Morgulis A.   Vladimirov V.   Govorukhin V.  

Dynamics of the flows through a finite channel with Yudovich's boundary conditions

Reporter: Morgulis A.

We address the flows of inviscid incompressible fluid in the finite channels subject to the following boundary conditions: the normal velocity is specified everywhere on the boundary and the vorticity is prescribed on the flow inlet. The boundary data are steady. Under such conditions the  fluxes of the energy and vorticity through the flow boundary are not equal to zero so that the inviscid fluid represents a non-conservative system. The communication is focused upon the dissipative phenomena in the dynamics of this system. In particular, we mark out the class of `dissipative' bc's for which the withdrawal of the flow vorticity and energy  dominates  the inflow of this quantities. Under dissipative bc's, we discover two qualitatively different patterns of the flow behaviour: some flows are able to wash out the excessive vorticity while others are  able to trap it.  The  flows of former kind evolve to the non-separated steady flow which is determined by the bc's completely. The flows of the latter kind  evolve to separated flows which may represent rather complex vortical configurations. These configurations  depend on the initial states of the flows  essentially. The non-dissipative bc's give rise to one more scenario. This is the onset of self-oscillations.

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