Electrodynamics of turbulent fluids with fluctuating electric conductivity

Consequences of fluctuating microscopic conductivity in mean-field electrodynamics of turbulent fluids are formulated and discussed. If the conductivity fluctuations are assumed to be uncorrelated with the velocity fluctuations then only the turbulence-originated magnetic diffusivity of the fluid is reduced and the decay time of a large-scale magnetic field or the cycle times of oscillating turbulent dynamo models are increased. If, however, the fluctuations of conductivity and flow in a certain well-defined direction are correlated, an additional diamagnetic pumping effect results, transporting the magnetic field in the opposite direction to the diffusivity flux vector $\langle \unicode[STIX]{x1D702}^{\prime }\boldsymbol{u}^{\prime }\rangle$ . In the presence of global rotation, even for homogeneous turbulence fields, an alpha effect appears. If the characteristic values of the outer core of the Earth or the solar convection zone are applied, the dynamo number of the new alpha effect does not reach supercritical values to operate as an $\unicode[STIX]{x1D6FC}^{2}$ -dynamo but oscillating $\unicode[STIX]{x1D6FC}\unicode[STIX]{x1D6FA}$ -dynamos with differential rotation are not excluded.

Fractional hyperviscosity induced growth of bottlenecks in energy spectrum of Burgers equation solutions

Energy spectrum of turbulent fluids exhibit a bump at an intermediate wavenumber, between the inertial and the dissipation range. This bump is called bottleneck. Such bottlenecks are also seen in the energy spectrum of the solutions of hyperviscous Burgers equation. Previous work have shown that this bump corresponds to oscillations in real space velocity field. In this paper, we present numerical and analytical results of how the bottleneck and its real space signature, the oscillations, grow as we tune the order of hyperviscosity. We look at a parameter regime α ∈ [1, 2] where α = 1 corresponds to normal viscosity and α = 2 corresponds to hyperviscosity of order 2. We show that even for the slightest fractional increment in the order of hyperviscosity (α) bottlenecks show up in the energy spectrum. Graphical abstract