O. G. Chkhetiani

The role of helicity in turbulent MHD flows

We have studied the behavior of a helical homogeneous small-scale MHD turbulent flow under the influence of a weak inhomogeneous large-scale disturbance. We have shown that turbulent energy redistribution in the presence of nonzero helicity occurs mainly over large scales. Helicity increases correlation time, leading to the weakening of a direct cascade and to the formation of steep spectra over small scales, with simultaneous turbulent energy growth over large scales. Furthermore, an expression for the effective viscosity of the mean flow is derived. It is shown that the magnetic field, in addition to the helicity, reduces the effective viscosity of the medium. This may be important in the study of MHD flow around obstacles in the presence of an external magnetic field.

Helicity generation in turbulent MHD flows

We study turbulent flow of a conducting liquid in a uniform external magnetic field. It is shown that intense helicity generation is possible in the presence of a mean shear flow. It is noted that even though the mean helicity of the initial flow can be zero, the presence of internal topological structure of the flow, for example the presence of helicity of different signs at different scales, is nevertheless necessary for helicity generation.

On the diffusion and clustering of a magnetic field in random velocity fields

We have derived an equation for the probability density of the magnetic energy in a random Gaussian, delta-correlated in time, divergent velocity field in the absence of molecular diffusion effects. Basic statistical characteristics of the energy have been calculated using this equation. Based on the ideas of statistical topography, we have studied the processes of magnetic field amplification in space and, in particular, the conditions for the formation of a cluster structure. These phenomena are coherent, occur with a probability equal to unity, and, hence, manifest themselves almost in all individual realizations of the process. The clustering effect is demonstrated with an exact solution for the magnetic field dynamics for the simplest model of a random divergent velocity field.

Helicity and potential vorticity in surface turbulence

An experimental measurement of all three components of the velocity and vorticity vectors, as well as the temperature and its gradient, and potential vorticity, has been described using four acoustic anemometers. Anemometers were placed at vertices of a tetrahedron, the horizontal base of which was a rectangular triangle with equal legs, and the upper point was exactly above the top of the right angle. The distance from the surface to the tetrahedron its base was 5.5 m, and the lengths of legs and a vertical edge were 5 m. A covariance–correlation matrix for turbulent variations in all measured values has been calculated. In the daytime horizontal and vertical components of the helicity are of the order of–0.03 and +0.01 m s–2, respectively. The nighttime signs remain unchanged, but the absolute values are several times smaller. The cospectra and spectral correlation coefficients have been calculated for all helicity components. The time variations in the components of “instantaneous” helicity and potential vorticity are demonstrated.

Inverse energy cascade in developed turbulence at the breaking of the symmetry of helical modes

The interactions breaking the symmetry of the positive and negative components of the total helicity have been considered with quasinormal approximations and the cascade model of helical turbulence. In the ideal case of the absence of one of them, the equations have two sign-definite integrals of motion; as a result, an inverse energy cascade occurs, as for two-dimensional turbulence. Owing to the instability of the second moments, whose mechanism was proposed in A. Belian, O. Chkhetiani, E. Golbraikh, and S. Moiseev, Physica A 258, 55 (1998), the generation of large-scale modes has been considered within the Fourier equations of hydrodynamics under the assumption of a quasinormal velocity field. The presence of background turbulence with large-scale helical perturbations and small-scale sources of the energy and helicity is a determining circumstance in this mechanism. The possibility of the inverse cascade in the case of incomplete degeneracy of one of the helicity components has been studied in the numerical experiments with the cascade model. It has been shown that the existence of the inverse (toward large scales) energy flux from small-scale perturbations requires a certain external-action-generated level of helical noise in large modes, which depends on the degree of “mixing” of different-sign helical components of the velocity field.

Structure functions of quasi-two-dimensional turbulence in a laboratory experiment

The results of experiments for turbulent flows in a thin layer of conducting fluid above a solid surface generated by the Ampere force when passing a current and under the action of a spatially periodic magnetic field are considered. The statistical characteristics of the flows are shown to exhibit three-dimensional (3D) dynamics even on horizontal scales exceeding the layer thickness by an order of magnitude. In this case, the third-order longitudinal structure functions of the velocity field are approximately linear in spatial displacement and negative, as in 3D turbulence, due to the dominant contribution of energy dissipation when the boundary condition for adhesion on the lower surface is met. The dissipation and basic energy production terms are estimated for the energy balance equation.

Experimental manifestation of vortices and Rossby wave blocking at the MHD excitation of quasi-two-dimensional flows in a rotating cylindrical vessel

Experiments on the excitation of counterpropagating zonal flows by the magnetohydrodynamic (MHD) method in a rotating cylindrical vessel with a conic bottom have been performed. Flows appear in a conducting fluid layer in the field of ring magnets under the action of a radial electric field. The velocity fields have been reconstructed by the particle image velocimetry (PIV) method. In the fast rotation regimes with a thin fluid layer, where the Rossby-Obukhov scale does not exceed the characteristic sizes of the vessel, the system of perturbations appears with almost immobile blocked anticyclones in the outer part of the flow and rapidly moving cyclones in the main stream. The diagram of regimes is plotted in the variables of the relative angular velocities of the averaged zonal flow and transfer of vortices about the system rotation axis. Attention is focused on the results for the regions of the diagram with slow motion of vortices with respect to the rotating coordinate system near the parameters for stationary Rossby waves (blocking of circulation). The results are compared to the results previously obtained in similar experiments using the source-sink method.

Estimating helicity in the atmospheric boundary layer from acoustic sounding data

Distributions of the velocity-field helicity in the atmospheric boundary layer have been obtained from acoustic sounding data. The helicity of large-scale motions (0.3–0.6 m/s2) exceeds (by an order of magnitude) its independently measured turbulent values, which are close to helicity averaged over the layer (0.02–0.12 m/s2). In the absence of strong convection, there is good correlation between helicity and wind velocity squared at upper sounding levels of 400 to 600 m.

Generation of thermal wind over a nonuniformly heated wavy surface

The problem of stationary convective flows over a nonuniformly heated wavy surface is studied in the context of a simplified analytical model. It is shown that the horizontally periodic heating of such a surface can lead to a “thermal wind” effect, i.e., the generation of a uniform horizontal flow far from the surface.

Decay of helicity in homogeneous turbulence

The self-similar relaxation of helicity in homogeneous turbulence has been considered taking into account integral invariants ∫0∞rm 〈u(x)ω(x + r)〉 dr = Imh (where ω = curlu and r = |r|). It has been shown that integral invariants with m = 3 for both helicity and energy are possible in addition to helical analogs of Loitsyanskii (m = 4) and Birkhoff-Saffman (m = 2) invariants associated with the conservation laws of momentum and angular momentum, respectively. Helicity always relaxes more rapidly than the energy. Its decay exponent is in the interval from −3/2 to −5/2 versus the interval from −6/5 to −10/7 for the energy.