Journal ArticleDOI
Optimal growth and transition to turbulence in channel flow with spanwise magnetic field
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In this article, the authors studied the instability and transition to turbulence in a magnetohydrodynamic channel flow with a uniform magnetic field imposed along the spanwise direction and showed 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.Abstract:
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.read more
Citations
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Comparative study of finite difference approaches in simulation of magnetohydrodynamic turbulence at low magnetic Reynolds number
TL;DR: In this paper, two approaches to finite difference approximation of turbulent flows of electrically conducting incompressible fluids in the presence of a steady magnetic field are analyzed, one based on high-order approximations and up-biased discretization of the nonlinear term, and another consistent of the second order and nearly fully conservative in regard of mass, momentum, kinetic energy, and electric charge conservation principles.
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Turbulent-laminar coexistence in wall flows with Coriolis, buoyancy or Lorentz forces
TL;DR: In this paper, the authors show that a regime of large-scale oblique laminar-turbulent patterns can be shifted up to large values of the Reynolds number by increasing the damping by the Coriolis, buoyancy or Lorentz force.
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Laminar-Turbulent Transition in Magnetohydrodynamic Duct, Pipe, and Channel Flows
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Natural convection in horizontal pipe flow with a strong transverse magnetic field
TL;DR: In this article, the authors analyzed mixed convection in a liquid metal flow in a horizontal pipe with imposed transverse magnetic field and found that the natural convection develops in the form of coherent quasi-two-dimensional rolls aligned with the magnetic field.
References
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Turbulence statistics in fully developed channel flow at low reynolds number
TL;DR: In this article, a direct numerical simulation of a turbulent channel flow is performed, where the unsteady Navier-Stokes equations are solved numerically at a Reynolds number of 3300, based on the mean centerline velocity and channel half-width, with about 4 million grid points.
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M. Y. Hussaini,Thomas A. Zang +1 more
TL;DR: Spectral methods have been widely used in simulation of stability, transition, and turbulence as discussed by the authors, and their applications to both compressible and incompressible flows, to viscous as well as inviscid flows, and also to chemically reacting flows are surveyed.
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TL;DR: In this article, the authors present a set of methods for the estimation of two-dimensional fluid flow, including a Fourier Galerkin method and a Chebyshev Collocation method.
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Numerical analysis of spectral methods : theory and applications
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TL;DR: Spectral Methods Survey of Approximation Theory Review of Convergence Theory Algebraic Stability Spectral Methods Using Fourier Series Applications of algebraic stability analysis Constant Coefficient Hyperbolic Equations Time Differencing Efficient Implementation of Spectral Method as discussed by the authors.
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TL;DR: In this article, the authors present an approach to the Viscous Initial Value Problem with the objective of finding the optimal growth rate and the optimal response to the initial value problem.