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Instability and transition to turbulence in a free shear layer affected by a parallel magnetic field

By A. Vorobev and O. Zikanov


Instability and transition to turbulence in a temporally evolving free shear layer of an electrically conducting fluid affected by an imposed parallel magnetic field is investigated numerically. The case of low magnetic Reynolds number is considered. It has long been known that the neutral disturbances of the linear problem are three-dimensional at sufficiently strong magnetic fields. We analyse the details of this instability solving the generalized Orr–Sommerfeld equation to determine the wavenumbers, growth rates and spatial shapes of the eigenmodes. The three-dimensional perturbations are identified as oblique waves and their properties are described. In particular, we find that at high hydrodynamic Reynolds number, the effect of the strength of the magnetic field on the fastest growing perturbations is limited to an increase of their oblique angle. The dimensions and spatial shape of the waves remain unchanged. The transition to turbulence triggered by the growing oblique waves is investigated in direct numerical simulations. It is shown that initial perturbations in the form of superposition of two symmetric waves are particularly effective in inducing three-dimensionality and turbulence in the flow.<br/

Topics: QA, TA
Year: 2007
OAI identifier:
Provided by: e-Prints Soton

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  6. (1971). Hydromagnetic instability of a free shear layer at small magnetic Reynolds numbers. doi
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  8. (1933). On the stability of three-dimensional disturbances of viscous fluid flow between parallel walls doi
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  11. S t u a r t ,J .T .1954 On the stability of viscous flow between parallel planes in the presence of a coplanar magnetic field. doi
  12. (1987). Secondary instability of a temporally growing mixing layer. doi
  13. (1981). Shear Flows Instabilities and Transition. doi
  14. (1963). Stability of a shear layer between parallel streams. doi
  15. (1960). Stability of parallel flow in a parallel magetic field at small magnetic Reynolds numbers. doi
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  17. (2004). Turbulent convection driven by surface cooling in shallow water doi
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