Transition to finger convection in double-diffusive convection

Finger convection is observed experimentally in an electrodeposition cell in which a destabilizing gradient of copper ions is maintained against a stabilizing temperature gradient. This double-diffusive system shows finger convection even if the total density stratification is unstable. Finger convection is replaced by an ordinary convection roll if convection is fast enough to prevent sufficient heat diffusion between neighboring fingers, or if the thermal buoyancy force is less than 1/30 of the compositional buoyancy force. At the transition, the ion transport is larger than without an opposing temperature gradient

Stability problem in dynamo

It is shown, that the saturated $\alpha$-effect taken from the nonlinear dynamo equations for the thin disk can still produce exponentially growing magnetic field in the case, when this field does not feed back on the $\alpha$. For negative dynamo number (stationary regime) stability is defined by the structure of the spectra of the linear problem for the positive dynamo numbers. Stability condition for the oscillatory solution (positive dynamo number) is also obtained and related to the phase shift of the original magnetic field, which produced saturated $\alpha$ and magnetic field in the kinematic regime. Results can be used for explanation of the similar effect observed in the shell models simulations as well in the 3D dynamo models in the plane layer and sphere

Tilt-over mode in a precessing triaxial ellipsoid

The tilt-over mode in a precessing triaxial ellipsoid is studied theoretically and numerically. Inviscid and viscous analytical models previously developed for the spheroidal geometry by Poincar\'e [Bull. Astr. 27, 321 (1910)] and Busse [J. Fluid Mech., 33, 739 (1968)] are extended to this more complex geometry, which corresponds to a tidally deformed spinning astrophysical body. As confirmed by three-dimensional numerical simulations, the proposed analytical model provides an accurate description of the stationary flow in an arbitrary triaxial ellipsoid, until the appearance at more vigorous forcing of time dependent flows driven by tidal and/or precessional instabilities.Comment: http://link.aip.org/link/doi/10.1063/1.350435

Some Unusual Properties of Turbulent Convection and Dynamos in Rotating Spherical Shells

The dynamics of convecting fluids in rotating spherical shells is governed at Prandtl numbers of the order unity by the interaction between differential rotation and roll-like convection eddies. While the differential rotation is driven by the Reynolds stresses of the eddies, its shearing action inhibits convection and causes phenomena such as localized convection and turbulent relaxation oscillations. The response of the system is enriched in the case of dynamo action. Lorentz forces may brake either entirely or partially the geostrophic differential rotation and give rise to two rather different dynamo states. Bistability of turbulent dynamos exists for magnetic Prandtl numbers of the order unity. While the ratios between mean magnetic and kinetic energies differ by a factor of 5 or more for the two dynamo states, the mean convective heat transports are nearly the same. They are much larger than in the absence of a magnetic field.Comment: To appear in Procs. IUTAM Symposium on Turbulence in the Atmosphere and Oceans, 08-7 = GA.06-0

Tidal instability in a rotating and differentially heated ellipsoidal shell

The stability of a rotating flow in a triaxial ellipsoidal shell with an imposed temperature difference between inner and outer boundaries is studied numerically. We demonstrate that (i) a stable temperature field encourages the tidal instability, (ii) the tidal instability can grow on a convective flow, which confirms its relevance to geo- and astrophysical contexts and (iii) its growth rate decreases when the intensity of convection increases. Simple scaling laws characterizing the evolution of the heat flux based on a competition between viscous and thermal boundary layers are derived analytically and verified numerically. Our results confirm that thermal and tidal effects have to be simultaneously taken into account when studying geophysical and astrophysical flows

Viscous dissipation by tidally forced inertial modes in a rotating spherical shell

We investigate the properties of forced inertial modes of a rotating fluid inside a spherical shell. Our forcing is tidal like, but its main property is that it is on the large scales. Our solutions first confirm some analytical results obtained on a two-dimensional model by Ogilvie (2005). We also note that as the frequency of the forcing varies, the dissipation varies drastically if the Ekman number E is low (as is usually the case). We then investigate the three-dimensional case and compare the results to the foregoing model. These solutions show, like their 2D counterpart, a spiky dissipation curve when the frequency of the forcing is varied; they also display small frequency intervals where the viscous dissipation is independent of viscosity. However, we show that the response of the fluid in these frequency intervals is crucially dominated by the shear layer that is emitted at the critical latitude on the inner sphere. The asymptotic regime is reached when an attractor has been excited by this shear layer. This property is not shared by the two-dimensional model. Finally, resonances of the three-dimensional model correspond to some selected least-damped eigenmodes. Unlike their two-dimensional counter parts these modes are not associated with simple attractors; instead, they show up in frequency intervals with a weakly contracting web of characteristics. Besides, we show that the inner core is negligible when its relative radius is less than the critical value 0.4E^{1/5}. For these spherical shells, the full sphere solutions give a good approximation of the flows (abridged abstract).Comment: 32 pages, 19 figs, accepted in J. Fluid Mec

Linear optical properties of one-dimensional Frenkel exciton systems with intersite energy correlations

We analyze the effects of intersite energy correlations on the linear optical properties of one-dimensional disordered Frenkel exciton systems. The absorption line width and the factor of radiative rate enhancement are studied as a function of the correlation length of the disorder. The absorption line width monotonously approaches the seeding degree of disorder on increasing the correlation length. On the contrary, the factor of radiative rate enhancement shows a non-monotonous trend, indicating a complicated scenario of the exciton localization in correlated systems. The concept of coherently bound molecules is exploited to explain the numerical results, showing good agreement with theory. Some recent experiments are discussed in the light of the present theory.Comment: 18 pages, 3 figues, REVTeX, to appear in Physical Review

Dynamo action at low magnetic Prandtl numbers: mean flow vs. fully turbulent motion

We compute numerically the threshold for dynamo action in Taylor-Green swirling flows. Kinematic calculations, for which the flow field is fixed to its time averaged profile, are compared to dynamical runs for which both the Navier-Stokes and the induction equations are jointly solved. The kinematic instability is found to have two branches, for all explored Reynolds numbers. The dynamical dynamo threshold follows these branches: at low Reynolds number it lies within the low branch while at high kinetic Reynolds number it is close to the high branch.Comment: 4 pages, 4 figure

Saturation and time dependence of geodynamo models

In this study we address the question under which conditions a saturated velocity field stemming from geodynamo simulations leads to an exponential growth of the magnetic field in a corresponding kinematic calculation. We perform global self-consistent geodynamo simulations and calculate the evolution of a kinematically advanced tracer field. The self-consistent velocity field enters the induction equation in each time step, but the tracer field does not contribute to the Lorentz force. This experiment has been performed by Cattaneo & Tobias (2009) and is closely related to the test field method by Schrinner et al. (2005, 2007). We find two dynamo regimes in which the tracer field either grows exponentially or approaches a state aligned with the actual self-consistent magnetic field after an initial transition period. Both regimes can be distinguished by the Rossby number and coincide with the dipolar and multipolar dynamo regimes identified by Christensen & Aubert (2006). Dipolar dynamos with low Rossby number are kinematically stable whereas the tracer field grows exponentially in the multipolar dynamo regime. This difference in the saturation process for dynamos in both regimes comes along with differences in their time variability. Within our sample of 20 models, solely kinematically unstable dynamos show dipole reversals and large excursions. The complicated time behaviour of these dynamos presumably relates to the alternating growth of several competing dynamo modes. On the other hand, dynamos in the low Rossby number regime exhibit a rather simple time dependence and their saturation merely results in a fluctuation of the fundamental dynamo mode about its critical state.Comment: 6 pages, 8 figure

Global dynamo models from direct numerical simulations and their mean-field counterparts

Context. The recently developed test-field method permits to compute dynamo coefficients from global, direct numerical simulations. The subsequent use of these parameters in mean-field models enables us to compare self-consistent dynamo models with their mean-field counterparts. So far, this has been done for a simulation of rotating magnetoconvection and a simple benchmark dynamo, which are both (quasi-)stationary. Aims. It is shown that chaotically time-dependent dynamos in a low Rossby number regime may be appropriately described by corresponding mean-field results. Also, it is pointed out under which conditions mean-field models do not match direct numerical simulations. Methods. We solve the equations of magnetohydrodynamics (MHD) in a rotating, spherical shell in the Boussinesq approximation. Based on this, we compute mean-field coefficients for several models with the help of the previously developed test-field method. The parameterization of the mean electromotive force by these coefficients is tested against direct numerical simulations. In addition, we use the determined dynamo coefficients in mean-field models and compare the outcome with azimuthally averaged fields from direct numerical simulations. Results. The azimuthally and time-averaged electromotive force in fast rotating dynamos is sufficiently well parameterized by the set of determined mean-field coefficients. In comparison to the previously considered (quasi-)stationary dynamo, the chaotic time-dependence leads to an improved scale separation and thus to a better agreement between direct numerical simulations and mean-field results.Comment: 6 pages, 6 figure