On the flow between a porous rotating disk and a plane

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Abstract
Axisymmetric flow of viscous incompressible fluid between a rotating porous disk and an impermeable fixed plane is investigated. It is shown that with injection and suction through a porous disk rotating with sufficiently large angular velocity there are many isolated steady self-similar solutions. In the case of suction through a fixed porous disk at a certain Reynolds number there exists bifurcation of the stable rotational regime of flow, implying a spontaneous break of the flow symmetry and an arbitrary rise of the fluid rotation within the framework of self-similarity. This unusual effect is discussed in detail, and the results of a relevant experiment are presented. Another unusual result is the existence of multicellular regimes consistent with suction, when the lift force acting on a rapidly rotating porous disk is anomalously large; in this case some of these regimes are stable relative to self-similar perturbations.With sufficiently strong suction and rotation the stationary solution with large lift becomes unstable and the regime of self-oscillations arises. Diagrams of the possible stationary flow regimes have been constructed, and the stable ones have been identified. At the limit of vanishing viscosity we find, in the case of the suction, non-classical boundary layers on the solid surfaces characterized by a finite jump of the normal component of the velocity and unlimited tangential components. In this limit, in the interior flow region the singular non-viscous solution with an infinite velocity of rotation arises, while all limited non-singular admissible non-viscous solutions are not stable.

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