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 Mike July 7, 2000 13:46

rotational and inviscid

Does anyone please tell me if inviscid flow can be rotational or not? What is the nature of rotational flow?

 Adrin Gharakhani July 7, 2000 14:09

Re: rotational and inviscid

Yes. Inviscid flow can be rotational. Rotational flow may be characterized by vorticity, which is the curl of velocity. A simple example is a vortex ring (like a cigarette smoke puff but without the diffusion process)

Check out fundamental fluid dynamic books.

It is important NOT to confuse potential flow with inviscid flow (which may be the source of your confusion). While potential flow satisfies the equation of motion of inviscid flow dynamics, the reverse is not necessarily true. That is, an inviscid flow is not necessarily potential (the former may contain vorticity, which induces rotational and not potential flow)

 Kalyan July 7, 2000 15:16

Re: rotational and inviscid

Inviscid flow can be rotational. As pointed out in an earlier reply, inviscid flows with vortices are good examples.

It might help to know that vorticity is conserved in inviscid flows, i.e., Euler equations are incapable of vorticity production. So in an inviscid flow computation, vorticity (in the form of point vortices or vortex blobs or continuous fields) can only come in as a part of the inflow and can not be produced or destroyed by the Euler equations.

Note also that the vortex rings can never be formed without viscosity though they can exist in a purely inviscid fluid.

 Adrin Gharakhani July 7, 2000 15:26

Re: rotational and inviscid

> Euler equations are incapable of vorticity production. So in an inviscid flow computation, vorticity (in the form of point vortices or vortex blobs or continuous fields) can only come in as a part of the inflow and can not be produced or destroyed by the Euler equations.

This is true _only_ for the incompressible (and constant density) case. Example: baroclinic vorticity generation (without solid boundaries).

 John C. Chien July 7, 2000 20:33

Re: rotational and inviscid

(1). It is not a good idea to mix these two terms at the same time. (2). At the begining, you have this equation called the Navier-Stokes equations, which represent the conservation of mass, momentum and energy. It contains viscosity terms. (3). Now, if you take the curl operation on the momentum equations, you will get this so-called "vorticity" equation. Remember that, the vorticity equation is derived from the momentum equation, so it has viscosity terms in it also. (4). If you set the viscosity terms to zero, you are going to get this mathematical equation, called "inviscid" equations, whether it is the inviscid momentum equations or the inviscid vorticity equation. (5). The inviscid momentum equation is generally called "Euler Equation" in contrast to the Navier-Stokes equations which has viscosity terms. (6). In the vorticity equation(derived from the Navier-Stokes equations), in addition to the viscosity terms, there are convection terms, stretching terms, production terms due to expansion, non-uniform density, and general body force. (7). So, even though you drop the viscosity terms, there are still many other terms in the vorticity equation, including the production terms. (8). So far, we have touched only the "inviscid" vs "viscous" forms of equation. (9). The rest of that is easy. The only time when the flow is "irrotational" is when the vorticity is everywhere zero. If there are still many terms in the vorticity equation (after dropping the viscosity terms), then you know that vorticity is normally non-zero. So, most of the time, it is rotational even without viscosity terms. (10). In old days, the inviscid equation was still very difficult to solve. So, the Euler equation was further simplified (second time) by setting the vorticity to zero (it is called "irrotational"). As a result, one can express the velocity in terms of the velocity potential and derive the so-called "potential flow"equation. (11). So, "potential flow" is "irrotational flow". And for the incompressible flow, the equation is the Laplace equation. The Laplace equation was the main focus in the 19th century. (12). Remember that, Euler equation and Laplace equation are simplified equations derived from the Navier-Stokes equations.(by setting the viscosity to zero, and then by setting the vorticity to zero, respectively)

 clifford bradford July 14, 2000 15:31

Re: rotational and inviscid

curved shocks can be a source of vorticity in an inviscid flow. i think there may be other potential sources but I can't remember what the others might be.

 Hua Zhou July 20, 2000 12:39

Re: rotational and inviscid

where the velocity varies, where there exist vortex; where the entropy increases, where creates vortex.

 Nick R April 20, 2011 02:25

Many thanks guys you explained things that confused me for awhile. Especial thanks to Adrian, John and Kalyan

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