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Vortical dynamo in turbulent multiphase flows

Tuesday 24th July 2012 - 15:35 to 15:55
INI Seminar Room 1
Session Chair: 
Eckart Meiburg
Magnetic disturbances are known to be amplified by helical turbulence. The possibility of amplification of large-scale hydrodynamic fields by small-scale helical turbulence is considered. The important difference between hydrodynamic and magnetic theories is that the latter describe the evolution of magnetic field on the background of a given hydrodynamic flow (kinematic dynamo), whereas in hydrodynamics such a situation is more complex. The hydrodynamic problem is self-consistent and non-linear. A generation of large-scale helical vortices resulting from the instability of small-scale helical turbulence with respect to two-scale disturbance is considered. In order to investigate such instability, we consider two cases: (1) an incompressible fluid containing rigid particles; (2) an incompressible fluid containing gas babbles. An equation describing the evolution of mean disturbances is derived and the instability increment is obtained. The analysis revealed that helical turbulence in an incompressible fluid with rigid particles and in incompressible fluid with gas babbles is unstable against vortical disturbances. The generation terms formally coinciding with those in the theory of hydromagnetic dynamo are contained in Reynolds averaged equations derived at the scale of mean motions. It should be noted that only helicity is enough for the process of generation in magnetohydrodynamics. In hydrodynamic theory, because of the mentioned differences, it is also necessary to take into account additional factors. In this paper two such additional factors are the presence of rigid particles or gas babbles whose motions provide the existence of divergence at a turbulent scale and thus provide a non-zero value of the Reynolds stresses in the averaged equations.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons