Flow of a vortical stream in the neighborhood of the critical point

A study was made of the axisymmetric flow of a viscous incompressible fluid in the neighborhood of the critical point of an obstacle when steady-state vortices oriented in the direction of the angular coordinate are introduced into the oncoming flow. A solution is presented of the equation for the transfer of a vortex in the case of an external flow containing a single largesize vortex in the low-frequency part of the spectrum. Using a finite integral Hankel transform, the problem is reduced to the solution of a system of ordinary differential equations. It is shown that a sufficiently large-size vortex can have a considerable effect on the structure of viscous flow near an obstacle.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 85–89, November–December, 1970.