Robertson at 15:47, 17 May 2016

2016-05-17T15:47:08Z

← Older revision		Revision as of 15:47, 17 May 2016
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	:<math>Eros_{rate}</math> = erosion rate, kg/m²/s, set at <math>5.0e^{-4}</math>		:<math>Eros_{rate}</math> = erosion rate, kg/m²/s, set at <math>5.0e^{-4}</math>
	:<math>1-porosity = 0.6</math>		:<math>1-porosity = 0.6</math>
	:<math>\tau_{w}=</math> shear stress exerted by the water <math>= \rho~ C_{d}~ V~ \left\| V \right\|</math>		:<math>\tau_{w}=</math> shear stress exerted by the water <math>= \rho~ C_{D}~ V~ \left\| V \right\|</math>
	:<math>\rho =</math> fluid density, kg/m³, = 998 kg/m³		:<math>\rho =</math> fluid density, kg/m³, = 998 kg/m³
	:<math>V =</math> magnitude of velocity <math>= \sqrt{u^{2} + v^{2}}</math>, m/s		:<math>V =</math> magnitude of velocity <math>= \sqrt{u^{2} + v^{2}}</math>, m/s

Robertson at 15:45, 17 May 2016

2016-05-17T15:45:51Z

← Older revision		Revision as of 15:45, 17 May 2016
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	==Forcing==		==Forcing==

	Inflow boundary condition only ~~<br>~~		Inflow boundary condition only
	<~~wikitex~~>~~No rotation $~~(\~~textcolor~~{blue}{f}~=~0)$</~~wikitex><br~~>		:No rotation <math>(\color{blue}{f}\color{black}{~=~0)}</math>
	No wind~~<br>~~		:No wind
	No heating/cooling~~<br>~~		:No heating/cooling

	==Boundary Conditions==		==Boundary Conditions==

	~~<wikitex>~~Inflow maintained as steady flow, depth-mean flow $\~~textcolor~~{blue}{<u>}~ =~ 1~ m/s$ <br>		Inflow maintained as steady flow, depth-mean flow <math>\color{blue}{<u>}\color{black}{~ =~ 1~ m/s}</math><br>
	Outflow = open <br>		Outflow = open <br>
	Sides = walls with no fluxes, no friction <br>		Sides = walls with no fluxes, no friction <br>
	Bottom roughness $\~~textcolor~~{blue}{Z_{0}}~=~ 0.005$</~~wikitex~~><br>		Bottom roughness <math>\color{blue}{Z_{0}}\color{black}{~=~ 0.005}</math><br>
	Sediment flux calculated by model <br>		Sediment flux calculated by model <br>
	Surface = free surface, no fluxes <br>		Surface = free surface, no fluxes <br>
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	Channel initial conditions:		Channel initial conditions:
	The test channel was modeled by establishing a grid parameterized with dx = 100 m , dy=100 m, f0 = 0, and h = 10 m (flat bottom). Initial conditions set a vertical logarithmic velocity profile for u (not required but provided reasonable starting values), v = 0, zeta (water surface height) = 0, SSC in the water column = 0, and bed thickness = 1 m (to provide unlimited supply). The model was forced with 2 methods :		The test channel was modeled by establishing a grid parameterized with dx = 100 m , dy=100 m, <math>f_{0} = 0</math>, and h = 10 m (flat bottom). Initial conditions set a vertical logarithmic velocity profile for <math>u</math> (not required but provided reasonable starting values), <math>v = 0</math>, <math>zeta</math> (water surface height)<math> = 0</math>, SSC in the water column = 0, and bed thickness = 1 m (to provide unlimited supply). The model was forced with 2 methods :

	—Simulation 1: Imposing a constant flow of 10 m³/s/m of width. This simulation allowed that water surface elevation to vary. Radiation boundary conditions were imposed for the water level along with a constant flow imposed by a depth averaged velocity ubar = 1.0 m/s at the upstream and downstream boundaries.		—Simulation 1: Imposing a constant flow of 10 m³/s/m of width. This simulation allowed that water surface elevation to vary. Radiation boundary conditions were imposed for the water level along with a constant flow imposed by a depth averaged velocity <math>ubar = 1.0 m/s</math> at the upstream and downstream boundaries.

	—Simulation 2: Imposing a constant bed slope and water surface slope of 4x10-5 m/m. This simulation forced the water surface elevation and hence the bottom stress. Radiation boundary conditions were imposed for the depth-averaged velocity along with a clamped water surface condition at each boundary. The bed slope of 4x10-5 was selected to produce a depth-averaged velocity of 1m/s (similar to simulation 1) with a Z0 = 0.005.		—Simulation 2: Imposing a constant bed slope and water surface slope of 4x10-5 m/m. This simulation forced the water surface elevation and hence the bottom stress. Radiation boundary conditions were imposed for the depth-averaged velocity along with a clamped water surface condition at each boundary. The bed slope of 4x10-5 was selected to produce a depth-averaged velocity of 1m/s (similar to simulation 1) with a <math>\color{blue}{Z_{0}}\color{black}{~=~ 0.005}</math>.

	For both simulations, vertical mixing was parameterized using six different closure schemes: MY25, KKLpara, KKLmin, KE, KW88, and ANA		For both simulations, vertical mixing was parameterized using six different closure schemes: MY25, KKLpara, KKLmin, KE, KW88, and ANA
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	ANA = analytical expression of a parabolic vertical eddy diffusivity and viscosity profile:		ANA = analytical expression of a parabolic vertical eddy diffusivity and viscosity profile:

	Kz = ~~k u~~* z (1 - z/D)		<math display="block">K_{z} = \kappa~ u_{*}~ z~ \left( 1 - {z \over D} \right)</math>
	~~where Kz = vertical eddy viscosity, m²~~/s
	~~z = height above the bottom, m~~
	~~D = depth of flow, m, = 10 m~~
	~~and u* = friction velocity which was calculated according to the logarithmic profile.~~

	~~[[Image~~:~~Equation_ustar~~.~~gif\|center]]~~		where:
			:<math>K_{z}</math> = vertical eddy viscosity, m²/s<br>
			:<math>z</math> = height above the bottom, m<br>
			:<math>D</math> = depth of flow, m, = 10 m<br>
			:<math>u_{*}</math> = friction velocity which was calculated according to the logarithmic profile.

	where k = 0.41 ~~and~~ u = 1.0 m/s.		<math display="block">u_{*} = {\kappa~ \overline{u} \over {ln \left( {D \over z_{0}}\right) - 1 + {z_{0} \over D}}} = 0.061~ m/s</math>


			where:
			:<math>\kappa = 0.41</math>
			:<math>\overline{u} = 1.0~ m/s</math>.

	Only suspended-sediment transport was modeled. At the center of each bottom level horizontal grid cell, the bed shear stress was estimated and used to calculate sediment resuspension using the relation:		Only suspended-sediment transport was modeled. At the center of each bottom level horizontal grid cell, the bed shear stress was estimated and used to calculate sediment resuspension using the relation:

	~~[[Image~~:~~Jw_eq_1_E~~.~~gif~~\|~~center]]~~		<math display="block">E = Eros_{rate} * (1 - porosity) * \left( { \tau_{w} - \tau_{c} \over \tau_{c}} \right)</math>

			where:
			:<math>E</math> = erosive flux, kg/m²/s
			:<math>Eros_{rate}</math> = erosion rate, kg/m²/s, set at <math>5.0e^{-4}</math>
			:<math>1-porosity = 0.6</math>
			:<math>\tau_{w}=</math> shear stress exerted by the water <math>= \rho~ C_{d}~ V~ \left\| V \right\|</math>
			:<math>\rho =</math> fluid density, kg/m³, = 998 kg/m³
			:<math>V =</math> magnitude of velocity <math>= \sqrt{u^{2} + v^{2}}</math>, m/s
			:<math>\tau_{c} =</math> critical shear stress for erosion, = 0.05 N/m²

	~~where E = erosive flux, kg/m²/s~~		The erosive flux was multiplied the bed area and by <math>dt</math> for each grid to provide a mass of sediment (kg) that would be exchanged between the bed and the water column. Deposition was calculated from the bottom boundary condition of the settling velocity algorithm. The depositional flux was divided by the grid horizontal area to yield a mass flux in kg. The erosive flux and depositional fluxes were added at each time step to obtain a net mass transfer that was added/subtracted from the bed and added/subtracted to the bottom cell in the water column. Bed erosion was not limited because the initial depth was set at 1.0 m and the model was not run long enough to erode to this level.
	~~Eros_rate = erosion rate, kg/ m²/s, set at 5.0 e - 4~~
	~~por_1 = 1-porosity = 0.6~~
	~~τw = shear stress exerted by the water, = ρ Cd V \|V\|~~
	~~ρ= fluid density, kg/m³, = 998 kg/m³~~
	~~V = magnitude of velocity = sqrt(u² + v²), m/s~~
	~~τc = critical shear stress for erosion, = 0.05 N/m²~~
	The erosive flux was multiplied the bed area and by dt for each grid to provide a mass of sediment (kg) that would be exchanged between the bed and the water column. Deposition was calculated from the bottom boundary condition of the settling velocity algorithm. The depositional flux was divided by the grid horizontal area to yield a mass flux in kg. The erosive flux and depositional fluxes were added at each time step to obtain a net mass transfer that was added/subtracted from the bed and added/subtracted to the bottom cell in the water column. Bed erosion was not limited because the initial depth was set at 1.0 m and the model was not run long enough to erode to this level.

	==Analysis Data==		==Analysis Data==
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	==Physical Constants==		==Physical Constants==

	<~~wikitex~~>~~Gravitational acceleration $~~\~~textcolor~~{blue}{g}~=~ 9.81~ m/s^{2}$<br>		Gravitational acceleration <math>\color{blue}{g}\color{black}{~=~ 9.81~ m/s^{2}}</math><br>
	Von Karman's constant $\~~textcolor~~{blue}{\kappa}~=~ 0.41$<br>		Von Karman's constant <math>\color{blue}{\kappa}\color{black}{~=~ 0.41}</math><br>
	Water density $\~~textcolor~~{blue}{\rho_{w}}~=~ 998~ kg/m^{3}$<br>		Water density <math>\color{blue}{\rho_{w}}\color{black}{~=~ 998~ kg/m^{3}}</math><br>
	Dynamic viscosity (and minimum diffusivity) $\~~textcolor~~{blue}{\nu}~=~ 1e-6~ m^{2}/s$</~~wikitex><br~~>		Dynamic viscosity (and minimum diffusivity) <math>\color{blue}{\nu}\color{black}{~=~ 1e-6~ m^{2}/s}</math>

	{{note}}'''Note:''' If a model incorporates physical constants that differ from these, and/or automatically calculates some values specified here, please specify the values used.		{{note}}'''Note:''' If a model incorporates physical constants that differ from these, and/or automatically calculates some values specified here, please specify the values used.

Robertson at 16:02, 21 September 2010

2010-09-21T16:02:53Z

Show changes

Arango: New page:
Sediment Test Channel Case

2007-06-07T22:08:37Z

New page: <div class="title">Sediment Test Channel Case</div>

New page

<div class="title">Sediment Test Channel Case</div>

TEST CHAN CASE - Revision history

Robertson at 15:47, 17 May 2016

Robertson at 15:45, 17 May 2016

Robertson at 16:02, 21 September 2010

Arango: New page: Sediment Test Channel Case

Arango: New page:
Sediment Test Channel Case