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# vortex particle simulation

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Can anyone give me an idea on how to make a vortex particle system?(e.g. a tornado)I''m interested in the physics behind the vortex(the particle movement in a vortex).

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if you want to do a vortex particle system, and just want to try it a simple way, without doing fluid dynamics, just do a standard particle cloud, with an attractor force at the center. Add the Coriolis force (google that), some fiction, and you should see a vortex like structure.
If you want to have a real vortex, as in water goind down the drain, it''s going to be much more complicated, since you will have to implement a Nvier-Stokes eq solver/simulator, plus, since the Coriolis force is quite weak in reality, you will need a good simulation precision.

An intermediated way would be to produce a smooth density function based on your particle positions, and deduce from its gradient a repulsive force (ie: the particles don''t want to pack close together, but the attractive force wants to pack the together). This way you''ll have a vortex-like jello.

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There is a way to simulate the concentric flow of air around a core axis that is physically based yet vastly simpler than a full CFD simulation. You can do this with what is called a potential vortex. It is based on potential flow theory, e.g., is based on a solution to the incompressible, inviscid, irrotational, linearized potential flow equations, which are a formalized simplification of the full Navier-Stokes equations.

Here is how to do it:

1) Define a vortex "circulation" term as a function of height, z, above the ground. You would want a larger circulation at z = 0, and a smaller circulation at altitude. You can experiment with different variations until you get something that looks good. You might start out with a linear function:

Circ(z) = max(1000.0 - (1.0 * z), 0.0)

If z is in meters, this would define a tornado that decays to zero strength at 1000 meters in the air

This is a bit of a guess just to get it to look good.

2) Define a tornado centerline, which just defines the shape of the core of the tornado. You can start with a straight vertical line, but of course real tornadoes don''t always have a perfectly vertical centerline.

As above, this is an approximation just for looks.

Vortex_Core(z) = location of the vortex core at altitude z.

3) The speed of the air at any point, e.g., the speed of any particle in space, due to the vortex, is a function of the altitude of the point (its z value) and its position relative to the centerline of the tornado at that point, the core of the potential vortex. Here is the formula for air velocity at any point:

speed(x, y, z) = Circ(z) / (2 * PI * r_xy)

where r_xy is the distance from the point to the vortex core, e.g.:

r_xy = sqrt((x - Vortex_Core(z).x)2 +            (y - Vortex_Core(z).y)2))

That is the potential vortex equation for velocity.

The velocity associated with that speed lies in the plane parallel to the xy plane and passing through the z value of the point and is perpendicular to the line from the vortex core to the point.

4) The radial distance from the particle to the vortex core will remain *roughly* constant, and you can choose this radial distance to be, say, 1/Circ(z).

Now, that won''t get you a truly physically-realistic tornado. The potential vortex equation is really correct only for purely 2D, inviscid, irrotational, incompressible flow. But you may very well be surprised at how good it can look with the proper guestimated function for circulation and centerline shape.

Graham Rhodes
Principal Scientist
Applied Research Associates, Inc.

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Thanks guys. I think that this will do the trick.

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[quote name='grhodes_at_work' timestamp='1079634329' post='2378794']
There is a way to simulate the concentric flow of air around a core axis that is physically based yet vastly simpler than a full CFD simulation. You can do this with what is called a potential vortex. It is based on potential flow theory, e.g., is based on a solution to the incompressible, inviscid, irrotational, linearized potential flow equations, which are a formalized simplification of the full Navier-Stokes equations.

Here is how to do it:

1) Define a vortex "circulation" term as a function of height, z, above the ground. You would want a larger circulation at z = 0, and a smaller circulation at altitude. You can experiment with different variations until you get something that looks good. You might start out with a linear function:

Circ(z) = max(1000.0 - (1.0 * z), 0.0)

If z is in meters, this would define a tornado that decays to zero strength at 1000 meters in the air

This is a bit of a guess just to get it to look good.

2) Define a tornado centerline, which just defines the shape of the core of the tornado. You can start with a straight vertical line, but of course real tornadoes don''t always have a perfectly vertical centerline.

As above, this is an approximation just for looks.

Vortex_Core(z) = location of the vortex core at altitude z.

3) The speed of the air at any point, e.g., the speed of any particle in space, due to the vortex, is a function of the altitude of the point (its z value) and its position relative to the centerline of the tornado at that point, the core of the potential vortex. Here is the formula for air velocity at any point:

speed(x, y, z) = Circ(z) / (2 * PI * r_xy)

where r_xy is the distance from the point to the vortex core, e.g.:

r_xy = sqrt((x - Vortex_Core(z).x)[sup]2[/sup] +
(y - Vortex_Core(z).y)[sup]2[/sup]))

That is the potential vortex equation for velocity.

The velocity associated with that speed lies in the plane parallel to the xy plane and passing through the z value of the point and is perpendicular to the line from the vortex core to the point.

4) The radial distance from the particle to the vortex core will remain *roughly* constant, and you can choose this radial distance to be, say, 1/Circ(z).

Now, that won''t get you a truly physically-realistic tornado. The potential vortex equation is really correct only for purely 2D, inviscid, irrotational, incompressible flow. But you may very well be surprised at how good it can look with the proper guestimated function for circulation and centerline shape.

Graham Rhodes
Principal Scientist
Applied Research Associates, Inc.
[/quote]

hi Rhodes,
i jus went thru ur method ..looks cool..
i m also doing a project on tornado with particles...(not fluids)
can u jus explain me in detail abt ur ur method......

kindly guide me coz i couldnt understand circulation term....

cheers
ganesh l

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