Generation of kinetic helicity from irrotational motions

Abstract

Vortical and helical fluctuations are an integral part of any turbulent fluid. A turbulent magnetohydrodynamic system with net kinetic helicity is known to support the growth of a large scale magnetic field through the dynamo mechanism. An analogous effect, called the kinetic α - effect has been shown to give rise to large scale structures in a turbulent hydrodynamic system. Thus, it appears that the mechanism for formation of large scale structures, magnetic or hydrodynamic, hinges on the presence of kinetic helicity, in an essential manner. It has been demonstrated that systems possessing nonzero net kinetic helicity and those with zero net kinetic helicity, but nonzero mean sqare helicity, can support the formation of large scale structures via the mechanism of inverse cascade of energy. The question, then arises, "what are the mechanisms for the production of small scale vortical and helical fluctuations, especially in astrophysical situations"? We examine two mechanisms for the generation of vorticity and helicity from longitudinal velocity fields, like those associated with, for example, acoustic waves, which by themselves are irrotational. We assume the existence of finite amplitude acoustic waves; these could be generated in a highly compressible medium such as obtains in astrophysical situations. We discuss (i)growth of vorticity field through a mechanism, Known as the Langmuir circulation, in which the ambient shear in the fluid couples with the longitudinal waves to produce vorticity and helicity and (ii)the conversion of part of the energy contained in a longitudianl velocity field into vortical and helical velocity fields when it propagates through a turbulent medium; this latter mechanism may be seen as the inverse of the Lighthill mechanism where part of the turbulent energy is converted into sound waves.