arXiv subjects

M. Reshetnyak

Publications and source records attributed to M. Reshetnyak.

9 recordsLinked to original sources

arXiv2016

Parker's model in geodynamo

We consider how information on geostrophic flows in the planetary cores, taken from 3D simulations in the sphere, can be used in 2D Parker's geodynamo model with the simple forms of the $α$-quenching. Using cluster computer systems dependence of dynamo equations solution on the magnitudes of $α$- and $ω$-effects is studied. We show that geostrophical flow can produce the well-known Z-structure of the poloidal magnetic field without the feed-back of the magnetic field onto the large-scale velocity field. The influence of fluctuations of $α$-effect on magnetic field generation, its spectral properties, in respect to the geodynamo applications, is also discussed.

physics.flu-dyn↗

arXiv2012

Domino model in geodynamo

Using Lagrangian formalism we consider evolution of the ensemble of interacting magnetohydrodynamic cyclones governed with Langevin type equations in the rotating medium. This problem is relevant to the planetary cores where the Rossby numbers are small and geostrophic balance takes place. We show that variations of the heat flux at the outer boundary of the spherical shell modulates frequency of the reversals of the mean magnetic field that is in accordance with the 3D dynamo simulations. Two scenarios of reversals were bserved. Either the axial dipole decreases in favour of quadrupole and then grows in opposite direction or the mean dipole tilts and reverses without decrease of its amplitude.

physics.flu-dyn↗

arXiv2011

Parker's dynamo and geomagnetic reversals

Fluctuations of the alpha-effect which break equatorial symmetry of the flow in the kinematic Parker's dynamo are considered. We show, that even small (a few percents) fluctuation can leed to the substantial assymmetry of the magnetic field in the hemispheres as well as the propagation of the dynamo wave through the equator plane. We also consider how change of the dynamo number can be used to explain different regimes of magnetic field generation in geodynamo.

physics.flu-dyn↗

arXiv2010

Nonlinearity in a dynamo

Using a rotating flat layer heated from below as an example, we consider effects which lead to stabilizing an exponentially growing magnetic field in magnetostrophic convection in transition from the kinematic dynamo to the full non-linear dynamo. We present estimates of the energy redistribution over the spectrum and helicity quenching by the magnetic field. We also study the alignment of the velocity and magnetic fields. These regimes are similar to those in planetary dynamo simulations.

physics.flu-dyn↗

arXiv2010

Direct and inverse cascades in the geodynamo

The rapid rotation of planets causes cyclonic thermal turbulence in their cores which may generate the large-scale magnetic fields observed outside the planets. We consider the model which enables us reproduce the typical features of small-scale geostrophic flows in physical and wave spaces. We present estimates of kinetic and magnetic energy fluxes as a function of the wave number. The joint existence of forward and inverse cascades are demonstrated. We also consider the mechanism of magnetic field saturation at the end of the kinematic dynamo regime.

physics.flu-dyn↗

arXiv2010

Stability problem in dynamo

It is shown, that the saturated $α$-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 $α$. 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 $α$ 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.

physics.flu-dyn↗

arXiv2009

Effects of anisotropy in geostrophic turbulence

The Boussinesq model of convection in a flat layer with heating from below is considered. We analyze the effects of anisotropy caused by rapid rotation in physical and wave spaces and demonstrate the suppression of energy transfer by rotation. We also examine the structure of the wave triangle in nonlinear interaction. The range of parameters is adapted to the models of convection in the geodynamo.

physics.flu-dyn↗

arXiv2003

The Subgrid Problem of the Thermal Convection in the Earth's Liquid Core

The problem of the turbulent thermal convection in the Earth's liquid core is considered. Following assumptions on decreasing of the spatial scales due to the rapid rotation, we propose the subgrid model of the eddy diffusivity, which is used in the large-scale model. This approach makes it possible to model realistic regimes with small Ekman and Rossby numbers ($E\sim 10^{-14}$, $R_o \sim 10^{-8}$) and a sufficiently large Rayleigh number $R_a \sim 10^{12}$. The obtained estimate of the averaged kinetic energy is comparable with observations. The model includes rotation of the solid core due to the viscous torque.

physics.flu-dyn↗

arXiv2003

The shell model approach to the rotating turbulence

Applications of the shell model of turbulence to the case of rapidly rotating bodies are considered. Starting from the classical GOY model we introduce the Coriolis force and obtain a $\sim k^{-2}$ spectrum for 3D hydrodynamical turbulence for the free decay regime as well for the regime with external forcing. Additional modifications of the GOY model providing a realistic form of the helicity are proposed.

physics.flu-dyn↗