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

Parameter	Description	Unit
First parameter	Average mass-concentration of suspended sediment	[kg/m3]
u₀	Flow velocity at the river mouth	[m/s]
b₀	Width at the river mouth	[m]
d₀	Depth at the river mouth	[m]
d₀	Angle of river mouth measured with respect to the coast normal	[degrees]
Lat	Latitude of river mouth location, affect the Coriolis Force	[degrees]
W	Width of the ocean/fjord, affects the spreading of the plume	[m]
L	Length of the ocean/fjord or lake	[m]

Parameter	Description	Unit
Rho-sediment	Saturated bulk density of sediment	[kg/m³]
Lambda	Removal rate of suspended sediment	[ 1/day]

Parameter	Description	Unit
Cs-ocean	Background sediment concentration of ocean	[kg/m³]
	Normalized width of coastal current	[-]
u2	alongshore velocity of the coastal current, can deflect the plume axis	[m/s]

Parameter	Description	Unit
-	Output interval (needs to be smaller than 1 to generate output, use 0.5)	[d]
File Format	netcdf or vtk choice, if file is switched on
deposition_rate file	if switched off, original csv files of plume will still be generated

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>]].

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.