Quasi-two dimensional perturbations in duct flows under transverse magnetic field

  title={Quasi-two dimensional perturbations in duct flows under transverse magnetic field},
  author={Alban Poth{\'e}rat},
  journal={arXiv: Fluid Dynamics},
  • A. Pothérat
  • Published 6 June 2020
  • Physics
  • arXiv: Fluid Dynamics
Inspired by the experiment from Moresco \& Alboussiere (2004, J. Fluid Mech.), we study the stability of a liquid metal flow in a rectangular, electrically insulating duct with a steady homogeneous transverse magnetic field. The Lorentz force tends to eliminate velocity variations along the magnetic field, leading to a quasi-two dimensional base flow with Hartmann boundary layers near the walls perpendicular to the magnetic field, and Shercliff layers near the walls parallel to the field. Since… 
Study of instabilities and quasi-two-dimensional turbulence in volumetrically heated magnetohydrodynamic flows in a vertical rectangular duct
We consider magnetohydrodynamic (MHD) rectangular duct flows with volumetric heating. The flows are upward, subject to a strong transverse magnetic field perpendicular to the temperature gradient,
Stability of pulsatile quasi-two-dimensional duct flows under a transverse magnetic field
This manuscript has been accepted for publication in Physical Review Fluids, see this https URL. The stability of a pulsatile quasi-two-dimensional duct flow was numerically investigated. Flow was
Magnetoconvection in a horizontal duct flow at very high Hartmann and Grashof numbers
Abstract Direct numerical simulations and linear stability analysis are carried out to study mixed convection in a horizontal duct with constant-rate heating applied at the bottom and an imposed
Turbulence in electromagnetically driven Keplerian flows
Abstract The flow of an electrically conducting fluid in a thin disc under the action of an azimuthal Lorentz force is studied experimentally. At small forcing, the Lorentz force is balanced by
Transient analysis of global dominant modes in quasi-static magnetohydrodynamic flows
The global maximum transient amplifications of an electrically conducting fluid under the influence of a transverse magnetic field in square duct were investigated. A range of Hartmann numbers for 10
Linear Stability Analysis of Liquid Metal Flow in an Insulating Rectangular Duct under External Uniform Magnetic Field
Linear stability analysis of liquid metal flow driven by a constant pressure gradient in an insulating rectangular duct under an external uniform magnetic field was carried out. In the present
Weakly nonlinear stability analysis of magnetohydrodynamic channel flow using an efficient numerical approach
We analyze weakly nonlinear stability of a flow of viscous conducting liquid driven by pressure gradient in the channel between two parallel walls subject to a transverse magnetic field. Using a
Study of instabilities and transitions for a family of quasi-two-dimensional magnetohydrodynamic flows based on a parametrical model
In this study, flow phenomena associated with inflectional and boundary-layer instabilities, as well as a mixed instability mode in quasi-two-dimensional magnetohydrodynamic flows in a rectangular
From three-dimensional to quasi-two-dimensional: transient growth in magnetohydrodynamic duct flows
This study seeks to elucidate the linear transient growth mechanisms in a uniform duct with square cross-section applicable to flows of electrically conducting fluids under the influence of an
A mixing-length model for side layers of magnetohydrodynamic channel and duct flows with insulating walls
We propose a simple extension of Prandtl's classical mixing-length model for channel flow in order to describe the effects of a uniform spanwise magnetic field. The mixing length is assumed to be


Instabilities in quasi-two-dimensional magnetohydrodynamic flows
The improvement of heat transfer conditions in liquid-metal magnetohydrodynamic (MHD) flows is of prime importance for self-cooled fusion blanket design concepts. For many years the research was
An effective two-dimensional model for MHD flows with transverse magnetic field
This paper presents a model for quasi-two-dimensional MHD flows between two planes with small magnetic Reynolds number and constant transverse magnetic field orthogonal to the planes. A method is
Steady motion of conducting fluids in pipes under transverse magnetic fields
ABSTRACT This paper studies the steady motion of an electrically conducting, viscous fluid along channels in the presence of an imposed transverse magnetic field when the walls do not conduct
The stability of the flow of an electrically conducting fluid between parallel planes under a transverse magnetic field
  • R. Lock
  • Physics
    Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
  • 1955
The stability under small disturbances is investigated of the two-dimensional laminar motion of an electrically conducting fluid under a transverse magnetic field. It is found that the dominating
Visual analysis of two-dimensional magnetohydrodynamics
Magnetohydrodynamics (MHD) offers a unique opportunity to study the behavior of two-dimensional turbulent flows. A strong external magnetic field B perpendicular to the flow direction of an
Magnetohydrodynamic flow in rectangular ducts. II
This paper is an extension of an earlier paper by Hunt (1965) on laminar motion of a conducting liquid in a rectangular duct under a uniform transverse magnetic field. The effect of the duct having
On the stability of the Hartmann layer
In this paper we are concerned with the theoretical stability of the laminar Hartmann layer, which forms at the boundary of any electrically conducting fluid flow under a steady magnetic field at
Experimental study of the instability of the Hartmann layer
Hartmann layers are a common feature in magnetohydrodynamics, where they organize the electric current distribution in the flow and hence the characteristics of the velocity field. In spite of their
The role of angular momentum in the magnetic damping of turbulence
Landau & Lifshitz showed that Kolmogorov's E∼t−10/7 law for the decay of isotropic turbulence rests on just two physical ideas: (a) the conservation of angular momentum, as expressed by Loitsyansky's