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The influence of shear on double-diffusive and settling-driven instabilities

  • N. Konopliv (a1), L. Lesshafft (a2) and E. Meiburg (a1)


The effects of shear on double-diffusive fingering and on the settling-driven instability are assessed by means of a transient growth analysis. Employing Kelvin waves within a linearized framework allows for the consideration of time-dependent waveforms in uniform shear. In this way, the effects of boundaries and of shear-driven instability modes can be eliminated, so that the influence of shear on the double-diffusive and settling-driven instabilities can be analysed in isolation. Shear is seen to dampen both instabilities, which is consistent with previous findings by other authors. The shear damping is more pronounced for parameter values that produce larger unsheared growth. These trends can be explained in terms of instantaneous linear stability results for the unsheared case. For both double-diffusive and settling-driven instabilities, low Prandtl number ( $Pr$ ) values result in less damping and an increased importance of the Orr mechanism, for which a quantitative scaling law is obtained.


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Alsinan, A., Meiburg, E. & Garaud, P. 2017 A settling-driven instability in two-component, stably stratified fluids. J. Fluid Mech. 816, 243267.
Burns, P. & Meiburg, E. 2012 Sediment-laden fresh water above salt water: linear stability analysis. J. Fluid Mech. 691, 279314.
Burns, P. & Meiburg, E. 2015 Sediment-laden fresh water above salt water: nonlinear simulations. J. Fluid Mech. 762, 156195.
Craik, A. D. D. & Criminale, W. O. 1986 Evolution of wavelike disturbances in shear flows: a class of exact solutions of the Navier–Stokes equations. Proc. R. Soc. Lond. A 406 (1830), 1326.
Drazin, P. G. & Reid, W. H. 1981 Hydrodynamic Stability. Cambridge University Press.
Gunzburger, M. 2000 Adjoint equation-based methods for control problems in incompressible, viscous flows. Flow Turbul. Combust. 65 (3), 249272.
Howard, L. N. 1961 Note on a paper of john w. miles. J. Fluid Mech. 10 (4), 509512.
Kelvin, L. 1887 Stability of fluid motion: rectilinear motion of viscous fluid between two parallel plates. Phil. Mag. 24 (5), 188196.
Knobloch, E. 1984 On the stability of stratified plane Couette flow. Geophys. Astrophys. Fluid Dyn. 29 (1–4), 105116.
Linden, P. F. 1974 Salt fingers in a steady shear flow. Geophys. Astrophys. Fluid Dyn. 6 (1), 127.
Lindzen, R. S. 1988 Instability of plane parallel shear flow (toward a mechanistic picture of how it works). Pure Appl. Geophys. 126 (1), 103121.
Radko, T. 2013 Double-Diffusive Convection. Cambridge University Press.
Radko, T., Ball, J., Colosi, J. & Flanagan, J. 2015 Double-diffusive convection in a stochastic shear. J. Phys. Oceanogr. 45 (12), 31553167.
Reali, J. F., Garaud, P., Alsinan, A. & Meiburg, E. 2017 Layer formation in sedimentary fingering convection. J. Fluid Mech. 816, 268305.
Rosen, G. 1971 General solution for perturbed plane Couette flow. Phys. Fluids 14 (12), 27672769.
Shepherd, T. G. 1985 Time development of small disturbances to plane Couette flow. J. Atmos. Sci. 42 (17), 18681872.
Smyth, W. D. & Kimura, S. 2007 Instability and diapycnal momentum transport in a double-diffusive, stratified shear layer. J. Phys. Oceanogr. 37, 15511565.
Smyth, W. D. & Kimura, S. 2011 Mixing in a moderately sheared salt-fingering layer. J. Phys. Oceanogr. 41, 13641384.
Yu, X., Hsu, T. & Balachandar, S. 2013 Convective instability in sedimentation: linear stability analysis. J. Geophys. Res. 118 (1), 256272.
Yu, X., Hsu, T. & Balachandar, S. 2014 Convective instability in sedimentation: 3-d numerical study. J. Geophys. Res. 119 (11), 81418161.
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The influence of shear on double-diffusive and settling-driven instabilities

  • N. Konopliv (a1), L. Lesshafft (a2) and E. Meiburg (a1)


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