arXiv subjects

Dmitry Krasnov

Publications and source records attributed to Dmitry Krasnov.

At least 19 recordsLinked to original sources

arXiv2026

Vortex promoters in MHD duct flow

We use 3D direct numerical simulations to study the effects of vortex promoters in liquid metal duct flow to sustain Q2D states which are formed in the presence of strong magnetic fields, such as those present in cooling blankets of fusion reactors. Both for electrically insulating and conducting walls. In case of insulating walls, disturbances are found to be sustained. For conducting walls, the disturbances may be extinguished immediately and replaced by a Walker- or Hunt-type flow with its own jet-detachment instability. Furthermore, we add heat transfer by imposing constant heat flux at the Shercliff walls. We classify and compare possible configurations with respect to their turbulent transport properties. For conducting ducts, no additional effect is observed. For insulating ducts in horizontal position, we observe a small effect. For vertical ducts, the buoyancy forces have a significant impact due to buoyancy-driven instabilities, which produce intermittent fluctuations. The analysis of the turbulent kinetic energy (TKE) and the Nusselt number show that flows with the largest TKE may not have the best heat transfer performance. This is caused by side jets removing heat faster than mixing the bulk flow. The buoyancy force and wall conductance ratio are found to play a key role in determining the flow structure. Part of our work is a parametric study at fixed Reynolds, Hartmann and Prandtl numbers, which allows us eventually to compose a phase diagram showcasing the different flow regimes.

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arXiv2026

Heat transport in magnetohydrodynamic duct flow regimes with conducting and insulating walls

The flow of a liquid metal (LM) in a rectangular duct segment, subject to a uniform transverse magnetic field and uniform heating at the side walls is explored in an ample parameter space using Direct Numerical Simulation (DNS). We modify electrical wall conductivity, (either highly conducting or perfectly insulating) and investigate the effects of the buoyancy force, both in horizontally and vertically orientated ducts. In the latter case, it may be directed either with the flow or against the flow, creating backflow regions. In this parameter space and with the presence of vortex promoters at the inlet of the duct we identify $4$ types of flow. We calculate the Nusselt number $Nu(t)$ for each of them and study the statistical properties to compare their heat transfer capabilities in future fusion reactor blankets.

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arXiv2025

Inflection point instability in Hartmann channel flow with variable electric conductivity

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 characteristics of this instability suggest a mechanism similar to the classical inviscid inflection-point instability of one-dimensional velocity profiles. The resulting transition to turbulence is demonstrated in direct numerical simulations.

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arXiv2025

Scale-resolved turbulent Prandtl number for Rayleigh-B\'{e}nard convection at $\boldsymbol{Pr =10^{-3}}$

We present a framework to calculate the scale-resolved turbulent Prandtl number $Pr_t$ for the well-mixed and highly inertial bulk of a turbulent Rayleigh-B\'{e}nard mesoscale convection layer at a molecular Prandtl number $Pr=10^{-3}$. It builds on Kolmogorov's refined similarity hypothesis of homogeneous isotropic fluid and passive scalar turbulence, based on log-normally distributed amplitudes of kinetic energy and scalar dissipation rates that are coarse-grained over variable scales $r$ in the inertial subrange. Our definition of turbulent (or eddy) viscosity and diffusivity does not rely on mean gradient-based Boussinesq closures of Reynolds stresses and convective heat fluxes. Such gradients are practically absent or indefinite in the bulk. The present study is based on direct numerical simulation of plane-layer convection at an aspect ratio of $\Gamma=25$ for Rayleigh numbers $10^5\leq Ra \leq 10^7$. We find that the turbulent Prandtl number is effectively up to 4 orders of magnitude larger than the molecular one, $\Pr_t\sim 10$. This holds particularly for the upper end of the inertial subrange, where the eddy diffusivity exceeds the molecular value, $\kappa_e(r)>\kappa$. Highly inertial low-Prandtl-number convection behaves effectively as a high-Prandtl number flow, which also supports previous models for the prominent application case of solar convection.

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arXiv2025

Turbulent mesoscale convection in the Boussinesq limit and beyond

Mesoscale convection covers an intermediate scale range between small-scale turbulence and the global organization of the convection flow. It is often characterized by an order of the convection patterns despite very high Rayleigh numbers and strong turbulent fluctuations. In this review, we discuss several aspects of mesoscale convection, which have been investigated by three-dimensional direct numerical simulations. The numerical studies are performed in a characteristic configuration of a plane layer that is heated from below and cooled from above or subject to constant heat flux at the top and bottom boundaries. We discuss the role of the thermal and mechanical boundary conditions for structure formation and study the impact of the domain shape as well as the Prandtl number. With respect to the latter, we focus on low values that arise in astrophysical convection and are partly not anymore accessible in laboratory experiments with liquid metals. Beside these experiments in the Boussinesq approximation, we report studies of non-Boussinesq mesoscale convection. This is done by investigating effects of compressibility and temperature dependence of material properties. The kinetic energy dissipation rate turns out to remain a central quantity for the turbulent mixing in compressible convection. Their different components, statistics, relation to the turbulent viscosity, and the multifractal properties are discussed.

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arXiv2024

Magnetoconvection in a Long Vertical Enclosure With Walls of Finite Electrical Conductivity

Magnetoconvection in a tall vertical box with vertical hot and cold walls, and an imposed steady uniform magnetic field perpendicular to the temperature gradient, is analyzed numerically. The geometry and the values of the non-dimensional parameters - the Prandtl number of 0.025, the Rayleigh number of $7.5 \times 10^5$, and the Hartmann number between 0 and 798 - match those of an earlier experiment. A parametric study of the effect of wall electric conductivity, across a wide range of conductance ratio values, on flow properties is performed. Two configurations of electric boundary conditions are explored. In one configuration, all walls have finite electric conductivity, while in the other, only the walls with constant temperature are electrically conducting. The flows are analyzed using their integral properties and distributions of velocity, temperature, and electric currents. It is found that, in general, the convection flow is suppressed by the magnetic field. However, this effect is strongly modified by the wall's electric conductivity and is markedly different for the two wall configurations. The associated changes in flow structure, rate of heat transfer, and flow's kinetic energy are revealed. It is also shown that the assumption of quasi-two-dimensionality may not be valid under some conditions, even at high Hartmann numbers.

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arXiv2023

Wall-attached convection under strong inclined magnetic fields

We employ a linear stability analysis and direct numerical simulations to study the characteristics of wall-modes in thermal convection in a rectangular box under strong and inclined magnetic fields. The walls of the convection cell are electrically insulated. The stability analysis assumes periodicity in the spanwise direction perpendicular to the plane of the homogeneous magnetic field. Our study shows that for a fixed vertical magnetic field, the imposition of horizontal magnetic fields results in an increase of the critical Rayleigh number along with a decrease in the wavelength of the wall modes. The wall modes become tilted along the direction of the resulting magnetic fields and therefore extend further into the bulk as the horizontal magnetic field is increased. Once the modes localized on the opposite walls interact, the critical Rayleigh number decreases again and eventually drops below the value for onset with a purely vertical field. We find that for sufficiently strong horizontal magnetic fields, the steady wall modes occupy the entire bulk and therefore convection is no longer restricted to the sidewalls. The above results are confirmed by direct numerical simulations of the nonlinear evolution of magnetoconvection.

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arXiv2023

Simulation of magnetohydrodynamic flows of liquid metals with heat transfer or magnetic stirring

We discuss the effects of nonhomogeneous magnetic fields in liquid metal flows in two different configurations. In the first configuration, we briefly report the impact of fringing magnetic fields in a turbulent Rayleigh-B{é}nard convection setup, where it was shown that the global heat transport decreases with an increase of fringe-width. The convective motion in regions of strong magnetic fields is confined near the sidewalls. In the second configuration, we numerically study the effects of an oscillating magnetic obstacle with different frequencies of oscillation on liquid metal flow in a duct. The Reynolds number is low such that the wake of the stationary magnetic obstacle is steady. The transverse oscillation of the magnet creates a sinusoidal time-dependent wake reminiscent of the vortex shedding behind solid obstacles. We examine the behavior of the streamwise and spanwise components of the Lorentz forces as well as the work done by the magnets on the fluid. The frequency of the oscillation of the streamwise component of Lorentz force is twice that of the spanwise component as in the case of lift and drag on solid cylindrical obstacles. The total drag force and the energy transferred from the magnets to the fluid show a non-monotonic dependence on the frequency of oscillation of the magnetic obstacle indicative of a resonant excitation of the sinusoidal vortex shedding.

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arXiv2023

Effects of strong fringing magnetic fields on turbulent thermal convection

We study the influence of fringing magnetic fields on turbulent thermal convection in a horizontally extended rectangular domain. The magnetic field is created in the gap between two semi-infinite planar magnetic poles, with the convection layer located near the edge of the gap. We employ direct numerical simulations in this setup for fixed Rayleigh and small Prandtl numbers, but vary the fringe-width by controlling the gap between the magnetic poles and the convection cell. The magnetic field generated by the magnets is strong enough to cease the flow in high magnetic flux region of the convection cell. We observe that as the local vertical magnetic field strength increases, the large scale structures become thinner and align themselves perpendicular to the longitudinal sidewalls. We determine the local Nusselt and Reynolds numbers as functions of the local Hartmann number (based on the vertical component of the magnetic field) and estimate the global heat and momentum transport. We show that the global heat transport decreases with increasing fringe-width for strong magnetic fields but increases with increasing fringe-width for weak magnetic fields. In the regions of large vertical magnetic fields, the convective motion becomes confined to the vicinity of the sidewalls. The amplitudes of these wall modes show a non-monotonic dependence on the fringe-width.

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arXiv2022

Similarities between characteristics of convective turbulence in confined and extended domains

To understand turbulent convection at very high Rayleigh numbers typical of natural phenomena, computational studies in slender cells are an option if the needed resources have to be optimized within available limits. However, the accompanying horizontal confinement affects some properties of the flow. Here, we explore the characteristics of turbulent fluctuations in the velocity and temperature fields in a cylindrical convection cell of aspect ratio 0.1 by varying the Prandtl number $Pr$ between 0.1 and 200 at a fixed Rayleigh number $Ra = 3 \times 10^{10}$, and find that the fluctuations weaken with increasing $Pr$, quantitatively as in aspect ratio 25. The probability density function (PDF) of temperature fluctuations in the bulk region of the slender cell remains mostly Gaussian, but increasing departures occur as $Pr$ increases beyond unity. We assess the intermittency of the velocity field by computing the PDFs of velocity derivatives and of the kinetic energy dissipation rate, and find increasing intermittency as $Pr$ decreases. In the bulk region of convection, a common result applicable to the slender cell, large aspect ratio cells, as well as in 2D convection, is that the turbulent Prandtl number decreases as $Pr^{-1/3}$.

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arXiv2022

Convective mesoscale turbulence at very low Prandtl numbers

Horizontally extended turbulent convection, termed mesoscale convection in natural systems, remains a challenge to investigate in both experiments and simulations. This is particularly so for very low molecular Prandtl numbers as in stellar convection and in Earth's outer core. The present study reports three-dimensional direct numerical simulations of turbulent Rayleigh-Bénard convection in square boxes of side length $L$ and height $H$ with the aspect ratio $Γ=L/H$ of 25, for Prandtl numbers that span almost 4 orders of magnitude, $10^{-3}\le Pr \le 7$, and Rayleigh numbers $10^5 \le Ra \le 10^7$, obtained by massively parallel computations on grids of up to $5.36\times 10^{11}$ points. The low end of this $Pr$-range cannot be accessed in controlled laboratory measurements. We report the essential properties of the flow and their trends with Rayleigh and Prandtl numbers, in particular the global transport of momentum and heat -- the latter decomposed into convective and diffusive contributions -- across the convection layer, mean vertical profiles of the temperature and temperature fluctuations, and the kinetic energy and thermal dissipation rates. We also explore the degree to which the turbulence in the bulk of the convection layer resembles classical homogeneous and isotropic turbulence in terms of spectra, increment moments, and dissipative anomaly, and find close similarities. Finally, we show that a characteristic scale on the order of the mesoscale seems to saturate to a wavelength of $λ\gtrsim 3H$ for $Pr\lesssim 0.005$. We briefly discuss possible implications of these results for the development of subgrid scale parameterization of turbulent convection.

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arXiv2020

Rayleigh-Bénard Convection in Strong Vertical Magnetic Field: Flow Structure and Verification of Numerical Method

Direct numerical simulations are performed to study turbulent Rayleigh-Bénard convection in a vertical cylindrical cavity with uniform axial magnetic field. Flows at high Hartmann and Rayleigh numbers are considered. The calculations reveal that, similarly to the behavior observed in Rayleigh-Bénard convection with strong rotation, flows at strong magnetic field develop a central vortex, while the heat transfer is suppressed.

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arXiv2020

Turbulent Rayleigh-Bénard convection in a strong vertical magnetic field

Direct numerical simulations are carried out to study flow structure and transport properties in turbulent Rayleigh-Bénard convection in a cylindrical cell of aspect ratio one with an imposed axial magnetic field. Flows at the Prandtl number 0.025 and the Rayleigh and Hartmann numbers up to $10^9$ and 1400 are considered. The results are consistent with those of earlier experimental and numerical data. As anticipated, the heat transfer rate and kinetic energy are suppressed by strong magnetic field. At the same time, their growth with the Rayleigh number is found to be faster in flows at high Hartmann numbers. This behaviour is attributed to the newly discovered flow regime characterized by prominent quasi two-dimensional structures reminiscent of vortex sheets observed earlier in simulations of magnetohydrodynamic turbulence. Rotating wall modes similar to those in the Rayleigh-Bénard convection with rotation are found in flows near the Chandrasekhar linear stability limit. Detailed analysis of the spatial structure of the flows and its effect of global transport properties is reported.

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arXiv2019

Decay of turbulence in a liquid metal duct flow with transverse magnetic field

Decay of honeycomb-generated turbulence in a duct with a static transverse magnetic field is studied via direct numerical simulations. The simulations follow the revealing experimental study of Sukoriansky et al. (1986), in particular the paradoxical observation of high-amplitude velocity fluctuations, which exist in the downstream portion of the flow when the strong transverse magnetic field is imposed in the entire duct including the honeycomb exit, but not in other configurations. It is shown that the fluctuations are caused by the large-scale quasi-two-dimensional structures forming in the flow at the initial stages of the decay and surviving the magnetic suppression. Statistical turbulence properties, such as the energy decay curves, two-point correlations and typical length scales are computed. The study demonstrates that turbulence decay in the presence of a magnetic field is a complex phenomenon critically depending on the state of the flow at the moment the field is introduced.

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arXiv2018

Wall modes in magnetoconvection at high Hartmann numbers

Three-dimensional turbulent magnetoconvection at a Rayleigh number of $Ra=10^7$ in liquid gallium at a Prandtl number $Pr=0.025$ is studied in a closed square cell for very strong external vertical magnetic fields $B_0$ in direct numerical simulations which apply the quasistatic approximation. As $B_0$ or equivalently the Hartmann number $Ha$ are increased, the convection flow that is highly turbulent in the absence of magnetic fields crosses the Chandrasekhar linear stability limit for which thermal convection is ceased in an infinitely extended layer and which can be assigned with a critical Hartmann number $Ha_{\rm c}$. Similar to rotating Rayleigh-Bénard convection, our simulations reveal subcritical sidewall modes that maintain a small but finite convective heat transfer for $Ha>Ha_{\rm c}$. We report a detailed analysis of the complex two-layer structure of these wall modes, their extension into the cell interior and a resulting sidewall boundary layer composition that is found to scale with the Shercliff layer thickness.

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arXiv2018

Koopman analysis of the long-term evolution in a turbulent convection cell

We analyse the long-time evolution of the three-dimensional flow in a closed cubic turbulent Rayleigh-Bénard convection cell via a Koopman eigenfunction analysis. A data-driven basis derived from diffusion kernels known in machine learning is employed here to represent a regularized generator of the unitary Koopman group in the sense of a Galerkin approximation. The resulting Koopman eigenfunctions can be grouped into subsets in accordance with the discrete symmetries in a cubic box. In particular, a projection of the velocity field onto the first group of eigenfunctions reveals the four stable large-scale circulation (LSC) states in the convection cell. We recapture the preferential circulation rolls in diagonal corners and the short-term switching through roll states parallel to the side faces which have also been seen in other simulations and experiments. The diagonal macroscopic flow states can last as long as a thousand convective free-fall time units. In addition, we find that specific pairs of Koopman eigenfunctions in the secondary subset obey enhanced oscillatory fluctuations for particular stable diagonal states of the LSC. The corresponding velocity field structures, such as corner vortices and swirls in the midplane, are also discussed via spatiotemporal reconstructions.

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arXiv2016

Heat and momentum transfer for magnetoconvection in a vertical external magnetic field

The scaling theory of Grossmann and Lohse (J. Fluid Mech. 407, 27 (2000)) for the turbulent heat and momentum transfer is extended to the magnetoconvection case in the presence of a (strong) vertical magnetic field. The comparison with existing laboratory experiments and direct numerical simulations in the quasistatic limit allows to restrict the parameter space to very low Prandtl and magnetic Prandtl numbers and thus to reduce the number of unknown parameters in the model. Also included is the Chandrasekhar limit for which the outer magnetic induction field B is large enough such that convective motion is suppressed and heat is transported by diffusion. Our theory identifies four distinct regimes of magnetoconvection which are distinguished by the strength of the outer magnetic field and the level of turbulence in the flow, respectively.

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arXiv2015

A hybrid finite-difference/boundary element procedure for the simulation of turbulent MHD duct flow at finite magnetic Reynolds numbers

A conservative coupled finite difference-boundary element computational procedure for the simulation of turbulent magnetohydrodynamic flow in a straight rectangular duct at finite magnetic Reynolds number is presented. The flow is assumed to be periodic in the streamwise direction and is driven by a mean pressure gradient. The duct walls are considered to be electrically insulating. The co-evolution of the velocity and magnetic fields as described respectively by the Navier-Stokes and the magnetic induction equations, together with the coupling of the magnetic field between the conducting domain and the non-conducting exterior is solved using the magnetic field formulation. The aim is to simulate localized magnetic fields interacting with turbulent duct flow. Detailed verification of the implementation of the numerical scheme is conducted in the limiting case of low magnetic Reynolds number by comparing with the results obtained using a quasistatic approach that has no coupling with the exterior. The rigorous procedure with non-local magnetic boundary conditions is compared versus simplified pseudo-vacuum boundary conditions and the differences are quantified. Our first direct numerical simulations of turbulent Hartmann duct flow at moderate magnetic Reynolds numbers and a low flow Reynolds number show significant differences in the duct flow turbulence, even at low interaction level between the flow and magnetic field

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