Session A8: Magnetohydrodynamics

Elevator mode convection in liquid metal blankets for fusion reactors

The work is motivated by the design of liquid-metal blankets for nuclear fusion reactors. Mixed convection in a downward flow in a vertical duct with strong contant-rate heating of one wall (the Grashof number up to $10^{12}$) and strong transverse magnetic field (the Hartmann number up to $10^4$) is considered. It is found that in an infinitely long duct the flow is dominated by exponentially growing elevator modes having the form of a combination of ascending and descending jets. An analytical solution approximating the growth rate of the modes is derived. Analogous flows in finite-length pipes and ducts are analyzed using the high-resolution numerical simulations. The results of the recent experiments are reproduced and explained. It is found that the flow evolves in cycles consisting of periods of exponential growth and breakdowns of the jets. The resulting high-amplitude fluctuations of temperature is a feature potentially dangerous for operation of a reactor blanket.   

Thermal convection in a horizontal duct with strong axial magnetic field

The work is motivated by design of liquid metal blankets of nuclear fusion reactors. The effect of convection on the flow within a toroidally oriented duct is analyzed. Non-uniform strong heating arising from capture of high-speed neutrons is imposed internally, while the walls are assumed to be isothermal. Very strong heating (the Grashof number up to $10^{11}$) and strong magnetic field (the Hartmann number up to $10^{4}$) corresponding to the realistic fusion reactor conditions are considered. Stability of two-dimensional flow states is analyzed using numerical simulations. The unstable modes at high Hartmann and Grashof number are found to have large wavelengths. The integral properties of developed three-dimensional flows are close to those of two-dimensional flows at the typical parameters of a fusion reactor. We also consider the effect of the weak transverse component of the magnetic field on the flow.   

Instability of secondary flows in an electromagnetically forced curved duct

In this presentation, we investigated the secondary flow forced electromagnetically between two fixed copper cylinders. The gap geometry corresponds to a rectangular curved duct with a large aspect ratio. We have performed low Hartmann number runs ($M<500$) and we used ultrasonic probes to access the azimuthal and axial velocity profiles. We have characterized a transition between magnetohydrodynamic and hydrodynamic regimes. These regimes are controlled by the Elsasser number. The hydrodynamic regime corresponds to a classic flow in rectangular curved duct presenting a single pair of stable contra-rotative vortices (2-cell mode) and shows a transition to double pair of vortices (4-cell mode) for large enough magnetic Dean number $K_M$ (Dean number adjusted by the magnetic field). We have explored the experimental stability diagram for $100 [Preview Abstract]

Longtime persistence of linear dynamic in magnetoconvection

We extend the Chandrasekhar's marginal stability of an infinite conducting fluid layer heated from below and subjected to a vertical magnetic field to non-zero growth rate. We show that this regime is relevant by comparing the linear stability results with direct numerical simulations (DNS). The growth-rate and wavelengths are accurately predicted by the linear eigenvalue problem, even at largely overcritical Rayleigh numbers. Moreover, it is found that the linear dynamics break down when the amplitude of the velocity perturbations is of the order of the characteristic buoyancy velocity $W_{buoy}=\sqrt{g\beta \Delta T h}$, with $g$ the gravitational acceleration, $\beta$ the thermal expansion coefficient, $\Delta T>0$ the bottom-top temperature difference and $h$ the height of the layer. At large timescales, there is no memory phenomenon from the onset of convection: the height of the enclosure is only responsible for the size of the structures.   

Non-linear interactions of magneto-Poincare and magnetostrophic waves in rotating shallow water magnetohydrodynamic

We have investigated the interaction of wave packets in the magnetohydrodynamic shallow water flows in external vertical magnetic field. Using the asymptotic multiscale methods we received that three magneto-Poincare waves interact, three magnetostrophic waves also interact, We obtained intermode interactions: two magnetostrophic waves and magneto-Poincare wave, two magneto-Poincare waves and magnetostrophic wave. In all cases we derived nonlinear equations of three waves interactions and showed the existence of two types of instability mechanisms: decay instabilities and parametric growth. It has been found that there are four types of decay instabilities: magneto-Poincare wave decays into two magneto-Poincare waves, magnetostrophic wave decays into two magnetostrophic waves, magneto-Poincare decays into one magnetostrophic and one magneto-Poincare wave, and magnetostrophic wave decays into one magneto-Poincare and one magnetostrophic wave. The growth rates of decay instabilities were received. Also four types of parametric growth were investigated: magneto-Poincare waves amplification, magnetostrophic waves amplification, magneto-Poincare wave growth in field of magnetostrophic wave, and magnetostrophic wave growth in field of magneto-Poincare wave.   

Stochastic Non-Resistive Magnetohydrodynamic System with L\'{e}vy Noise

The incompressible, viscous and resistive magnetohydrodynamic (MHD) system consists of the Navier-Stokes equations coupled with the Maxwell equations. MHD has many applications in various fields ranging from Astrophysics to nuclear fusion devices. When the magnetic diffusivity is taken to be zero, we get the incompressible, viscous and non-resistive MHD equations. In this work, we consider the incompressible, viscous and non-resistive MHD equations with L\'{e}vy noise in two and three dimensions. We prove the local in time existence and uniqueness (path wise) strong solution to the stochastic non-resistive MHD system up to a maximal stopping time. For proving this, we first consider a class of bounded solutions with finite higher order energy in space variable and prove the solutions of the smoothed version of the stochastic MHD system exist. We find a collection of positive stopping times on which the norms of the smoothed version solution are uniformly bounded. For any stopping time from this collection, the smoothed version solution is a Cauchy sequence and hence is convergent. An application of Sobolev interpolation results and Banach-Alaoglu theorem yield the existence of local in time strong solution. We finally show that this local strong solution is path wise unique.   

Irregular magnetohydrodynamic shock refraction in the presence of a normal magnetic field

Shock refraction occurs when an incident shock encounters a density interface, which is important in a number of applications. When all waves resulting from the interaction meet at a point, this is termed regular shock refraction. In magnetohydrodynamics, analytical solutions for regular refraction cases show that magnetohydrodynamic waves transport vorticity from the shocked density interface so that it is not a shear layer. This is the mechanism that underpins the suppression of shock driven instabilities in the presence of a magnetic field. Here, we examine the case of irregular shock refraction where the initial magnetic field is normal to the incident shock. Regular analytical solutions are used to map the boundary of the irregular refraction region in parameter space. Beyond this boundary, the structure of irregular solutions is investigated via numerical simulations. Particular attention is given to whether all fluid interface emanating from wave intersection points are free of vorticity.   

Vorticity transport in shock driven plasma flows: A comparison of MHD and two-fluid models

Suppression of the Richtmyer-Meshkov instability in a plasma, through the application of a seed magnetic field, has been studied in the framework of ideal magnetohydrodymanics. These studies have shown that suppression is achieved through the transport of vorticity by magnetohydrodynamic waves away from a perturbed fluid-fluid interface where it was baroclinically generated by shock impact. The implementation of a more physically accurate, fully electromagnetic, two-fluid plasma representation allows a more realistic investigation of vorticity transport in shock driven plasma flows. Results comparing ideal one-dimensional two-fluid and magnetohydrodymanic flows are presented. Substantial increases in the complexity of the flow field and vorticity transport dynamics are observed with important ramifications for the stabilization of shock driven interfaces.   

Turbulence in the Heliosheath: spectral analysis from Voyager 1 and 2 data

The Voyager 2 spacecraft is traveling through the heliosheath, the outermost layer in heliosphere where the solar wind is slowed by the interstellar gas, while Voyager 1 has entered the local interstellar medium. The they are providing the fist in-situ measurement of plasma and magnetic fields in that regions. We focus on the differences between the energetic particle intensity variations seen by the Voyager 1 and 2 crafts that are crossing the sectored and the unipolar as well as the sectored heliosheath regions, respectively. We try to provide a spectral analysis of the full heliosheath, characterizing the plasma and magnetic field turbulence through the estimate of the spectral properties in the different frequency ranges. Signal reconstruction techniques are mandatory to reconstruct spectra due to extreme data sparsity (up to 97\%\ missings in high resolution data beyond 80 AU). We use three different methods: correlation computation coupled with the maximum likelihood reconstruction, compress sensing and a genetic algorithm to estimate the gap influence on reconstructed spectra. These methods have been previously validated on 1979 data and synthetic hydrodynamics fluid turbulent fields. Results on power density, energy and helicity spectra will