Dmitry Krasnov

Numerical study of turbulent magnetohydrodynamic channel flow

Mean flow properties of turbulent magnetohydrodynamic channel flow with electrically insulating channel walls are studied using high-resolution direct numerical simulations. The Lorentz force due to the homogeneous wall-normal magnetic field is computed in the quasi-static approximation. For strong magnetic fields, the mean velocity profile shows a clear three-layer structure consisting of a viscous region near each wall and a plateau in the middle connected by logarithmic layers. This structure reflects the significance of viscous, turbulent, and electromagnetic stresses in the streamwise momentum balance dominating the viscous, logarithmic, and plateau regions, respectively. The width of the logarithmic layers changes with the ratio of Reynolds- and Hartmann numbers. Turbulent stresses typically decay more rapidly away from the walls than predicted by mixing-length models.

Small-scale universality in fluid turbulence

Significance Since the time Kolmogorov postulated the universality of small-scale turbulence, an important research topic has been to experimentally establish it beyond doubt. The likelihood of small-scale universality increases with increasing distance (say, in wave number space) from the nonuniversal large scales. This distance increases as some power of the flow Reynolds number, and so a great deal of emphasis has been put on creating and quantifying very high Reynolds number flows under controlled conditions. The present paper shows that the universal properties of inertial range turbulence (thought to exist only at very high Reynolds numbers) are already present in an incipient way even at modest Reynolds numbers and hence changes the paradigm of research in this field. Turbulent flows in nature and technology possess a range of scales. The largest scales carry the memory of the physical system in which a flow is embedded. One challenge is to unravel the universal statistical properties that all turbulent flows share despite their different large-scale driving mechanisms or their particular flow geometries. In the present work, we study three turbulent flows of systematically increasing complexity. These are homogeneous and isotropic turbulence in a periodic box, turbulent shear flow between two parallel walls, and thermal convection in a closed cylindrical container. They are computed by highly resolved direct numerical simulations of the governing dynamical equations. We use these simulation data to establish two fundamental results: (i) at Reynolds numbers Re ∼ 102 the fluctuations of the velocity derivatives pass through a transition from nearly Gaussian (or slightly sub-Gaussian) to intermittent behavior that is characteristic of fully developed high Reynolds number turbulence, and (ii) beyond the transition point, the statistics of the rate of energy dissipation in all three flows obey the same Reynolds number power laws derived for homogeneous turbulence. These results allow us to claim universality of small scales even at low Reynolds numbers. Our results shed new light on the notion of when the turbulence is fully developed at the small scales without relying on the existence of an extended inertial range.

Magnetohydrodynamic turbulence in a channel with spanwise magnetic field

The effect of a uniform spanwise magnetic field on a turbulent channel flow is investigated for the case of a low magnetic Reynolds number. Direct numerical simulation (DNS) and large eddy simulation (LES) computations are performed for two values of the hydrodynamic Reynolds number (104 and 2×104) and with the Hartmann number varying in a wide range. It is shown that the main effect of the magnetic field is the suppression of turbulent velocity fluctuations and momentum transfer in the wall-normal direction. This leads to drag reduction and transformation of the mean flow profile. The centerline velocity grows, the mean velocity gradients near the wall decrease, and the typical horizontal dimensions of the coherent structures enlarge upon increasing the Hartmann number. Comparison between LES and DNS results shows that the dynamic Smagorinsky model accurately reproduces the flow transformation.

Optimal linear growth in magnetohydrodynamic duct flow

Transient linear growth in laminar magnetohydrodynamic duct flow is analysed. The duct is straight with rectangular cross-section and electrically insulating walls. The applied uniform magnetic field is oriented perpendicular to the mean flow direction and parallel to one of the walls. Optimal perturbations and their maximum amplifications over finite time intervals are computed. The optimal perturbations are increasingly damped by the magnetic field, localized in the boundary layers parallel to the magnetic field irrespective of the duct aspect ratio. Typically, the optimal perturbations have non-vanishing streamwise wavenumber as found in magnetohydrodynamic channel flow with spanwise magnetic field. The Hartmann boundary layers perpendicular to the magnetic field do not contribute to the transient growth.

Optimal growth and transition to turbulence in channel flow with spanwise magnetic field

Instability and transition to turbulence in a magnetohydrodynamic channel flow are studied numerically for the case of a uniform magnetic field imposed along the spanwise direction. Optimal perturbations and their maximum amplifications over finite time intervals are computed in the framework of the linear problem using an iterative scheme based on direct and adjoint governing equations. It is shown that, at sufficiently strong magnetic field, the maximum amplification is no longer provided by classical streamwise rolls, but rather by rolls oriented at an oblique angle to the basic flow direction. The angle grows with the Hartmann number Ha and reaches the limit corresponding to purely spanwise rolls at Ha between 50 and 100 depending on the Reynolds number. Direct numerical simulations are applied to investigate the transition to turbulence at a single subcritical Reynolds number Re = 5000 and various Hartmann numbers. The transition is caused by the transient growth and subsequent breakdown of optimal perturbations, which take the form of one or two symmetric optimal modes (streamwise, oblique or spanwise modes depending on Ha) with low-amplitude three-dimensional noise added at the moment of strongest energy amplification. A sufficiently strong magnetic field (Ha larger than approximately 30) is found to completely suppress the instability. At smaller Hartmann numbers, the transition is observed but it is modified in comparison with the pure hydrodynamic case.

Large-scale intermittency of liquid-metal channel flow in a magnetic field

We predict a novel flow regime in liquid metals under the influence of a magnetic field. It is characterized by long periods of nearly steady, two-dimensional flow interrupted by violent three-dimensional bursts. Our prediction has been obtained from direct numerical simulations in a channel geometry at low magnetic Reynolds number and translates into physical parameters which are amenable to experimental verification under laboratory conditions. The new regime occurs in a wide range of parameters and may have implications for metallurgical applications.

Instability of magnetohydrodynamic flow in an annular channel at high Hartmann number

Instability of a flow of an electrically conducting fluid in an annular channel is analyzed. Strong constant magnetic field is imposed in the axial direction. Similarly to toroidal duct experiments, the flow is driven by the azimuthal Lorentz force resulting from the interaction between the magnetic field and the radial electric currents created by a difference of electric potential imposed between the cylinders. The instability of the base flow, while clearly of centrifugal nature, is significantly different from the Dean instability detected earlier in hydrodynamic systems and similar MHD systems at low and moderate magnetic fields. Growing perturbations are oscillating and axisymmetric and consist of counter-rotating toroidal vortices arranged side by side in the radial direction and having meridional cross-sections in the form of elongated ellipses oriented slightly obliquely to the axial direction. Simulations of the secondary flow show an interesting feature of periodic transitions between two symmetric solutions.

Electromagnetic drag on a magnetic dipole near a translating conducting bar

The electromagnetic drag force and torque acting on a magnetic dipole due to the translatory motion of an electrically conducting bar with square cross section and infinite length is computed by numerical analysis for different orientations and locations of the dipole. The study is motivated by the novel techniques termed Lorentz force velocimetry and Lorentz force eddy current testing for noncontact measurements of the velocity of a conducting liquid and for detection of defects in the interior of solid bodies, respectively. The present, simplified configuration provides and explains important scaling laws and reference results that can be used for verification of future complete numerical simulations of more realistic problems and complex geometries. The results of computations are also compared with existing analytical solutions for an infinite plate and with a newly developed asymptotic theory for large distances between the bar and the magnetic dipole. We finally discuss the optimization problem of f...

Statistics of the energy dissipation rate and local enstrophy in turbulent channel flow

Abstract Using high-resolution direct numerical simulations, the height and Reynolds number dependence of high-order statistics of the energy dissipation rate and local enstrophy are examined in incompressible, fully developed turbulent channel flow. The statistics are studied over a range of wall distances, spanning the viscous sublayer to the channel flow centerline, for friction Reynolds numbers R e τ = 180 and R e τ = 381 . The high resolution of the simulations allows dissipation and enstrophy moments up to fourth order to be calculated. These moments show a dependence on wall distance, and Reynolds number effects are observed at the edge of the logarithmic layer. Conditional analyses based on locations of intense rotation are also carried out in order to determine the contribution of vortical structures to the dissipation and enstrophy moments. Our analysis shows that, for the simulation at the larger Reynolds number, small-scale fluctuations of both dissipation and enstrophy show relatively small variations for z + ≳ 100 .

Statistics of velocity gradients in wall-bounded shear flow turbulence

Abstract The statistical properties of velocity gradients in a wall-bounded turbulent channel flow are discussed on the basis of three-dimensional direct numerical simulations. Our analysis is concentrated on the trend of the statistical properties of the local enstrophy ω 2 ( x , t ) and the energy dissipation rate ϵ ( x , t ) with increasing distance from the wall. We detect a sensitive dependence of the largest amplitudes of both fields (which correspond with the tail of the distribution) on the spectral resolution. The probability density functions of each single field as well as their joint distribution vary significantly with increasing distance from the wall. The largest fluctuations of the velocity gradients are found in the logarithmic layer. This is in agreement with recent experiments which observe a bursting of hairpin vortex packets into the logarithmic region.