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Please use this identifier to cite or link to this item: https://libjncir.jncasr.ac.in/xmlui/handle/10572/2440
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dc.contributor.authorShukla, Priyanka
dc.contributor.authorAnsari, Istafaul H.
dc.contributor.authorvan der Meer, Devaraj
dc.contributor.authorLohse, Detlef
dc.contributor.authorAlam, Meheboob
dc.date.accessioned2017-02-21T07:03:03Z-
dc.date.available2017-02-21T07:03:03Z-
dc.date.issued2014
dc.identifier.citationShukla, P; Ansari, IH; van der Meer, D; Lohse, D; Alam, M, Nonlinear instability and convection in a vertically vibrated granular bed. Journal of Fluid Mechanics 2014, 761, 123-167, http://dx.doi.org/10.1017/jfm.2014.624en_US
dc.identifier.citationJournal of Fluid Mechanicsen_US
dc.identifier.citation761en_US
dc.identifier.issnThe nonlinear instability of the density-inverted granular Leidenfrost state and the resulting convective motion in strongly shaken granular matter are analysed via a weakly nonlinear analysis of the hydrodynamic equations. The base state is assumed to be quasi-steady and the effect of harmonic shaking is incorporated by specifying a constant granular temperature at the vibrating plate. Under these mean-field assumptions, the base-state temperature decreases with increasing height away from the vibrating plate, but the density profile consists of three distinct regions: (i) a collisional dilute layer at the bottom, (ii) a levitated dense layer at some intermediate height and (iii) a ballistic dilute layer at the top of the granular bed. For the nonlinear stability analysis (Shukla & Alam, J. Fluid Mech., vol. 672, 2011b, pp. 147-195), the nonlinearities up to cubic order in the perturbation amplitude are retained, leading to the Landau equation, and the related adjoint stability problem is formulated taking into account appropriate boundary conditions. The first Landau coefficient and the related modal eigenfunctions (the fundamental mode and its adjoint, the second harmonic and the base-flow distortion, and the third harmonic and the cubic-order distortion to the fundamental mode) are calculated using a spectral-based numerical method. The genesis of granular convection is shown to be tied to a supercritical pitchfork bifurcation from the density-inverted Leidenfrost state. Near the bifurcation point the equilibrium amplitude (A(e)) is found to follow a square-root scaling law, A(e) similar to root Delta, with the distance Delta from the bifurcation point. We show that the strength of convection (measured in terms of velocity circulation) is maximal at some intermediate value of the shaking strength, with weaker convection at both weaker and stronger shaking. Our theory predicts that at very strong shaking the convective motion remains concentrated only near the top surface, with the bulk of the expanded granular bed resembling the conduction state of a granular gas, dubbed as a floating-convection state. The linear and nonlinear patterns of the density and velocity fields are analysed and compared with experiments qualitatively. Evidence of 2:1 resonance is shown for certain parameter combinations. The influences of bulk viscosity, effective Prandtl number, shear work and free-surface boundary conditions on nonlinear equilibrium states are critically assessed.
dc.identifier.urihttps://libjncir.jncasr.ac.in/xmlui/10572/2440-
dc.descriptionhttp://dx.doi.org/10.1017/jfm.2014.624en_US
dc.description.abstract@Cambridge Univ Press, 2014en_US
dc.description.uri0022-1120en_US
dc.description.uri1469-7645en_US
dc.publisherEnglishen_US
dc.rightsCambridge Univ Pressen_US
dc.subjectMechanicsen_US
dc.subjectFluids & Plasmas Physicsen_US
dc.subjectComplex Fluidsen_US
dc.subjectConvectionen_US
dc.subjectNonlinear Instabilityen_US
dc.subjectPlane Couette-Flowen_US
dc.subjectShear-Banding Instabilityen_US
dc.subjectUnstable Parallel Flowsen_US
dc.subjectNon-Linear Mechanicsen_US
dc.subjectPoiseuille Flowen_US
dc.subjectDynamics Simulationsen_US
dc.subjectBoundary-Conditionsen_US
dc.subjectStability Analysisen_US
dc.subjectWave Disturbancesen_US
dc.subjectInelastic Spheresen_US
dc.titleNonlinear instability and convection in a vertically vibrated granular beden_US
dc.typeArticleen_US
Appears in Collections:Research Articles (Meheboob Alam)

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