Generation of vortices in protogalactic medium

A theory of the generation of vortex caused by nonbarotropy of protogalactic medium motions is constructed. Vortices of a galaxy scale arise at propogation of potential nonrotational perturbations in the gas protocluster produced by shock waves. Pressure in protocluster is nearly homogeneous, while density is substantially inhomogeneous. This disturbs barotropy in perturbations. The Kelvin-Helmholtz theorem does not hold true under these conditions. A qualitative picture of the process is given. An appropriate asymptotic solution in the WKB approximation is obtained. Quantitative evaluations show that the amplitude of secondary vortices is sufficient to provide a fast rotation of protogalaxies formed by fragmentation of the protocluster