Helmholtz decomposition revisited: Vorticity generation and trailing edge condition. I. Incompressible flows. (English) Zbl 0625.76027
Exterior incompressible viscous and nonviscous flows are examined by means of the Helmholtz decomposition, with special emphasis on the issue of the boundary conditions for the vorticity. Using physical considerations, the author shows that vorticity is generated by the boundary condition on the normal component of the velocity, for both inviscid and viscous flows. In viscous flows, the vorticity is then diffused into the surroundings: this yields that the no-slip conditions are thus automatically satisfied (since the presence of a vortex layer on the surface is required to obtain a velocity slip at the boundary). This result is then used to show that in order for the solution to the Euler equations to be the limit of the solution to the Navier-Stokes equations, a trailing-edge condition (that the vortices be shed as soon as they are formed) must be satisfied. Many of the results follow by physical considerations, without a rigorous proof. The use of the results for a computational scheme is also discussed.
Reviewer: P.Secchi
MSC:
| 76B47 | Vortex flows for incompressible inviscid fluids |
Keywords:
Helmholtz decomposition; boundary conditions; no-slip conditions; vortex layer; Euler equations; Navier-Stokes equations; trailing-edge conditionReferences:
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