh$ and determined that the Newton-Raphson method suggested by [[Bibliography#SoulsbyR_2005a | Soulsby (2005)]] is a good all-around method that is fast, accurate, and stable under all possible conditions. | ||
To use this: | To use this: | ||
Revision as of 20:25, 2 November 2008
<wikitex> A stable and precise method for calculating the product of wavenumber x depth $kh$ in the linear gravity-wave dispersion equation is implemented in the version of SSW_BBL.h located in Sherwood's branch. The dispersion equation is $\omega^2 = gk$ tanh($kh$), where $\omega$ is the angular frequency of the wave ($2pi/T$) where $T$ is period (s), $g$ is gravitational acceleration {\text{m}}^2 {\text{s}}^{-1}, $h$ is water depth (m), and $k$ is wavenumber ($2pi/\lambda$) 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 $kh$ and determined that the Newton-Raphson method suggested by Soulsby (2005) is a good all-around method that is fast, accurate, and stable under all possible conditions.
To use this:
#undef SSW_HUNT_KH
The alternative is a fifth-order polynomial approximation attributed to Hunt (1979) by Dean and Dalrymple (1991), p72. </wikitex>
