RPM2 - Revision history

Robertson at 11:52, 18 May 2016

2016-05-18T11:52:17Z

← Older revision		Revision as of 11:52, 18 May 2016
Line 1:		Line 1:
	<div class="title">Ripple Predictor Mark 2</div>		<div class="title">Ripple Predictor Mark 2</div>
	~~<wikitex>~~
	Time-dependent ripple geometry is implemented in subroutine RPM2 using the approach described in [[Bibliography#SoulsbyR2005a \| Soulsby and Whitehouse (2005)]]. Presently, this routine is in the version of SSW_BBL.h located in [https://www.myroms.org/projects/cstm/browser/branches/crs/cstm_trunk Sherwood's branch].		Time-dependent ripple geometry is implemented in subroutine RPM2 using the approach described in [[Bibliography#SoulsbyR2005a \| Soulsby and Whitehouse (2005)]]. Presently, this routine is in the version of SSW_BBL.h located in [https://www.myroms.org/projects/cstm/browser/branches/crs/cstm_trunk Sherwood's branch].

	Ripple geometry is described by ripple height $\eta$ (m), wavelength $\lambda$ (m), and orientation $\theta$ (positive clockwise from the $y$-axis). The orientation is defined as follows. Under unidirectional flow (no waves), ripple orientation is the same as the current direction. Under pure waves, ripple orientation is in the direction of wave propagation. For linear ripples (assumed here), ripple orientation is perpendicular to the ripple crest. In a slight modification of the original algorithm, the ripple orientation is actually stored as $x$- and $y$- components $\theta_x$ and $\theta_y$.		Ripple geometry is described by ripple height <math>\eta</math> (m), wavelength <math>\lambda</math> (m), and orientation <math>\theta</math> (positive clockwise from the <math>y</math>-axis). The orientation is defined as follows. Under unidirectional flow (no waves), ripple orientation is the same as the current direction. Under pure waves, ripple orientation is in the direction of wave propagation. For linear ripples (assumed here), ripple orientation is perpendicular to the ripple crest. In a slight modification of the original algorithm, the ripple orientation is actually stored as <math>x</math>- and <math>y</math>- components <math>\theta_x</math> and <math>\theta_y</math>.

	The [[Bibliography#SoulsbyR2005a \| Soulsby and Whitehouse (2005)]] approach is to calculate equilibrium ripple geometry under existing conditions, and then nudge the existing ripple geometry toward equilibrium at a rate that depends on sediment-transport conditions. Ripples remain unchanged if the transport threshold is not exceeded. The formula for updating ripple height is as follows.		The [[Bibliography#SoulsbyR2005a \| Soulsby and Whitehouse (2005)]] approach is to calculate equilibrium ripple geometry under existing conditions, and then nudge the existing ripple geometry toward equilibrium at a rate that depends on sediment-transport conditions. Ripples remain unchanged if the transport threshold is not exceeded. The formula for updating ripple height is as follows.
	$$
	\eta _{t} = \eta _{t-1} + (\eta _{eq} - \eta _{t-1} )(1 - \exp ( -\frac{\beta}{T_e} \Delta t) )		<math display="block">\eta _{t} = \eta _{t-1} + (\eta _{eq} - \eta _{t-1} )(1 - \exp ( -\frac{\beta}{T_e} \Delta t) )</math>
	$$
	where $\eta_t$ is the ripple height to be calculated for the present time, $\eta_{t-1}$ is ripple height at the previous step,		where <math>\eta_t</math> is the ripple height to be calculated for the present time, <math>\eta_{t-1}</math> is ripple height at the previous step,
	$\eta_{eq}$ is the equilibrium ripple height under present conditions,		<math>\eta_{eq}</math> is the equilibrium ripple height under present conditions, <math>\beta</math> is the evolution rate of ripple height under present conditions, <math>T_{e}</math> is the time scale for ripple evolution, and <math>\Delta t</math> is the time step. Similar equations are used to nudge <math>\lambda</math> and components of ripple direction <math>\theta_x</math> and <math>\theta_y</math> toward the equilibrium associated with present sediment-transport conditions.
	$\beta$ is the evolution rate of ripple height under present conditions, $T_{e}$ is the time scale for ripple evolution, and $\Delta t$ is the time step. Similar equations are used to nudge $\lambda$ and components of ripple direction $\theta_x$ and $\theta_y$ toward the equilibrium associated with present sediment-transport conditions.

	The Shields parameters for waves alone and for currents alone are calculated, and the equilibrium geometry and evolution rate is determined by the larger of the two.		The Shields parameters for waves alone and for currents alone are calculated, and the equilibrium geometry and evolution rate is determined by the larger of the two.
Line 17:		Line 16:

	One potential modification to this routine might be to calculate wash-out criteria and evolution rates based on the combined wave-current stress.		One potential modification to this routine might be to calculate wash-out criteria and evolution rates based on the combined wave-current stress.

	~~</wikitex>~~

Csherwood at 18:23, 2 November 2008

2008-11-02T18:23:16Z

← Older revision		Revision as of 18:23, 2 November 2008
Line 1:		Line 1:
	<div class="title">Ripple Predictor Mark 2</div>		<div class="title">Ripple Predictor Mark 2</div>
	<wikitex>		<wikitex>
	Time-dependent ripple geometry is implemented in subroutine RPM2 using the approach described in [[Bibliography#SoulsbyR2005a \| Soulsby and Whitehouse (2005)]].		Time-dependent ripple geometry is implemented in subroutine RPM2 using the approach described in [[Bibliography#SoulsbyR2005a \| Soulsby and Whitehouse (2005)]]. Presently, this routine is in the version of SSW_BBL.h located in [https://www.myroms.org/projects/cstm/browser/branches/crs/cstm_trunk Sherwood's branch].

	Ripple geometry is described by ripple height $\eta$ (m), wavelength $\lambda$ (m), and orientation $\theta$ (positive clockwise from the $y$-axis). The orientation is defined as follows. Under unidirectional flow (no waves), ripple orientation is the same as the current direction. Under pure waves, ripple orientation is in the direction of wave propagation. For linear ripples (assumed here), ripple orientation is perpendicular to the ripple crest. In a slight modification of the original algorithm, the ripple orientation is actually stored as $u$- and $v$- components $\theta_x$ and $\theta_y$.		Ripple geometry is described by ripple height $\eta$ (m), wavelength $\lambda$ (m), and orientation $\theta$ (positive clockwise from the $y$-axis). The orientation is defined as follows. Under unidirectional flow (no waves), ripple orientation is the same as the current direction. Under pure waves, ripple orientation is in the direction of wave propagation. For linear ripples (assumed here), ripple orientation is perpendicular to the ripple crest. In a slight modification of the original algorithm, the ripple orientation is actually stored as $x$- and $y$- components $\theta_x$ and $\theta_y$.

	The [[Bibliography#SoulsbyR2005a \| Soulsby and Whitehouse (2005)]] approach is to calculate equilibrium ripple geometry under existing conditions, and then nudge the existing ripple geometry toward equilibrium at a rate that depends on sediment-transport conditions. Ripples remain unchanged if the transport threshold is not exceeded. The formula for updating ripple height is as follows.		The [[Bibliography#SoulsbyR2005a \| Soulsby and Whitehouse (2005)]] approach is to calculate equilibrium ripple geometry under existing conditions, and then nudge the existing ripple geometry toward equilibrium at a rate that depends on sediment-transport conditions. Ripples remain unchanged if the transport threshold is not exceeded. The formula for updating ripple height is as follows.
Line 14:		Line 14:

	The Shields parameters for waves alone and for currents alone are calculated, and the equilibrium geometry and evolution rate is determined by the larger of the two.		The Shields parameters for waves alone and for currents alone are calculated, and the equilibrium geometry and evolution rate is determined by the larger of the two.


	One potential modification to this routine might be to calculate wash-out criteria and evolution rates based on the combined wave-current stress.		One potential modification to this routine might be to calculate wash-out criteria and evolution rates based on the combined wave-current stress.

	</wikitex>		</wikitex>

Csherwood at 18:02, 2 November 2008

2008-11-02T18:02:20Z

← Older revision		Revision as of 18:02, 2 November 2008
Line 3:		Line 3:
	Time-dependent ripple geometry is implemented in subroutine RPM2 using the approach described in [[Bibliography#SoulsbyR2005a \| Soulsby and Whitehouse (2005)]].		Time-dependent ripple geometry is implemented in subroutine RPM2 using the approach described in [[Bibliography#SoulsbyR2005a \| Soulsby and Whitehouse (2005)]].

	Ripple geometry is described by ripple height $\eta$ (m), wavelength $\lambda$ (m), and orientation $\theta$ (positive clockwise from the $y$-axis). The orientation is defined as follows. Under unidirectional flow (no waves), ripple orientation is the same as the current direction. Under pure waves, ripple orientation is in the direction of wave propagation. For linear ripples (assumed here), ripple orientation is perpendicular to the ripple crest. ~~The~~ ripple orientation is actually stored as $u$- and $v$- components.		Ripple geometry is described by ripple height $\eta$ (m), wavelength $\lambda$ (m), and orientation $\theta$ (positive clockwise from the $y$-axis). The orientation is defined as follows. Under unidirectional flow (no waves), ripple orientation is the same as the current direction. Under pure waves, ripple orientation is in the direction of wave propagation. For linear ripples (assumed here), ripple orientation is perpendicular to the ripple crest. In a slight modification of the original algorithm, the ripple orientation is actually stored as $u$- and $v$- components $\theta_x$ and $\theta_y$.

	The [[Bibliography#SoulsbyR2005a \| Soulsby and Whitehouse (2005)]] approach is to calculate equilibrium ripple geometry under existing conditions, and then nudge the existing ripple geometry toward equilibrium at a rate that depends on sediment-transport conditions. Ripples remain unchanged if the transport threshold is not exceeded. The formula for updating ripple height is as follows.		The [[Bibliography#SoulsbyR2005a \| Soulsby and Whitehouse (2005)]] approach is to calculate equilibrium ripple geometry under existing conditions, and then nudge the existing ripple geometry toward equilibrium at a rate that depends on sediment-transport conditions. Ripples remain unchanged if the transport threshold is not exceeded. The formula for updating ripple height is as follows.
Line 11:		Line 11:
	where $\eta_t$ is the ripple height to be calculated for the present time, $\eta_{t-1}$ is ripple height at the previous step,		where $\eta_t$ is the ripple height to be calculated for the present time, $\eta_{t-1}$ is ripple height at the previous step,
	$\eta_{eq}$ is the equilibrium ripple height under present conditions,		$\eta_{eq}$ is the equilibrium ripple height under present conditions,
	$\beta$ is the evolution rate of ripple height under present conditions, $T_{e}$ is the time scale for ripple evolution, and $\Delta t$ is the time step. Similar equations are used to nudge $\lambda$ and components of ripple direction$\theta_x$ and $\theta_y$ toward the equilibrium associated with present sediment-transport conditions.		$\beta$ is the evolution rate of ripple height under present conditions, $T_{e}$ is the time scale for ripple evolution, and $\Delta t$ is the time step. Similar equations are used to nudge $\lambda$ and components of ripple direction $\theta_x$ and $\theta_y$ toward the equilibrium associated with present sediment-transport conditions.

	The Shields parameters for waves alone and for currents alone are calculated, and the equilibrium geometry and evolution rate is determined by the larger of the two.		The Shields parameters for waves alone and for currents alone are calculated, and the equilibrium geometry and evolution rate is determined by the larger of the two.

Csherwood at 18:00, 2 November 2008

2008-11-02T18:00:08Z

← Older revision		Revision as of 18:00, 2 November 2008
Line 1:		Line 1:
	<div class="title">Ripple Predictor Mark 2</div>		<div class="title">Ripple Predictor Mark 2</div>
			<wikitex>
			Time-dependent ripple geometry is implemented in subroutine RPM2 using the approach described in [[Bibliography#SoulsbyR2005a \| Soulsby and Whitehouse (2005)]].

	~~Time-dependent ripple geometry is implemented in subroutine RPM2 using the approach described in [[Bibliography#SoulsbyR2005a \| Soulsby and Whitehouse (2005)]].~~
	~~<wikitex>~~
	Ripple geometry is described by ripple height $\eta$ (m), wavelength $\lambda$ (m), and orientation $\theta$ (positive clockwise from the $y$-axis). The orientation is defined as follows. Under unidirectional flow (no waves), ripple orientation is the same as the current direction. Under pure waves, ripple orientation is in the direction of wave propagation. For linear ripples (assumed here), ripple orientation is perpendicular to the ripple crest. The ripple orientation is actually stored as $u$- and $v$- components.		Ripple geometry is described by ripple height $\eta$ (m), wavelength $\lambda$ (m), and orientation $\theta$ (positive clockwise from the $y$-axis). The orientation is defined as follows. Under unidirectional flow (no waves), ripple orientation is the same as the current direction. Under pure waves, ripple orientation is in the direction of wave propagation. For linear ripples (assumed here), ripple orientation is perpendicular to the ripple crest. The ripple orientation is actually stored as $u$- and $v$- components.

Line 11:		Line 11:
	where $\eta_t$ is the ripple height to be calculated for the present time, $\eta_{t-1}$ is ripple height at the previous step,		where $\eta_t$ is the ripple height to be calculated for the present time, $\eta_{t-1}$ is ripple height at the previous step,
	$\eta_{eq}$ is the equilibrium ripple height under present conditions,		$\eta_{eq}$ is the equilibrium ripple height under present conditions,
	$\beta$ is the evolution rate of ripple height under present conditions, $\T_{ev}$ is the time scale for ripple evolution, and $\Delta t$ is the time step. Similar equations are used to nudge $\lambda$ and components of ripple direction$\theta_x$ and $\theta_y$ toward the equilibrium associated with present sediment-transport conditions.		$\beta$ is the evolution rate of ripple height under present conditions, $T_{e}$ is the time scale for ripple evolution, and $\Delta t$ is the time step. Similar equations are used to nudge $\lambda$ and components of ripple direction$\theta_x$ and $\theta_y$ toward the equilibrium associated with present sediment-transport conditions.

	The Shields parameters for waves alone and for currents alone are calculated, and the equilibrium geometry and evolution rate is determined by the larger of the two.		The Shields parameters for waves alone and for currents alone are calculated, and the equilibrium geometry and evolution rate is determined by the larger of the two.

Csherwood at 17:58, 2 November 2008

2008-11-02T17:58:55Z

← Older revision		Revision as of 17:58, 2 November 2008
Line 3:		Line 3:
	Time-dependent ripple geometry is implemented in subroutine RPM2 using the approach described in [[Bibliography#SoulsbyR2005a \| Soulsby and Whitehouse (2005)]].		Time-dependent ripple geometry is implemented in subroutine RPM2 using the approach described in [[Bibliography#SoulsbyR2005a \| Soulsby and Whitehouse (2005)]].
	<wikitex>		<wikitex>
	Ripple geometry is described by ripple height $\eta$ (m), wavelength $\lambda$ (m), and orientation $\theta$ (positive clockwise from the $y$-axis). The orientation is defined ~~by the direction of horizontal momentum flux in the bottom boundary layer~~. ~~In other words, under~~ unidirectional flow (no waves), ripple orientation is the current direction~~, and under~~ pure waves, ripple orientation is in the direction of wave propagation. ~~In general~~, ripple orientation is perpendicular to the ripple crest. The ripple orientation is actually stored as $u$- and $v$- components.		Ripple geometry is described by ripple height $\eta$ (m), wavelength $\lambda$ (m), and orientation $\theta$ (positive clockwise from the $y$-axis). The orientation is defined as follows. Under unidirectional flow (no waves), ripple orientation is the same as the current direction. Under pure waves, ripple orientation is in the direction of wave propagation. For linear ripples (assumed here), ripple orientation is perpendicular to the ripple crest. The ripple orientation is actually stored as $u$- and $v$- components.

			The [[Bibliography#SoulsbyR2005a \| Soulsby and Whitehouse (2005)]] approach is to calculate equilibrium ripple geometry under existing conditions, and then nudge the existing ripple geometry toward equilibrium at a rate that depends on sediment-transport conditions. Ripples remain unchanged if the transport threshold is not exceeded. The formula for updating ripple height is as follows.
	$$		$$
	\eta _{t ~~+ 1~~} = \eta _t + (\eta _{eq} - \eta _t )(1 - \exp ( - b\Delta t))		\eta _{t} = \eta _{t-1} + (\eta _{eq} - \eta _{t-1} )(1 - \exp ( -\frac{\beta}{T_e} \Delta t) )
	$$		$$
			where $\eta_t$ is the ripple height to be calculated for the present time, $\eta_{t-1}$ is ripple height at the previous step,
			$\eta_{eq}$ is the equilibrium ripple height under present conditions,
			$\beta$ is the evolution rate of ripple height under present conditions, $\T_{ev}$ is the time scale for ripple evolution, and $\Delta t$ is the time step. Similar equations are used to nudge $\lambda$ and components of ripple direction$\theta_x$ and $\theta_y$ toward the equilibrium associated with present sediment-transport conditions.

			The Shields parameters for waves alone and for currents alone are calculated, and the equilibrium geometry and evolution rate is determined by the larger of the two.

			One potential modification to this routine might be to calculate wash-out criteria and evolution rates based on the combined wave-current stress.

	</wikitex>		</wikitex>

Csherwood at 17:10, 2 November 2008

2008-11-02T17:10:51Z

← Older revision		Revision as of 17:10, 2 November 2008
Line 4:		Line 4:
	<wikitex>		<wikitex>
	Ripple geometry is described by ripple height $\eta$ (m), wavelength $\lambda$ (m), and orientation $\theta$ (positive clockwise from the $y$-axis). The orientation is defined by the direction of horizontal momentum flux in the bottom boundary layer. In other words, under unidirectional flow (no waves), ripple orientation is the current direction, and under pure waves, ripple orientation is in the direction of wave propagation. In general, ripple orientation is perpendicular to the ripple crest. The ripple orientation is actually stored as $u$- and $v$- components.		Ripple geometry is described by ripple height $\eta$ (m), wavelength $\lambda$ (m), and orientation $\theta$ (positive clockwise from the $y$-axis). The orientation is defined by the direction of horizontal momentum flux in the bottom boundary layer. In other words, under unidirectional flow (no waves), ripple orientation is the current direction, and under pure waves, ripple orientation is in the direction of wave propagation. In general, ripple orientation is perpendicular to the ripple crest. The ripple orientation is actually stored as $u$- and $v$- components.

			$$
			\eta _{t + 1} = \eta _t + (\eta _{eq} - \eta _t )(1 - \exp ( - b\Delta t))
			$$


	</wikitex>		</wikitex>

Csherwood at 16:57, 2 November 2008

2008-11-02T16:57:01Z

← Older revision		Revision as of 16:57, 2 November 2008
Line 1:		Line 1:
	<div class="title">Ripple Predictor Mark 2</div>		<div class="title">Ripple Predictor Mark 2</div>

	Time-dependent ripple geometry is implemented in subroutine RPM2 using the approach described in Soulsby and Whitehouse (2005).		Time-dependent ripple geometry is implemented in subroutine RPM2 using the approach described in [[Bibliography#SoulsbyR2005a \| Soulsby and Whitehouse (2005)]].
	<wikitex>		<wikitex>
	Ripple geometry is described by ripple height $\eta$ (m), wavelength $\lambda$ (m), and orientation $\theta$ (positive clockwise from the $y$-axis). The orientation is defined by the direction of horizontal momentum flux in the bottom boundary layer. In other words, under unidirectional flow (no waves), ripple orientation is the current direction, and under pure waves, ripple orientation is in the direction of wave ~~propogation~~. In general, ripple orientation is perpendicular to the ripple crest. The ripple orientation is actually stored as $u$- and $v$- components.		Ripple geometry is described by ripple height $\eta$ (m), wavelength $\lambda$ (m), and orientation $\theta$ (positive clockwise from the $y$-axis). The orientation is defined by the direction of horizontal momentum flux in the bottom boundary layer. In other words, under unidirectional flow (no waves), ripple orientation is the current direction, and under pure waves, ripple orientation is in the direction of wave propagation. In general, ripple orientation is perpendicular to the ripple crest. The ripple orientation is actually stored as $u$- and $v$- components.

	</wikitex>		</wikitex>

Csherwood: New page:
Ripple Predictor Mark 2
Time-dependent ripple geometry is implemented in subroutine RPM2 using the approach described in Soulsby and Whitehouse (2005). ...

2008-11-02T16:45:39Z

New page: <div class="title">Ripple Predictor Mark 2</div> Time-dependent ripple geometry is implemented in subroutine RPM2 using the approach described in Soulsby and Whitehouse (2005). <wikitex> ...

New page

<div class="title">Ripple Predictor Mark 2</div>

Time-dependent ripple geometry is implemented in subroutine RPM2 using the approach described in Soulsby and Whitehouse (2005).
<wikitex>
Ripple geometry is described by ripple height $\eta$ (m), wavelength $\lambda$ (m), and orientation $\theta$ (positive clockwise from the $y$-axis). The orientation is defined by the direction of horizontal momentum flux in the bottom boundary layer. In other words, under unidirectional flow (no waves), ripple orientation is the current direction, and under pure waves, ripple orientation is in the direction of wave propogation. In general, ripple orientation is perpendicular to the ripple crest. The ripple orientation is actually stored as $u$- and $v$- components.

</wikitex>