A Route to Magnetic Field Reversals: An Example of an ABC-Forced Nonlinear Dynamo

We are investigating numerically the nonlinear behaviour of a space-periodic MHD system with ABC forcing. Most computations are performed for magnetic Reynolds numbers increasing from 0 to 60 and a fixed kinematic Reynolds number, small enough for the trivial solution with a zero magnetic field to be stable to velocity perturbations. At the critical magnetic Reynolds number for the onset of instability of the trivial solution the dominant eigenvalue of the kinematic dynamo problem is real. In agreement with the bifurcation theory new steady states with non-vanishing magnetic field appear in this bifurcation. Subsequent bifurcations are investigated. A regime is detected, where chaotic variations of the magnetic field orientation (analogous to magnetic field reversals) are observed in the temporal evolution of the system.     

Instability of flows near the onset of convection in a rotating layer with stress-free horizontal boundaries

We investigate instability of convective flows of simple structure (rolls, standing and travelling waves) in a rotating layer with stress-free horizontal boundaries near the onset of convection. We show that the flows are always unstable to perturbations, which are linear combinations of large-scale modes and short-scale modes, whose wave numbers are close to those of the perturbed flows. Depending on asymptotic relations of small parameters α (the difference between the wave number of perturbed flows and the critical wave number for the onset of convection) and ε (ε² being the overcriticality and the perturbed flow amplitude being O(ε)), either small-angle or Eckhaus instability is prevailing. In the case of small-angle instability for rolls the largest growth rate scales as ε^8/5, in agreement with results of Cox and Matthews (Cox, S.M. and Matthews, P.C., Instability of rotating convection. J. Fluid. Mech., 2000, 403, 153–172) obtained for rolls with k = k _c . For waves, the largest growth rate is of the order ε^4/3. In the case of Eckhaus instability the growth rate is of the order of α².     

Fluids migration and dynamics of a blocks-and-faults system

We explore the impact of fluids migrating through a fault network on the dynamics of lithosphere, both on slow movements and seismicity. For that purpose fluids in the fault zones are incorporated into modelling of blocks-and-faults systems, which takes into account driving forces and the system's geometry. Simulations have been performed for two-dimensional models: an idealised “brick wall” structure, and a coarse image of Sinai Subplate. Migrating fluids originating in different locations are considered, as well as fluids trapped in closed pockets. Basic features of the modelled and observed seismicity are in good accord, as shown by comparison with the earthquake catalog compiled by Geophysical Institute of Israel.     

Heteroclinic Cycles in Nature

Izvestiya, Physics of the Solid Earth - Heteroclinic cycle is an invariant of a dynamical system comprised of steady states (or more general invariant subsets) and heteroclinic trajectories. The...     

A Numerical Algorithm for Time Integration of the Problems of Ideal Magnetohydrodynamics Based on Analyticity of Their Solutions

Izvestiya, Physics of the Solid Earth - Abstract—We show that a solution of the system of three-dimensional equations of ideal magnetohydrodynamics is analytic in the spatial and temporal...     

The onset of convection in a rotating layer of viscous fluid with an imposed magnetic field: the dependence on the prandlt numbers

The onset of Boussinesq convection in a horizontal layer of an electrically conducting incompressible fluid is considered. The layer rotating about a vertical axis is heated from below; a vertical magnetic field is imposed. Rigid electrically insulating boundaries are assumed. The loss of stability of the trivial steady state, which occurs as the Rayleigh numbers increase, can be accompanied by the development of a monotonic or an oscillatory instability, depending on the parameter values of the problem at hand (the Taylor number, the Chandrasekhar number, the kinematic and the magnetic Prandtl numbers). When the instability is monotonic, the emerging convective rolls themselves are also unstable if the Taylor number is sufficiently large (the so-called Küppers-Lortz instability takes place). In the present work it is studied how the critical value of the Rayleigh number, the type of the trivial steady state instability, and the critical value of the Taylor number for the Küppers-Lortz instability depend on the kinematic and the magnetic Prandtl numbers. We consider the values of the Prandtl number not exceeding 1, which is typical for the outer core of the Earth.     

Effect of dietary docosahexaenoic acid on lipogenesis and lipolysis in black sea bream, Acanthopagrus schlegeli

1 IntroductionIt is well known that varying dietary fatty acidprofile affects the tissue fatty acid composition and e-ven the growth performance in fish ( Bell et al.,2002; Figueiredo -Silva et al., 2005; Harel andPlace, 2003; Schulz et al., 2005; Tocher et al.,2003). Docosahexaenoic acid (DHA), an importantessential fatty acid for marine species, has the effectnot only on the fatty acid profile of fish body tissue,but also on biological and physiological conditions(Ishizaki et al., 2000; …     

Magnetic field generation by convective flows in a plane layer: the dependence on the Prandtl numbers

Investigation of magnetic field generation by convective flows is carried out for three values of kinematic Prandtl number: P = 0.3, 1 and 6.8. We consider Rayleigh–Bénard convection in Boussinesq approximation assuming stress-free boundary conditions on horizontal boundaries and periodicity with the same period in the x and y directions. Convective attractors are modelled for increasing Rayleigh numbers for each value of the kinematic Prandtl number. Linear and non-linear dynamo action of these attractors is studied for magnetic Prandtl numbers P _m ≤ 100. Flows, which can act as magnetic dynamos, have been found for all the three considered values of P, if the Rayleigh number R is large enough. The minimal R, for which of magnetic field generation occurs, increases with P. The minimum (over R) of critical P_m for magnetic field generation in the kinematic regime is admitted for P = 0.3. Thus, our study indicates that smaller values of P are beneficial for magnetic field generation.