SoulsbyKH - Revision history

Robertson at 11:58, 18 May 2016

2016-05-18T11:58:58Z

← Older revision		Revision as of 11:58, 18 May 2016
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	<div class="title">Methods for Calculating ''kh''</div>		<div class="title">Methods for Calculating ''kh''</div>
	~~<wikitex>~~The dispersion equation for surface gravity waves 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 (m2 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 \| 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.
			The dispersion equation for surface gravity waves is <math>\omega^2 = gk~ \text{tanh}(kh)</math>, where <math>\omega</math> is the angular frequency of the wave (<math>2\pi/T</math>) where <math>T</math> is period (s), <math>g</math> is gravitational acceleration (m2 s-1), <math>h</math> is water depth (m), and <math>k</math> is wavenumber (<math>2\pi/\lambda</math>) where <math>\lambda</math> is wavelength (m). <math>k</math> is difficult to calculate because it is implicit.[[Bibliography#WibergP_2008a \| Wiberg and Sherwood (2008)]] reported on the speed and accuracy of several explicit and iterative methods for approximating <math>kh</math>. Two good methods are implemented in ROMS/CSTMS.

	A fifth-order polynomial approximation attributed to Hunt (1979) by [[Bibliography#DeanR_1991a \| Dean and Dalrymple (1991), p72]] is used when SSW_HUNT_KH is defined, and the Newton-Raphson method suggested by [[Bibliography#SoulsbyR_2005a \| Soulsby (2005)]] is used when SSW_SOULSBY_KH is defined.		A fifth-order polynomial approximation attributed to Hunt (1979) by [[Bibliography#DeanR_1991a \| Dean and Dalrymple (1991), p72]] is used when SSW_HUNT_KH is defined, and the Newton-Raphson method suggested by [[Bibliography#SoulsbyR_2005a \| Soulsby (2005)]] is used when SSW_SOULSBY_KH is defined.

	{{warning}} '''Note:''' The Soulsby option and these two CPP defs are only implemented in the version of SSW_BBL.h located in [https://www.myroms.org/projects/cstm/browser/branches/crs/cstm_trunk Sherwood's branch]. Define one of these two options:		{{warning}} '''Note:''' The Soulsby option and these two CPP defs are only implemented in the version of SSW_BBL.h located in [https://www.myroms.org/projects/cstm/browser/branches/crs/cstm_trunk Sherwood's branch]. Define one of these two options:
	<div class="box">#define SSW_SOULSBY_KH<br />#undef SSW_HUNT_KH</div~~></wikitex~~>		<div class="box">#define SSW_SOULSBY_KH<br />#undef SSW_HUNT_KH</div>

Csherwood at 00:33, 4 November 2008

2008-11-04T00:33:51Z

← Older revision		Revision as of 00:33, 4 November 2008
Line 1:		Line 1:
	<div class="title">Methods for Calculating ''kh''</div>		<div class="title">Methods for Calculating ''kh''</div>
	<wikitex>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 (m2 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 \| 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.		<wikitex>The dispersion equation for surface gravity waves 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 (m2 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 \| 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 [[Bibliography#DeanR_1991a \| Dean and Dalrymple (1991), p72]] is used when SSW_HUNT_KH is defined, and the Newton-Raphson method suggested by [[Bibliography#SoulsbyR_2005a \| Soulsby (2005)]] is used when SSW_SOULSBY_KH is defined.		A fifth-order polynomial approximation attributed to Hunt (1979) by [[Bibliography#DeanR_1991a \| Dean and Dalrymple (1991), p72]] is used when SSW_HUNT_KH is defined, and the Newton-Raphson method suggested by [[Bibliography#SoulsbyR_2005a \| Soulsby (2005)]] is used when SSW_SOULSBY_KH is defined.

	{{warning}} '''Note:''' The Soulsby option and these two CPP defs are only implemented in the version of SSW_BBL.h located in [https://www.myroms.org/projects/cstm/browser/branches/crs/cstm_trunk Sherwood's branch]. ~~Only define~~ one of these two options:		{{warning}} '''Note:''' The Soulsby option and these two CPP defs are only implemented in the version of SSW_BBL.h located in [https://www.myroms.org/projects/cstm/browser/branches/crs/cstm_trunk Sherwood's branch]. Define one of these two options:
	<div class="box">#define SSW_SOULSBY_KH<br />#undef SSW_HUNT_KH</div></wikitex>		<div class="box">#define SSW_SOULSBY_KH<br />#undef SSW_HUNT_KH</div></wikitex>

Csherwood at 19:16, 3 November 2008

2008-11-03T19:16:31Z

← Older revision		Revision as of 19:16, 3 November 2008
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	<div class="title">~~Soulsby Method~~ for Calculating ''kh''</div>		<div class="title">Methods for Calculating ''kh''</div>
	<wikitex>		<wikitex>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 (m2 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 \| 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 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.
	[[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:~~		A fifth-order polynomial approximation attributed to Hunt (1979) by [[Bibliography#DeanR_1991a \| Dean and Dalrymple (1991), p72]] is used when SSW_HUNT_KH is defined, and the Newton-Raphson method suggested by [[Bibliography#SoulsbyR_2005a \| Soulsby (2005)]] is used when SSW_SOULSBY_KH is defined.
	~~<div class="box">#define SSW_SOULSBY_KH<br />#undef SSW_HUNT_KH</div>~~
	~~The alternative is a~~ fifth-order polynomial approximation attributed to Hunt (1979) by [[Bibliography#DeanR_1991a \| Dean and Dalrymple (1991), p72]].		{{warning}} '''Note:''' The Soulsby option and these two CPP defs are only implemented in the version of SSW_BBL.h located in [https://www.myroms.org/projects/cstm/browser/branches/crs/cstm_trunk Sherwood's branch]. Only define one of these two options:
	</wikitex>		<div class="box">#define SSW_SOULSBY_KH<br />#undef SSW_HUNT_KH</div></wikitex>

Csherwood at 20:25, 2 November 2008

2008-11-02T20:25:31Z

← Older revision		Revision as of 20:25, 2 November 2008
Line 3:		Line 3:
	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 ~~and Wiberg~~ (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.		[[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:

Csherwood at 20:15, 2 November 2008

2008-11-02T20:15:23Z

← Older revision		Revision as of 20:15, 2 November 2008
Line 1:		Line 1:
	<div class="title">Soulsby Method for Calculating ''kh''</div>		<div class="title">Soulsby Method for Calculating ''kh''</div>
	<wikitex>		<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 [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 and Wiberg (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.		[[Bibliography#WibergP_2008a \| Sherwood and Wiberg (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:

	<div class="box">#define SSW_SOULSBY_KH<br />#undef SSW_HUNT_KH</div>		<div class="box">#define SSW_SOULSBY_KH<br />#undef SSW_HUNT_KH</div>
			The alternative is a fifth-order polynomial approximation attributed to Hunt (1979) by [[Bibliography#DeanR_1991a \| Dean and Dalrymple (1991), p72]].
	The alternative is a fifth-order polynomial approximation		</wikitex>
	<\wikitex>

Csherwood: New page:
Soulsby Method for Calculating ''kh''
A stable and precise method for calculating the product of wavenumber x depth $KH$ in the linear gravity-wave dispe...

2008-11-02T19:43:03Z

New page: <div class="title">Soulsby Method for Calculating ''kh''</div> <wikitex> A stable and precise method for calculating the product of wavenumber x depth $KH$ in the linear gravity-wave dispe...

New page

<div class="title">Soulsby Method for Calculating ''kh''</div>
<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 [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.
[[Bibliography#WibergP_2008a | Sherwood and Wiberg (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:

<div class="box">#define SSW_SOULSBY_KH<br />#undef SSW_HUNT_KH</div>

The alternative is a fifth-order polynomial approximation
<\wikitex>