Skip to main content Accessibility help
×
Home

The linear stability of a Stokes layer with an imposed axial magnetic field

  • CHRISTIAN THOMAS (a1), ANDREW P. BASSOM (a1) and CHRISTOPHER DAVIES (a2)

Abstract

The effects of a uniform axial magnetic field directed towards an oscillating wall in a semi-infinite viscous fluid (or Stokes layer) is investigated. The linear stability and disturbance characteristics are determined using both Floquet theory and via direct numerical simulations. Neutral stability curves and critical parameters for instability are presented for a range of magnetic field strengths. Results indicate that a magnetic field directed towards the boundary wall is stabilizing, which is consistent with that found in many steady flows.

Copyright

Corresponding author

Email address for correspondence: bassom@maths.uwa.edu.au

References

Hide All
Akhavan, R., Kamm, R. D. & Shapiro, A. H. 1991 An investigation of transition to turbulence in bounded oscillatory Stokes flows. Part 2. Numerical simulations. J. Fluid Mech. 225, 423444.
Blennerhassett, P. J. & Bassom, A. P. 2002 The linear stability of flat Stokes layers. J. Fluid Mech. 464, 393410.
Blennerhassett, P. J. & Bassom, A. P. 2006 The linear stability of high-frequency oscillatory flow in a channel. J. Fluid Mech. 556, 125.
Blennerhassett, P. J. & Bassom, A. P. 2007 The linear stability of high-frequency flow in a torsionally oscillating cylinder. J. Fluid Mech. 576, 491505.
Clamen, M. & Minton, P. 1977 An experimental investigation of flow in an oscillatory pipe. J. Fluid Mech. 77, 421431.
Davies, C. & Carpenter, P. W. 2001 A novel velocity–vorticity formulation of the Navier–Stokes equations with applications to boundary layer disturbance evolution. J. Comp. Phys. 172, 119165.
Davis, S. H. 1976 The stability of time-periodic flows. Annu. Rev. Fluid Mech. 8, 5774.
Eckmann, D. M. & Grotberg, J. B. 1991 Experiments on transition to turbulence in oscillatory pipe flow. J. Fluid Mech. 222, 329350.
Fornberg, B. 1996 A Practical Guide to Pseudospectral Methods. Cambridge University Press.
Gao, P. & Lu, X. Y. 2006 a Effect of wall suction/blowing on the linear stability of flat Stokes layers. J. Fluid Mech. 551, 303308.
Gao, P. & Lu, X. Y. 2006 b Effect of surfactants on the long-wave stability of oscillatory fluid flow. J. Fluid Mech. 562, 345354.
Hall, P. 1978 The linear stability of flat Stokes layers. Proc. R. Soc. Lond. A 359, 151166.
Hall, P. 2003 On the stability of the Stokes layers at high Reynolds numbers. J. Fluid Mech. 482, 115.
Healey, J. J. 2006 A new convective instability of the rotating-disk boundary layer with growth normal to the disk. J. Fluid Mech. 560, 279310.
Hicks, T. W. & Riley, N. 1989 Boundary layers in magnetic Czochralski crystal growth. J. Cryst. Growth 96, 957968.
Jasmine, H. A. & Gajjar, J. S. B. 2005 Convective and absolute instability in the incompressible boundary layer on a rotating disk in the presence of a uniform magnetic field. J. Engng Maths 52, 337353.
von Kerczek, C. & Davis, S. H. 1974 Linear stability theory of oscillatory Stokes layers. J. Fluid Mech. 62, 753773.
Luo, J. & Wu, X. 2010 On the linear stability of a finite Stokes layer: instantaneous versus Floquet modes. Phys. Fluids 22, 054106.
Organ, A. E. & Riley, N. 1987 Oxygen transport in magnetic Czochralski growth of Silicon. J. Cryst. Growth 82, 465476.
Seminara, G. & Hall, P. 1976 Centrifugal instability of a Stokes layer. Proc. R. Soc. Lond. A 350, 299316.
Thomas, C., Bassom, A. P., Blennerhassett, P. J. & Davies, C. 2010 Direct numerical simulations of small disturbances in the classical Stokes layer. J. Engng Maths, doi: 10.1007/S10665-010-9381-0.
Trefethen, L. N. 2000 Spectral Methods in MATLAB. SIAM.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

The linear stability of a Stokes layer with an imposed axial magnetic field

  • CHRISTIAN THOMAS (a1), ANDREW P. BASSOM (a1) and CHRISTOPHER DAVIES (a2)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed