Mathematical Physics

    

The Reverse Side of Helmholtz Paradox: Flow with Zero Laplacian Generates a Constant Vortex

Authors: Sergey V. Ershkov

The reverse side of Helmholtz paradox is presented here. Helmholtz paradox itself had been formulated as follows: - in the ideal (non-viscid) newtonian fluids any vorticity should be stable (constant) during infinite time. It means that if vortex arise in non-viscid newtonian fluid, such a vortex should have the constant strength all the time. In our note to Helmholtz paradox, we proved that Vortex with constant angular velocity of rotation could be generated only by the flow with zero Laplacian (thus, such a flow is not viscid for the case of incompressible newtonian fluids). Thus, we could conclude in addition to Helmholtz paradox: not only any vortex should be constant in the ideal (non-viscid) newtonian fluids, but if vortex is constant it means that such a flow is proved to be ideal (unviscid) due to zero Laplacian.

Comments: 6 Pages. Keywords: Helmholtz paradox, constant vortex, incompressible ideal flow

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Submission history

[v1] 2013-11-25 14:36:42
[v2] 2013-11-26 08:50:02
[v3] 2013-11-27 01:35:23
[v4] 2013-11-28 14:20:49

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