Model help:Plume: Difference between revisions
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where longitudinal velocity (u) and lateral velocity component (v) are non-dimensionalized by the river mouth velocity, u0, and longitudinal distance, x, and lateral distance, y, are non-dimensioned by the river mouth width, b0. | |||
3) Non-conservative concentration along and surrounding the centerline position | 3) Non-conservative concentration along and surrounding the centerline position | ||
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Revision as of 11:20, 15 August 2014
Plume
Plume models a hypopycnal sediment plume draining from a river mouth into a lake or the ocean
Model introduction
Plume simulates the sediment transport and deposition of single-grain size sediment from a river mouth entering into a marine basin by creating a turbulent jet. The model calculates a steady-state hypopycnal plume as a result of river water and sediment discharge based on simplified advection-diffusion equations. The model allows for plume deflection due to systematic coastal currents or Coriolis force
Model parameters
Uses ports
This will be something that the CSDMS facility will add
Provides ports
This will be something that the CSDMS facility will add
Main equations
- River plumes
1) Advection-diffusion equation
[math]\displaystyle{ {\frac{\partial u I}{\partial x}} + {\frac{\partial v I}{\partial y}} + \lambda I = {\frac{\partial}{\partial y}} \left ( K {\frac{\partial I}{\partial y}}\right ) + {\frac{\partial}{\partial x}} \left (K {\frac{\partial I}{\partial x}}\right ) }[/math]
where x is the longitudinal direction (m), y is the lateral direction (m), u is longitudinal velocity (m/sec), v is lateral velocity (m/sec), I is the sediment “inventory” or mass per unit area of the plume (kg/m2), λ is the first order removal rate constant (sec−1) for the grain size in question, and K is the sediment diffusivity due to turbulence (m2/sec).
2) Plume's centerline
[math]\displaystyle{ {\frac{x}{b_{0}}}=1.53 + 0.90 \left ({\frac{u_{0}}{v_{0}}}\right ) \left ({\frac{y}{b_{0}}}\right )^\left (0.37\right ) }[/math]
where longitudinal velocity (u) and lateral velocity component (v) are non-dimensionalized by the river mouth velocity, u0, and longitudinal distance, x, and lateral distance, y, are non-dimensioned by the river mouth width, b0.
3) Non-conservative concentration along and surrounding the centerline position
[math]\displaystyle{ C\left (x,y\right ) = C_{0}exp\left (-\lambda t \right ) \sqrt{{\frac{b_{0}}{\sqrt{\pi}C_{1} x}}} exp [-\left ({\frac{y}{\sqrt{2} C_{1} x}}\right )^2] }[/math]
[math]\displaystyle{ t\left (x,y\right ) = {\frac{u_{0} + u_{c}\left (x\right ) + 7u\left (x,y\right )}{9}} }[/math] (10)
[math]\displaystyle{ u_{c}\left (x\right ) = u_{0} \sqrt{{\frac{b_{0}}{\sqrt{\pi} C_{1} x}}} }[/math] (11)
[math]\displaystyle{ u\left (x,y\right ) = u_{0} \sqrt{{\frac{b_{0}}{\sqrt{\pi} C_{1} x }}} exp [-\left ({\frac{y}{\sqrt{2} C_{1} x}}\right )^2] }[/math] (12)
Notes
Any notes, comments, you want to share with the user
Numerical scheme
Examples
An example run with input parameters, BLD files, as well as a figure / movie of the output
Follow the next steps to include images / movies of simulations:
- Upload file: http://csdms.colorado.edu/wiki/Special:Upload
- Create link to the file on your page: [[Image:<file name>]].
See also: Help:Images or Help:Movies
Developer(s)
Name of the module developer(s)
References
Key papers
Links
Any link, eg. to the model questionnaire, etc.