The hydrodynamical alpha-effect in a compressible medium

The problem of the interaction of large-scale vortices with small-scale homogeneous isotropic helical turbulence in a compressible medium is considered. Averaged equations are derived using a closure procedure which is based on the functional technique. It is shown that the averaged vorticity equation has solutions that grow exponentially in time and which describe the effect of amplification of large-scale helical vortices by turbulence (hydrodynamical α-effect). The dependence of the growth rate on the compressibility is analysed, the limiting cases of incompressible fluid and turbulence δ-correlated in time being considered. The applications of the hydrodynamical α-effect discussed include the Earth's atmosphere and interstellar gas of spiral galaxies.