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Register a new userEnergy distribution in nonaxisymmetric magnetic Taylor-Couette flow
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Azimuthal magnetorotational instability is a mechanism that generates nonaxisymmetric field pattern. Nonlinear simulations in an infinite Taylor-Couette system with current-free external field show, that not only the linearly unstable mode m=1 appears, but also an inverse cascade transporting energy into the axisymmetric field is possible. By varying the Reynolds number of the flow and the Hartmann number for the magnetic field, we find that the ratio between axisymmetric (m=0) and dominating nonaxisymmetric mode (m=1) can be nearly free chosen. On the surface of the outer cylinder this mode distribution appears similarly, but with weaker axisymmetric fields. We do not find significant differences in the case that a constant current within the flow is added.
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Recent studies have brought into question the view that at sufficiently high Reynolds number turbulence is an asymptotic state. We present the first direct observation of the decay of turbulent states in Taylor-Couette flow with lifetimes spanning five orders of magnitude. We also show that there is a regime where Taylor-Couette flow shares many of the decay characteristics observed in other shear flows, including Poisson statistics and the coexistence of laminar and turbulent patches. Our data suggest that characteristic decay times increase super-exponentially with increasing Reynolds number but remain bounded in agreement with the most recent data from pipe flow and with a recent theoretical model. This suggests that, contrary to the prevailing view, turbulence in linearly stable shear flows may be generically transient.
Differentially rotating flows of unmagnetized, highly conducting plasmas have been created in the Plasma Couette Experiment. Previously, hot-cathodes have been used to control plasma rotation by a stirring technique [C. Collins et al., Phys. Rev. Lett. 108, 115001(2012)] on the outer cylindrical boundary---these plasmas were nearly rigid rotors, modified only by the presence of a neutral particle drag. Experiments have now been extended to include stirring from an inner boundary, allowing for generalized circular Couette flow and opening a path for both hydrodynamic and magnetohydrodynamic experiments, as well as fundamental studies of plasma viscosity. Plasma is confined in a cylindrical, axisymmetric, multicusp magnetic field, with $T_e< 10$ eV, $T_i<1$ eV, and $n_e<10^{11}$ cm$^{-3}$. Azimuthal flows (up to 12 km/s, $M=V/c_ssim 0.7$) are driven by edge ${bf J times B}$ torques in helium, neon, argon, and xenon plasmas, and the experiment has already achieved $Rmsim 65$ and $Pmsim 0.2 - 12$. We present measurements of a self-consistent, rotation-induced, species-dependent radial electric field, which acts together with pressure gradient to provide the centripetal acceleration for the ions. The maximum flow speeds scale with the Alfv{e}n critical ionization velocity, which occurs in partially ionized plasma. A hydrodynamic stability analysis in the context of the experimental geometry and achievable parameters is also explored.
The stability problem of MHD Taylor-Couette flows with toroidal magnetic fields is considered in dependence on the magnetic Prandtl number. Only the most uniform (but not current-free) field with B_in = B_out has been considered. For high enough Hartmann numbers the toroidal field is always unstable. Rigid rotation, however, stabilizes the magnetic (kink-)instability. The axial current which drives the instability is reduced by the electromotive force induced by the instability itself. Numerical simulations are presented to probe this effect as a possibility to measure the turbulent conductivity in a laboratory. It is shown numerically that in a sodium experiment (without rotation) an eddy diffusivity 4 times the molecular diffusivity appears resulting in a potential difference of ~34 mV/m. If the cylinders are rotating then also the eddy viscosity can be measured. Nonlinear simulations of the instability lead to a turbulent magnetic Prandtl number of 2.1 for a molecular magnetic Prandtl number of 0.01. The trend goes to higher values for smaller Pm.
We investigate the instability and nonlinear saturation of temperature-stratified Taylor-Couette flows in a finite height cylindrical gap and calculate angular-momentum transport in the nonlinear regime. The model is based on an incompressible fluid in Boussinesq approximation with a positive axial temperature gradient applied. While both ingredients itself, the differential rotation as well as the stratification due to the temperature gradient, are stable, together the system becomes subject of the stratorotational instability and nonaxisymmetric flow pattern evolve. This flow configuration transports angular momentum outwards and will therefor be relevant for astrophysical applications. The belonging viscosity $alpha$ coefficient is of the order of unity if the results are adapted to the size of an accretion disc. The strength of the stratification, the fluids Prandtl number and the boundary conditions applied in the simulations are well-suited too for a laboratory experiment using water and a small temperature gradient below five Kelvin. With such a rather easy realizable set-up the SRI and its angular momentum transport could be measured in an experiment.
We study the nonlinear mode competition of various spiral instabilities in magnetised Taylor-Couette flow. The resulting finite-amplitude mixed-mode solution branches are tracked using the annular-parallelogram periodic domain approach developed by Deguchi & Altmeyer (2013). Mode competition phenomena are studied in both the anti-cyclonic and cyclonic Rayleigh-stable regimes. In the anti-cyclonic sub-rotation regime, with the inner cylinder rotating faster than the outer, Hollerbach, Teeluck & Rudiger (2010) found competing axisymmetric and non-axisymmetric magneto-rotational linearly unstable modes within the parameter range where experimental investigation is feasible. Here we confirm the existence of mode competition and compute the nonlinear mixed-mode solutions that result from it. In the cyclonic super-rotating regime, with the inner cylinder rotating slower than the outer, Deguchi (2017) recently found a non-axisymmetric purely hydrodynamic linear instability that coexists with the non-axisymmetric magneto-rotational instability discovered a little earlier by Rudiger, Schultz, Gellert & Stefani (2016). We show that nonlinear interactions of these instabilities give rise to rich pattern-formation phenomena leading to drastic angular momentum transport enhancement/reduction.
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