B{\'e}nard convection in a slowly rotating penny shaped cylinder subject to constant heat flux boundary conditions

We consider axisymmetric Boussinesq convection in a shallow cylinder radius, L, and depth, H (<< L), which rotates with angular velocity $\Omega$ about its axis of symmetry aligned to the vertical. Constant heat flux boundary conditions, top and bottom, are adopted, for which the onset of instability occurs on a long horizontal length scale provided that $\Omega$ is sufficiently small. We investigate the nonlinear development by well-established two-scale asymptotic expansion methods. Comparisons of the results with the direct numerical simulations (DNS) of the primitive governing equations are good at sufficiently large Prandtl number, $\sigma$. As $\sigma$ is reduced, the finite amplitude range of applicability of the asymptotics reduces in concert. Though the large meridional convective cell, predicted by the DNS, is approximated adequately by the asymptotics, the azimuthal flow fails almost catastrophically, because of significant angular momentum transport at small $\sigma$, exacerbated by the cylindrical geometry. To appraise the situation, we propose hybrid methods that build on the meridional streamfunction $\psi$ derived from the asymptotics. With $\psi$ given, we solve the now linear azimuthal equation of motion for the azimuthal velocity v by DNS. Our ''hybrid'' methods enable us to explain features of the flow at large Rayleigh number, found previously by Oruba, Davidson \& Dormy (J. Fluid Mech.,vol. 812, 2017, pp. 890-904)

Memory Effects in Turbulent Dynamo: Generation and Propagation of Large Scale Magnetic Field

We are concerned with large scale magnetic field dynamo generation and propagation of magnetic fronts in turbulent electrically conducting fluids. An effective equation for the large scale magnetic field is developed here that takes into account the finite correlation times of the turbulent flow. This equation involves the memory integrals corresponding to the dynamo source term describing the alpha-effect and turbulent transport of magnetic field. We find that the memory effects can drastically change the dynamo growth rate, in particular, non-local turbulent transport might increase the growth rate several times compared to the conventional gradient transport expression. Moreover, the integral turbulent transport term leads to a large decrease of the speed of magnetic front propagation.Comment: 13 pages, 2 figure

Geodynamo alpha-effect derived from box simulations of rotating magnetoconvection

The equations for fully compressible rotating magnetoconvection are numerically solved in a Cartesian box assuming conditions roughly suitable for the geodynamo. The mean electromotive force describing the generation of mean magnetic flux by convective turbulence in the rotating fluid is directly calculated from the simulations, and the corresponding alpha-coefficients are derived. Due to the very weak density stratification the alpha-effect changes its sign in the middle of the box. It is positive at the top and negative at the bottom of the convection zone. For strong magnetic fields we also find a clear downward advection of the mean magnetic field. Both of the simulated effects have been predicted by quasi-linear computations (Soward, 1979; Kitchatinov and Ruediger, 1992). Finally, the possible connection of the obtained profiles of the EMF with mean-field models of oscillating alpha^2-dynamos is discussed.Comment: 17 pages, 9 figures, submitted to Phys. Earth Planet. Inte

Screw dynamo in a time-dependent pipe flow

The kinematic dynamo problem is investigated for the flow of a conducting fluid in a cylindrical, periodic tube with conducting walls. The methods used are an eigenvalue analysis of the steady regime, and the three-dimensional solution of the time-dependent induction equation. The configuration and parameters considered here are close to those of a dynamo experiment planned in Perm, which will use a torus-shaped channel. We find growth of an initial magnetic field by more than 3 orders of magnitude. Marked field growth can be obtained if the braking time is less than 0.2 s and only one diverter is used in the channel. The structure of the seed field has a strong impact on the field amplification factor. The generation properties can be improved by adding ferromagnetic particles to the fluid in order to increase its relative permeability,but this will not be necessary for the success of the dynamo experiment. For higher magnetic Reynolds numbers, the nontrivial evolution of different magnetic modes limits the value of simple `optimistic' and `pessimistic' estimates.Comment: 10 pages, 12 figure

Acute effects of intravenous nisoldipine on left ventricular function and coronary hemodynamics

The hemodynamic effects of nisoldipine were investigated in 16 patients with suspected coronary artery disease who underwent routine cardiac catheterization. Nisoldipine was given intravenously in a dose of 6 micrograms/kg over 3 minutes and measurements made before and after drug administration during spontaneous and matched atrial paced heart rate. During sinus rhythm, nisoldipine produced a significant increase in heart rate (19%, p less than 10(-5]. Left ventricular systolic pressure decreased 28% (p less than 10(-6) and left ventricular end-diastolic pressure did not change significantly (5%, difference not significant). Coronary sinus and great cardiac vein blood flow increased by 21% (p less than 0.02) and 25% (p less than 0.005), respectively, after nisoldipine administration. Simultaneously, mean aortic pressure decreased 33% (p less than 10(-6]; consequently, the global and regional coronary vascular resistances decreased by 50% (p less than 10(-4]. The decreases in global (-8%) and regional (-4%) myocardial oxygen consumption did not reach statistical significance. A 6% (not significant) increase in end-diastolic volume and an 11% (p less than 0.002) decrease in end-systolic volume resulted in an increase of 21% in stroke volume (p less than 10(-4] with a consistent increase in ejection fraction (+16%, p less than 10(-5]. Total systemic vascular resistance was reduced by 30% (p less than 0.0002). During spontaneous heart rate and matched atrial pacing, the time constant of isovolumic relaxation as assessed by a biexponential model, was significantly shortened.(ABSTRACT TRUNCATED AT 250 WORDS

Acute effects of intravenous nisoldipine on left ventricular function and coronary hemodynamics

The hemodynamic effects of nisoldipine were investigated in 16 patients with suspected coronary artery disease who underwent routine cardiac catheterization. Nisoldipine was given intravenously in a dose of 6 micrograms/kg over 3 minutes and measurements made before and after drug administration during spontaneous and matched atrial paced heart rate. During sinus rhythm, nisoldipine produced a significant increase in heart rate (19%, p less than 10(-5]. Left ventricular systolic pressure decreased 28% (p less than 10(-6) and left ventricular end-diastolic pressure did not change significantly (5%, difference not significant). Coronary sinus and great cardiac vein blood flow increased by 21% (p less than 0.02) and 25% (p less than 0.005), respectively, after nisoldipine administration. Simultaneously, mean aortic pressure decreased 33% (p less than 10(-6]; consequently, the global and regional coronary vascular resistances decreased by 50% (p less than 10(-4]. The decreases in global (-8%) and regional (-4%) myocardial oxygen consumption did not reach statistical significance. A 6% (not significant) increase in end-diastolic volume and an 11% (p less than 0.002) decrease in end-systolic volume resulted in an increase of 21% in stroke volume (p less than 10(-4] with a consistent increase in ejection fraction (+16%, p less than 10(-5]. Total systemic vascular resistance was reduced by 30% (p less than 0.0002). During spontaneous heart rate and matched atrial pacing, the time constant of isovolumic relaxation as assessed by a biexponential model, was significantly shortened.(ABSTRACT TRUNCATED AT 250 WORDS

Non-local effects in the mean-field disc dynamo. II. Numerical and asymptotic solutions

The thin-disc global asymptotics are discussed for axisymmetric mean-field dynamos with vacuum boundary conditions allowing for non-local terms arising from a finite radial component of the mean magnetic field at the disc surface. This leads to an integro-differential operator in the equation for the radial distribution of the mean magnetic field strength, $Q(r)$ in the disc plane at a distance $r$ from its centre; an asymptotic form of its solution at large distances from the dynamo active region is obtained. Numerical solutions of the integro-differential equation confirm that the non-local effects act similarly to an enhanced magnetic diffusion. This leads to a wider radial distribution of the eigensolution and faster propagation of magnetic fronts, compared to solutions with the radial surface field neglected. Another result of non-local effects is a slowly decaying algebraic tail of the eigenfunctions outside the dynamo active region, $Q(r)\sim r^{-4}$, which is shown to persist in nonlinear solutions where $\alpha$-quenching is included. The non-local nature of the solutions can affect the radial profile of the regular magnetic field in spiral galaxies and accretion discs at large distances from the centre.Comment: Revised version, as accepted; Geophys. Astrophys. Fluid Dyna

Defect Chaos of Oscillating Hexagons in Rotating Convection

Using coupled Ginzburg-Landau equations, the dynamics of hexagonal patterns with broken chiral symmetry are investigated, as they appear in rotating non-Boussinesq or surface-tension-driven convection. We find that close to the secondary Hopf bifurcation to oscillating hexagons the dynamics are well described by a single complex Ginzburg-Landau equation (CGLE) coupled to the phases of the hexagonal pattern. At the bandcenter these equations reduce to the usual CGLE and the system exhibits defect chaos. Away from the bandcenter a transition to a frozen vortex state is found.Comment: 4 pages, 6 figures. Fig. 3a with lower resolution no

Eddy diffusivity in convective hydromagnetic systems

An eigenvalue equation, for linear instability modes involving large scales in a convective hydromagnetic system, is derived in the framework of multiscale analysis. We consider a horizontal layer with electrically conducting boundaries, kept at fixed temperatures and with free surface boundary conditions for the velocity field; periodicity in horizontal directions is assumed. The steady states must be stable to short (fast) scale perturbations and possess symmetry about the vertical axis, allowing instabilities involving large (slow) scales to develop. We expand the modes and their growth rates in power series in the scale separation parameter and obtain a hierarchy of equations, which are solved numerically. Second order solvability condition yields a closed equation for the leading terms of the asymptotic expansions and respective growth rate, whose origin is in the (combined) eddy diffusivity phenomenon. For about 10% of randomly generated steady convective hydromagnetic regimes, negative eddy diffusivity is found.Comment: 18 pages. Added numerical reults. Submitted to European Physical Journal