The linear marginal instability of an axisymmetric MHD Taylor-Couette flow of infinite vertical extension is considered. For flows with a resting outer cylinder there is a well-known characteristic Reynolds number even without magnetic field but for sufficiently weak magnetic fields there are solutions with smaller Reynolds numbers so that a characteristic minimum exists. The minimum only exist...

A linear stability analysis is applied to determine the onset of oscillatory thermocapillary convection in cylindrical liquid bridges of large Prandtl numbers (4 6 Pr 6 50). We focus on the relationships between the critical Reynolds number Rec, the azimuthal wave number m, the aspect ratio Γ and the Prandtl number Pr. A detailed Rec-Pr stability diagram is given for liquid bridges with various...

Nonhelical hydromagnetic forced turbulence is investigated using large scale simulations on up to 256 processors and 1024(3) mesh points. The magnetic Prandtl number is varied between 1/8 and 30, although in most cases it is unity. When the magnetic Reynolds number is based on the inverse forcing wave number, the critical value for dynamo action is shown to be around 35 for magnetic Prandtl num...

Layer formation in a thermally destabilized fluid with stable density gradient has been observed in laboratory experiments and has been proposed as a mechanism for mixing molecular weight in late stages of stellar evolution in regions which are unstable to semiconvection. It is not yet known whether such layers can exist in a very low viscosity fluid: this work undertakes to address that questi...

The magnetic Prandtl number PrM is the ratio of viscosity to resistivity. In astrophysical disks the diffusion of angular momentum (viscosity) and magnetic fields (resistivity) are controlled by turbulence. Phenomenological models of the evolution of large scale poloidal magnetic fields in disks suggest that the turbulent magnetic Prandtl number PrM,T controls the rate of escape of vertical fie...

The turbulent Prandtl number has been calculated in the two-loop approximation of the epsilon expansion of the stochastic theory of turbulence. The strikingly small value obtained for the two-loop correction explains the good agreement of the earlier one-loop result with the experiment. This situation is drastically different from other available nontrivial two-loop results, which exhibit corre...

Dynamo action in a fully helical Beltrami (ABC) flow is studied using both direct numerical simulations and subgrid modeling. Sufficient scale separation is given in order to allow for largescale magnetic energy build-up. Growth of magnetic energy obtains down to a magnetic Prandtl number PM = RM/RV close to 0.005, where RV and RM are the kinetic and magnetic Reynolds numbers. The critical magn...

In turbulent MHD systems where the ratio of fluid viscosity and magnetic diffusivity (the magnetic Prandtl number, Pr = ν/η) is very large, there exists a broad range of subviscous scales available to magnetic fluctuations, but not to hydrodynamic ones. This MHD regime is encountered, for example, in such astrophysical environments as the interstellar medium and protogalactic plasmas, where Pr ...

The physics of thermomechanical coupling of the continental lithosphere and its surrounding mantle is studied using a simple hydrodynamic model in which a fluid is heated from below and is bounded by rigid side walls. Rayleigh numbers up to 10 are considered. A series of finite-element stability analyses is employed to characterize systematically the nature of convective instability in such a s...