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Jason Wang July 20, 1999 22:41

2-D problem simple?
Hi, every one! I would like to know if some one try to establish the real 2-d turbulance model for 2-d depth averaged hydraudynamic models, I fact, I established a model, but I am not very sure of it. If some one has done this, could you discuss this with me? sinserely yours Jason Wang

Patrick Godon July 21, 1999 10:24

Re: 2-D problem simple?
What is the 2D depth averaged model? Is it a sort of shallow water approximation, or a kind of 2D compressible? Integrated in the vertical direction? What is the geometry of the problem? I work on some 2D turbulent flows, but I am not sure what you mean. Give us some more details, thanks.


Jason Wang July 22, 1999 20:14

Re: 2-D problem simple?
Dear Patrick, I mean the depth averaged hydraudynamic models closed with 2-d depth averaged k-e or other turbulence models. I want to know the form of all the equations. Colud you tell me some of them? Thank you very much!

Patrick Godon July 23, 1999 09:07

Re: 2-D problem simple?
there are two things that you are mentioning:

-1) depth average, two-dimensional (2D). You take 3D equations (say in Cartesian system, x,y, and z) and then you want to get rid of z. You average over z and get only 2D equations in (x,y). There are several ways of doing that. The one I know is as follow:

take for example the density rho(x,y,z,t), then you define

sigma(x,y,t) = integral(rho)dz from z=H1 to z=H2 (H1 and H2 are the boundaries in the z dimension). Then you define a new density (say rhonew) as:

rhonew (x,y,t) = sigma(x,y,t)/(H2-H1)

You actually need to integrate all the equations and then divide them by (H2-H1) and then replace sigam by rhonew as given above.

-2) The other thing you mentioned is modeling turbulence. I am modeling the turbulence by direct simulations, using a high order accuracy method. I am not using any k-e model. Depending on what is the problem you are modeling there are different ways of modeling the 2D turbulent flow. If the model in fact a Shallow Water Equation, you can just simulate the turbulence, by solving for the Potential flow. You can make sure you conserve vorticity, etc...

Since I don't know what is your physical problem that you are trying to model, it is very difficult to say anything about modeling. I can help you mainly if you are modeling a flow similar to an atmosphere (which is usually what people do on an hemisphere, 2d average turbulence). If your physical problem is much different than that, then you may want to post a message with a title like : k-e turbulent modeling of 2D average depth flow, etc.. .

I cannot tell you the form of the equations is I don't know if the flow is viscous, compressible, rotating. Also what forces are acting (gravity or other..)? What coordinate system are you interest in (spherical, cylindrical, polars, Cartesian)? Do you have an energy equation with source of energy and leaks? etc... In which dimension are you integrating?


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