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  • Cambridge University Press  (5)
  • American Association for the Advancement of Science (AAAS)
  • 2010-2014  (5)
  • 1
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    Stability of a vortex in radial density stratification: role of wave interactions (2011)
    Cambridge University Press
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    Publication Date: 2011-05-25
    Description: We study the stability of a vortex in an axisymmetric density distribution. It is shown that a light-cored vortex can be unstable in spite of the ‘stable stratification’ of density. Using a model flow consisting of step jumps in vorticity and density, we show that a wave interaction mediated by shear is the mechanism for the instability. The requirement is for the density gradient to be placed outside the vortex core but within the critical radius of the Kelvin mode. Conversely, a heavy-cored vortex, found in other studies to be unstable in the centrifugal Rayleigh–Taylor sense, is stabilized when the density jump is placed in this region. Asymptotic solutions at small Atwood numberAtshow growth rates scaling asAt1/3close to the critical radius, andAt1/2further away. By considering a family of vorticity and density profiles of progressively increasing smoothness, going from a step to a Gaussian, it is shown that sharp gradients are necessary for the instability of the light-cored vortex, consistent with recent work which found Gaussian profiles to be stable. For sharp gradients, it is argued that wave interaction can be supported due to the presence ofquasi-modes. Probably for the first time, a quasi-mode which decays exponentially is shown to interact with a neutral wave to give exponential growth in the combined case. We finally study the nonlinear stages using viscous direct numerical simulations. The initial exponential instability of light-cored vortices is arrested due to a restoring centrifugal buoyancy force, leading to stable non-axisymmetric structures, such as a tripolar state for an azimuthal wavenumber of 2. The study is restricted to two dimensions, and neglects gravity.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 2
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    The effect of wall heating on instability of channel flow – CORRIGENDUM (2011)
    Cambridge University Press
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    Publication Date: 2011-03-02
    Description: During an attempt to work on a stratified flow problem envisaged as a sequel of the paper by Sameen & Govindarajan (2007), it was found that the original paper contained errors in §§ 3.4 and 4.3 due to a factor of iα, which was inadvertently missed in two places in the code (i) in the buoyancy term due to the use of vertical velocity and streamfunction interchangeably, and (ii) in the apportionment between kinetic and potential energy in the Gmax calculation. Because of this, there were significant differences in the effect of Grashof number on stability. Figure 1 is the modified figure 9 of the original paper, for Pr =7 and ΔT = 25 K. The Poiseuille–Rayleigh–Bénard mode appears at Gr = 39.12 and is seen not to merge with the Poiseuille mode, unlike the conclusion made earlier. This modification applies at any Prandtl number from 10−2 to 102. The corrected versions of figures 17 and 21, showing Gmax contours for different Pr at Gr = 0 and different Gr for Pr = 1, are plotted in figures 2 and 3, respectively. The large growth reported at β = 0 was thus erroneous. The other main conclusions of the paper, that Prandtl number changes transient growth qualitatively, but not the least stable eigenmode, whereas viscosity stratification, which has a huge impact on exponential growth/decay, does not change transient growth much, remain the same. The secondary instabilities also remain unchanged. The stability equations (3.2) to (3.4) in the paper should read (for explanation, please refer to Sameen & Govindarajan 2007) (1)(2)(3)
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 3
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    Linear stability of double-diffusive two-fluid channel flow (2011)
    Cambridge University Press
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    Publication Date: 2011-10-14
    Description: Double-diffusive density stratified systems are well studied and have been shown to display a rich variety of instability behaviour. However double-diffusive systems where the inhomogeneities in solute concentration are manifested in terms of stratified viscosity rather than density have been studied far less and, to the best of the authors' knowledge, not in high-Reynolds-number shear flows. In a simple geometry, namely the two-fluid channel flow of such a system, we find a new double-diffusive mode of instability. The instability becomes stronger as the ratio of diffusivities of the two scalars increases, even in a situation where the net Schmidt number decreases. The double-diffusive mode is destabilized when the layer of viscosity stratification overlaps with the critical layer of the perturbation. © 2011 Cambridge University Press.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 4
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    Instability of a free-shear layer in the vicinity of a viscosity-stratified layer (2014)
    Cambridge University Press
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    Publication Date: 2014-07-11
    Description: The stability of a mixing layer made up of two miscible fluids, with a viscosity-stratified layer between them, is studied. The two fluids are of the same density. It is shown that unlike other viscosity-stratified shear flows, where species diffusivity is a dominant factor determining stability, species diffusivity variations over orders of magnitude do not change the answer to any noticeable degree in this case. Viscosity stratification, however, does matter, and can stabilize or destabilize the flow, depending on whether the layer of varying velocity is located within the less or more viscous fluid. By making an inviscid model flow with a slope change across the ‘viscosity’ interface, we show that viscous and inviscid results are in qualitative agreement. The absolute instability of the flow can also be significantly altered by viscosity stratification.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 5
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    Vortex-induced instabilities and accelerated collapse due to inertial effects of density stratification (2010)
    Cambridge University Press
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    Publication Date: 2010-02-09
    Description: A vortex placed at a density interface winds it into an ever-tighter spiral. We show that this results in a combination of a centrifugal Rayleigh-Taylor (CRT) instability and a spiral Kelvin-Helmholtz (SKH) type of instability. The SKH instability arises because the density interface is not exactly circular, and dominates at large times. Our analytical study of an inviscid idealized problem illustrates the origin and nature of the instabilities. In particular, the SKH is shown to grow slightly faster than exponentially. The predicted form lends itself for checking by a large computation. From a viscous stability analysis using a finite-cored vortex, it is found that the dominant azimuthal wavenumber is smaller for lower Reynolds number. At higher Reynolds numbers, disturbances subject to the combined CRT and SKH instabilities grow rapidly, on the inertial time scale, while the flow stabilizes at low Reynolds numbers. Our direct numerical simulations are in good agreement with these studies in the initial stages, after which nonlinearities take over. At Atwood numbers of 0.1 or more, and a Reynolds number of 6000 or greater, both stability analysis and simulations show a rapid destabilization. The result is an erosion of the core, and breakdown into a turbulence-like state. In studies at low Atwood numbers, the effect of density on the inertial terms is often ignored, and the density field behaves like a passive scalar in the absence of gravity. The present study shows that such treatment is unjustified in the vicinity of a vortex, even for small changes in density when the density stratification is across a thin layer. The study would have relevance to any high-Péclet-number flow where a vortex is in the vicinity of a density-stratified interface. Copyright © Cambridge University Press 2010.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Published by Cambridge University Press
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