Surface reactions with participation of oxides of molybdenum and tungsten

The kinetics of surface reactions in one-dimensional and radial (two-dimensional) distribution of diffusant MoO3 (WO3) on the surface of the substrate MeO (Me is Cd, Ni, Pb, Mn, Cu) were investigated. A kinetic equation satisfactorily describes the rate of surface reactions in the case of radial distribution of diffusant on the substrate. It’s found that when the radial distribution of diffusant the growth of layer on the substrate surface eventually slows down and stops almost completely, due to the outflow of the diffusant deeps into the substrate. When the one-dimensional distribution of diffusant the surface interaction is not slowed down and does not stop at an arbitrarily large times

Nonaxisymmetric MHD instabilities of Chandrasekhar states in Taylor-Couette geometry

We consider axially periodic Taylor-Couette geometry with insulating boundary conditions. The imposed basic states are so-called Chandrasekhar states, where the azimuthal flow $U_\phi$ and magnetic field $B_\phi$ have the same radial profiles. Mainly three particular profiles are considered: the Rayleigh limit, quasi-Keplerian, and solid-body rotation. In each case we begin by computing linear instability curves and their dependence on the magnetic Prandtl number Pm. For the azimuthal wavenumber m=1 modes, the instability curves always scale with the Reynolds number and the Hartmann number. For sufficiently small Pm these modes therefore only become unstable for magnetic Mach numbers less than unity, and are thus not relevant for most astrophysical applications. However, modes with m>10 can behave very differently. For sufficiently flat profiles, they scale with the magnetic Reynolds number and the Lundquist number, thereby allowing instability also for the large magnetic Mach numbers of astrophysical objects. We further compute fully nonlinear, three-dimensional equilibration of these instabilities, and investigate how the energy is distributed among the azimuthal (m) and axial (k) wavenumbers. In comparison spectra become steeper for large m, reflecting the smoothing action of shear. On the other hand kinetic and magnetic energy spectra exhibit similar behavior: if several azimuthal modes are already linearly unstable they are relatively flat, but for the rigidly rotating case where m=1 is the only unstable mode they are so steep that neither Kolmogorov nor Iroshnikov-Kraichnan spectra fit the results. The total magnetic energy exceeds the kinetic energy only for large magnetic Reynolds numbers Rm>100.Comment: 12 pages, 14 figures, submitted to Ap

Surface reactions with participation of oxides of molybdenum and tungsten: the influence of external factors

This work is a continuation of the article “Surface reactions with participation of oxides of molybdenum and tungsten”, published in the previous issue of the journal. The influence of the electric field and the pressure of oxygen in the gas phase on the rate of surface reactions for the synthesis of molybdates of manganese and copper were investigated. It’s found that for the synthesis reaction of molybdate of copper the nature of the dependency of the rate of synthesis and rate of surface reactions from the external parameters are the same, indicating the crucial contribution of surface diffusion to the reactive mass transfer. For the synthesis reaction of molybdate of manganese the dependences of the rate of synthesis and of rate of surface reactions by external parameters differ, indicating that for this reaction, surface diffusion isn’t the main mechanism of mass transfer

Transition to chaos and modal structure of magnetized Taylor-Couette flow

Taylor-Couette flow is often used as a simplified model for complex rotating flows in the interior of stars and accretion disks. The flow dynamics in these objects is influenced by magnetic fields. For example, quasi-Keplerian flows in Taylor-Couette geometry become unstable to a travelling or standing wave in an external magnetic field if the fluid is conducting; there is an instability even when the flow is hydrodynamically stable. This magnetorotational instability leads to the development of chaotic states and, eventually, turbulence, when the cylinder rotation is sufficiently fast. The transition to turbulence in this flow can be complex, with the coexistence of parameter regions with spatio-temporal chaos and regions with quasi-periodic behaviour, involving one or two additional modulating frequencies. Although the unstable modes of a periodic flow can be identified with Floquet analysis, here we adopt a more flexible equation-free data-driven approach. We analyse the data from the transition to chaos in the magnetized Taylor-Couette flow and identify the flow structures related to the modulating frequencies with Dynamic Mode Decomposition; this method is based on approximating nonlinear dynamics with a linear infinite-dimensional Koopman operator. With the use of these structures, one can construct a nonlinear reduced model for the transition

Transition to magnetorotational turbulence in Taylor-Couette flow with imposed azimuthal magnetic field

The magnetorotational instability (MRI) is thought to be a powerful source of turbulence and momentum transport in astrophysical accretion discs, but obtaining observational evidence of its operation is challenging. Recently, laboratory experi-ments of Taylor–Couette flow with externally imposed axial and azimuthal magnetic fields have revealed the kinematic and dynamic properties of the MRI close to the instability onset. While good agreement was found with linear stability analyses, little is known about the transition to turbulence and transport properties of the MRI. We here report on a numerical investigation of the MRI with an imposed azimuthal magnetic field. We show that the laminar Taylor–Couette flow becomes unstable to a wave rotating in the azimuthal direction and standing in the axial direction via a supercritical Hopf bifurcation. Subsequently, the flow features a catastrophic transition to spatio-temporal defects which is mediated by a subcritical subharmonic Hopf bifurcation. Our results are in qualitative agreement with the PROMISE ex-periment and dramatically extend their realizable parameter range. We find that as the Reynolds number increases defects accumulate and grow into turbulence, yet the momentum transport scales weakly

Dynamo action in a quasi-Keplerian Taylor-Couette flow

We numerically compute the flow of an electrically conducting fluid in a Taylor-Couette geometry where the rotation rates of the inner and outer cylinders satisfy \Omega_o/\Omega_i=(r_o/r_i)-3/2. In this quasi-Keplerian regime a non-magnetic system would be Rayleigh-stable for all Reynolds numbers Re, and the resulting purely azimuthal flow incapable of kinematic dynamo action for all magnetic Reynolds numbers Rm. For Re=10^4 and Rm=10^5 we demonstrate the existence of a finite-amplitude dynamo, whereby a suitable initial condition yields mutually sustaining turbulence and magnetic fields, even though neither could exist without the other. This dynamo solution results in significantly increased outward angular momentum transport, with the bulk of the transport being by Maxwell rather than Reynolds stresses