Peter Frick

Long-term numerical simulations of turbulent Rayleigh–Bénard convection of an incompressible fluid with Pr=0.7 in a cylindrical cell of unit aspect ratio and moderate Rayleigh number Ra=108 are performed to analyze the dynamics of reorientations in large-scale circulation (LSC). Special attention is paid to the comparative analysis of the vertical component of the integral angular momentum (mean azimuthal flow) and the characteristics of the LSC, including its intensity, orientation, and angular velocity. Observed rotations of the LSC plane occur either without a significant decrease in LSC intensity, or with cessation of LSC followed by LSC regeneration in a random direction. A pattern common to all reorientations has been revealed—the lower the intensity of the circulation, the higher the angular velocities of the LSC plane rotation. It is shown that the rotation of the LSC plane does not correlate with the mean azimuthal rotation of the fluid, the magnitude of which fluctuates randomly, changing sign. Moreover, unlike the cubic cell, the reorientation is not accompanied by a noticeable increase in the angular momentum. Thus, the reorientation of the LSC in a cylindrical cell is not associated with the azimuthal rotation of the fluid. Furthermore, the characteristics of the LSC follow those of the buoyancy force moment with a short time delay.

Based on the data recorded during the Parker Solar Probe mission, it can be suggested that there is no balance between kinetic and magnetic energy in the vicinity of the Sun. The spectra collected at different radial distances show an energy transfer from one component to another, followed by a change in inertial range slope and large-scale break shifted towards lower wave numbers. Using the shell (cascade) modeling approach, we attempt to explain and understand this observed spectra transformation, considering a free-decay turbulence process and modeling a simple transition to a quasistationary equilibrium between the magnetic and kinetic energies. Varying the parameters of turbulence mirror asymmetry (helicity), we numerically simulate changes in spectral indexes, large-scale shift position, and inertial range transformations, comparing our model results with spacecraft observations of solar wind turbulence. We present and discuss the chaotic nature of the spectral magnetic helicity distributions, as well as the fact that helicity can accumulate at large scales. The applicability of a simple magnetohydrodynamics shell model to repeat the key features of solar wind turbulence dynamics offers wide possibilities for its further use.

The stability of a flow of an electrically conducting, incompressible fluid in a channel with an imposed uniform wall-normal magnetic field and electrically insulating walls is studied using linear stability analysis and direct numerical simulations. The novelty of the system, which differentiates it from the classical Hartmann channel flow, is that, as in some technological applications of liquid metals, the electric conductivity and viscosity of the fluid vary across the channel. This variation is found to have a strong influence on the stability characteristics of the flow. Specifically, a linear variation in electric conductivity significantly alters the base velocity profile, leading to pronounced asymmetry and the development of inflection points. When this transformation is sufficiently strong, the flow becomes linearly unstable at Reynolds numbers much lower than the threshold for the linear instability of the Hartmann channel flow. The instability exhibits distinct features: a large typical axial wavelength and the localization of perturbation growth in the channel core. The resulting transition to turbulence is demonstrated in direct numerical simulations.

A parametric study of two-disk dynamo is carried out in three-dimensional parameter spaces: the magnetic Prandtl number Pm (the ratio of viscous to Ohmic dissipation), the dimensionless dissipation μ, and the ratio α of torques applied to two disks. At Pm of the order of unity, chaotic solutions do not exist at all. Small inclusions of chaotic modes appear at Pm∼0.1. A further decrease in Pm leads to the formation of a wideband of chaos in the (μ,α) plane with superimposed oblique windows of stationary solutions. The rare-reversal chaos is a regime characterized by long-lived quasi-stationary states with weak oscillations of variables, ending with a sharp burst of oscillations with a possible transition to the other stationary solution and corresponding change of field polarity, i.e., a reversal. This regime was detected at Pm≤0.0001 only in a narrow domain. The longest time interval of constant polarity was observed in simulations for Pm=1.37×10−9, α=1.1, and μ=5.39 lasts 9000 dimensionless units of time. It has been found that, in a two-disk dynamo system, for any chaotic mode, there is an unambiguous dependence of the current oscillation amplitude on the time remaining until the next field reversal. Thus, despite the fact that the duration of each interval is a random value, at any stage of the field evolution, for a known set of governing parameters, it is possible to determine the time of the next reversal by recording the current amplitude of oscillations.

The dependence of reconstructed velocity fields on time delays for two cases with different types of tracers in a typical nozzle flow is studied. Cases with water droplets that vary substantially in size and small oil droplets are considered. Increasing the initial interrogation window has been shown to be quite efficient for reconstructing the velocity field in cases of relatively large time delays exceeding the optimal time delay value. It is shown that the loss of information with an increase in time delay is a gradual process.

Liquid metal flows generated in a cylindrical cell by the alternating magnetic field of a continuous or a sectioned inductor are studied numerically. It is found that the inductor parameters significantly affect the energy distribution of liquid metal velocity fluctuations. The more intense fluctuations are shift to the cell ends and the intensity of the fluctuations decreases as the inductor length increases. Using a sectioned inductor consisting of a set of solenoids accumulates the effect of the end boundaries of each section and generates an intense flow distributed over a cylindrical cell. A sufficiently uniform distribution of the velocity fluctuation field along the cell can be obtained without increasing the total number of ampere turns.

The boundary conditions at the Earth’s surface have a significant influence on the planetary and synoptic scale flows that form in the atmosphere. In the Earth’s real atmosphere, it is difficult to isolate and study the influence of boundary conditions, because the spatial structure of large-scale flows and their temporal variations are strongly influenced by the distribution of land and ocean, surface relief, the hydrological cycle, and other factors. It is possible to study the role of the underlying surface using idealized models of Earth-like planets. This paper presents a comparative analysis of the structure and dynamics of the atmospheric general circulation and baroclinic waves for idealized, zonally homogeneous planets. Numerical experiments are performed using the WRF-ARW software package for the built-in characteristics of the Earth’s atmosphere and the terrestrial parameters of planetary motion and insolation. Three model configurations are considered: a desert planet (DP), a desert planet with an equatorial ocean (EOP), and an aquaplanet (AP) with a fixed meridional temperature distribution. It is shown that the DP is characterized by strong seasonal variations, leading to remarkable features both in the structure of the mean general circulation and in the distribution of velocity and temperature pulsations. On an EOP, the meridional velocity and temperature pulsations are similar to those observed in the Earth’s atmosphere. They are concentrated at midlatitudes and separated by height, with the maximum of temperature pulsations in the lower part of the troposphere and the maximum of velocity in its upper part. On the AP, the temperature pulsations are significantly smaller in amplitude and shifted into the middle layers of the troposphere. Simulations have shown that, despite zonally homogeneous boundary conditions and the absence of relief, the intensity, lifetime, phase, and group velocity of the baroclinic waves vary significantly on all the model planets. On a DP and an EOP, there is a pronounced season of maximum wave activity. On the AP, there are no strong seasonal variations, but long intervals of westward blocking are observed. The spectral composition of the baroclinic waves and their seasonal variability have been analyzed.

We investigate small-scale magnetic energy generation in a turbulent conducting flow using two different approaches. One is based on the Kazantsev-Kraichnan (KK) model, developed for a random velocity field with short time correlations, and the other uses the shell magnetohydrodynamic (MHD) method, which describes a turbulent energy cascade on a finite number of spectral shells. We consider only the kinematic (linear) regime and show an exponential growth of magnetic energy for sufficiently large magnetic Reynolds numbers (Rm) in both approaches. By comparing the dependencies of the growth rates at different Rm, we try to answer the question how the model assumptions-of short time correlations or of finite spectral shells-affect the turbulent dynamo possibility and the position of the Rm threshold at which this generation starts. We analyze the generation behavior at different Reynolds and magnetic Prandtl numbers, which are not explicitly included in the KK model but taken into account in the shell approach. Based on the obtained results, we try to discuss why the small-scale generation has not been observed in real MHD dynamo experiments so far.