# Model help:Plume

## 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]

[math]\displaystyle{ u_{c}\left (x\right ) = u_{0} \sqrt{{\frac{b_{0}}{\sqrt{\pi} C_{1} x}}} }[/math]

[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]

where C1=0.109, from Albertson et al., 1950.

## Notes

Any notes, comments, you want to share with the user

There is an example of visualization of Plume output with Matlab described under the Model Questionair

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: https://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)

James Syvitski, Eric Hutton

## References

- Hutton and Syvitski, 2008. Sedflux-2.0: An advanced process-response model that generates three-dimensional stratigraphy. Computers and Geosciences, v. 34. doi:10.1016/j.cageo.2008.02.013
- Syvitski et al., 1998. PLUME1.1: Deposition of sediment from a fluvial plume (doi:10.1016/S0098-3004(97)00084-8
- Peckham, S.D., 2008. A new method for estimating suspended sediment concentrations and deposition rates from satellite imagery based on the physics of plumes. Computer & Geosciences, 34, 1198-1222. doi:10.1016/j.cageo.2008.02.009

## Links

Any link, eg. to the model questionnaire, etc.