Abstract
Direct numerical simulation is applied to investigate instability and transition to turbulence in the flow of an electrically conducting incompressible fluid between two parallel unbounded insulating walls affected by a wall-normal magnetic field (the Hartmann flow). An explanation is based on the streak growth and breakdown mechanism described earlier for other shear flows. The mechanism is investigated using a two-step procedure that includes 2D optimal perturbations and the subsequent 3D instability of the modulated streaky flow. The calculations produce a critical range between 350 and 400 for the Hartmann thickness based Reynolds number that agrees with recent experimental investigations.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
G. Branover, A. Tsinober, Magnetohydrodynamics of incompressible fluids. Nauka, Fys. Mat. Lit., Moscow, 1970
D. Gerard-Varet, Amplification of small perturbations in a Hartmann layer, Phys. of Fluids 14 (2002)1458–1467
D.S. Krasnov, E. Zienicke, O. Zikanov, T. Boeck, A. Thess, Numerical study of instability and transition to turbulence in the Hartmann flow, submitted to J. Fluid Mech.
R.J. Lingwood, T. Alboussière, On the stability of the Hartmann layer, Phys. of Fluids 11 (1999) 2058–2068
P. Moresco, T. Alboussière, Experimental study of the instability of the Hartmann layer, submitted to J. Fluid Mech.
P.J. Schmid, D.S. Henningson, Stability and transition in shear flows, Springer, Berlin, 2001
O. Zikanov, A. Thess, Direct numerical simulation of forced MHD turbulence at low magnetic Reynolds number. J. Fluid Mech. 358 (1998) 299–333
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer Science+Business Media Dordrecht
About this paper
Cite this paper
Krasnov, D.S., Zienicke, E., Thess, A., Zikanov, O., Boeck, T. (2004). Numerical Simulation of Transition to Turbulence in MHD Channel Flow. In: Friedrich, R., Geurts, B.J., Métais, O. (eds) Direct and Large-Eddy Simulation V. ERCOFTAC Series, vol 9. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-2313-2_21
Download citation
DOI: https://doi.org/10.1007/978-1-4020-2313-2_21
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-6575-9
Online ISBN: 978-1-4020-2313-2
eBook Packages: Springer Book Archive