Advection and diffusion in river network

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cyrilgarneau@gmail.com
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Joined: Tue Oct 18, 2011 12:28

Advection and diffusion in river network

Postby cyrilgarneau@gmail.com » Mon Sep 23, 2013 14:38

Dear all,

I am setting a tracer experiment (rhodamin B) in river and I want to set the diffusion to proper value. So, my question is: How is computed the diffusion?

More specifically, the wiki talks about molecular diffusivity and suggests a default value of 1e-8. I tried to reconstruct the diffusion computation from the source code and I find:
Flux = Flux_old + diffusivity * GRAD_Concentration * Vertical_Area

So, I cannot figure from which (partial differential) equation is the equation above.
But more importantly, is the molecular diffusion really important at the river scale? With the default value (DIFFUSIVITY : 1e-8), I computed the following ratio:
Diffusion / Advection
from the Advection_Diffusion subroutine in ModuleDrainageNetwork.f90 and it stays between 1e-26 and 1e-10, with an average around 1e-20. Since the transport of a property is computed from the sum (Diffusion + Advection), it means that the diffusion in river is technically unexistant, which sounds strange. This also means that to observe diffusion in my river, I would need to use a Diffusivity of at least 10 to 1e+10. I guess that there is someting wrong in my development, but I cannot figure what!

Can anyone help me?

Thank you,

Cyril

davidbrito
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Posts: 187
Joined: Thu Jan 01, 1970 00:00

Re: Advection and diffusion in river network

Postby davidbrito » Thu Oct 17, 2013 14:10

Hello Cyril,

The diffusion is from the property transport equation (d/dx (A.Diff.(dC/dx))). A is Area, Diff is diffusivity C is concentration. Hope that i did not got it wrong.
Concentrations are defined in center nodes and diffusion flux in the reaches (just like faces between nodes).
Diffusion flux through the faces (both upstream and downstream faces) is a gradient of property multiplied by diffusivity and area. With this descritized the gradient of property is concentration of node upstream and downstream divided by the length between nodes:

Code: Select all

GradProp    = (Property%ConcentrationOld (DownNodePos) - Property%ConcentrationOld (NodePos)) &
                                / DownReach%Length


And the flux has to be summed if the node has several downstream reaches:

Code: Select all

DownFlux    =  DownFlux + Property%Diffusivity * GradProp * DownReach%VerticalArea


And the differential term is a integration for all surfaces so needs to sum donwstream and upstream faces fluxes.



If the diffusivity that the user uses is mollecular diffusivity as you say 1e-8 (one moleccule path going from higher concentration to lower) than of course in a river where velocity is much important the diffusion term will be neglective! But if you were studying only a stretch with stading water than maybe dont.

What happens is that in modelling for diffusivity it goes not only the molecular one but also the processes not solved by average velocity.
Meaning that because velocity is not in reality the average in the entire section (there exist turbulence and vortices that mix properties) than a higher value is putted in diffusivity to take this is effect because the diffusion term what does is mix more in both upwind and downwind direction.

So if you want to mix more you have to increase the diffusivity. Maybe because your river has a lot of obstacles, curves... that increase mixing.


Best regards,
David


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