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A flow on the verge of turbulent breakdown

  • J.-M. Chomaz (a1)

Abstract

Stably stratified sheared flows are ubiquitous in geophysical flows from the ocean to the stars, and the route to turbulence in these flows remains an open question. The article by Lefauve et al. (J. Fluid Mech., vol. 848, 2018, pp. 508–544) is an invitation to this journey. With impressive experimental precision mastered by few teams in the world, the nature of the coherent structure that dominates the flow on the verge of turbulent breakdown is revealed and analysed through one- or two-dimensional modern stability analysis of an experimentally obtained base flow. The effect of confinement is surprisingly strong, advocating for leaving the textbook flows, inhomogeneous in only one direction, for the more complex shores of real flows, now accessible to analysis of multidimensional stability problems. The route explored by Lefauve et al. (2018) renews with the long tradition of the supercritical bifurcation scenario, it revisits the linear stability theory with possibility of resonances, critical layers and more to be imagined, since complex base flows are now available to explore both experimentally and analytically.

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Copyright

Corresponding author

Email address for correspondence: jmchomaz@gmail.com

References

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Brown, G. & Roshko, A. 1974 On density effects and large structure in turbulent mixing layers. J. Fluid Mech. 64, 775816.
Holmboe, J. 1962 On the behavior of symmetric waves in stratified shear layers. Geophys. Publ. 24, 67113.
Kolmogorov, A. N. 1941 The local structure of turbulence in incompressible viscous fluids at very large Reynolds numbers. Dokl. Akad. Nauk. SSSR 30, 2993035. Reprinted in 1991 Proc. R. Soc. Lond. A 434, 9–13.
Lefauve, A., Partridge, J. L., Zhou, Q., Dalziel, S. B., Caulfield, C. P. & Linden, P. F. 2018 The structure and origin of confined Holmboe waves. J. Fluid Mech. 848, 508544.
Maurer, J. & Libchaber, A. 1979 Rayleigh–Bénard experiment in liquid helium; frequency locking and the onset of turbulence. J. Phys. Lett. 40, 419423.
Ortiz, S., Chomaz, J.-M. & Loiseleux, T. 2002 Spatial Holmboe instability. Phys. Fluids 14, 25852597.
Reynolds, O. 1883 An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels. Phil. Trans. R. Soc. Lond. 174, 935982.
Schmid, P. J. & Henningson, D. S. 2001 Advanced Mathematical Methods for Scientists and Engineers. Springer.
Winant, C. D. & Browand, F. K. 1974 Vortex pairing – mechanism of turbulent mixing layer growth at moderate Reynolds-number. J. Fluid Mech. 63, 237271.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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