Vortex structures in shear flows

Large-scale vortex structures in shear flows are investigated. An effective method of describing these objects, which makes it possible to go beyond the framework of weak nonlinearity, is proposed. This is especially important in investigating spatially isolated structures. Evolution-type equations describing the shape of the vortex structures are obtained and their steady-state solutions are examined. A detailed classification of the structures in two-dimensional and cylindrical channels is given. Attention is drawn to the qualitative similarity of some of these structures to the well-known structures in real turbulent flows (wall eddies, turbulent slugs). It is established that isolated vortex structures in a pipe whose radius is fairly large as compared with their transverse dimension have kinematic characteristics similar to those of Hill vortices. The prospects of the method are discussed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 65–75, March–April, 1989.The author wishes to thank G. S. Golitsyn for his interest and G. I. Barenblatt and V. M. Gryanik for discussing the results and offering useful advice.