Inertio–elastic instability of a vortex column

Roy, Anubhab; Garg, Piyush; Reddy, J. Shashi Kiran; Subramanian, Ganesh

doi:10.1017/jfm.2022.122

Cited by 5 publications

(2 citation statements)

References 68 publications

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“…Recently a new instability mechanism has been found for a Rankine vortex in dilute polymer solutions (Roy et al. 2022). The instability occurs due to the resonant interaction of a pair of elastic shear waves aided by the differential convection of the irrotational shearing flow outside the vortex core.…”

Section: Introductionmentioning

confidence: 99%

“…Analogous destabilization mechanisms have been shown to exist for shallow water flows (Ford 1994) and stratified flows (Schecter & Montgomery 2004;Le Dizès & Billant 2009), where outgoing waves draw energy from the mean flow. Recently a new instability mechanism has been found for a Rankine vortex in dilute polymer solutions (Roy et al 2022). The instability occurs due to the resonant interaction of a pair of elastic shear waves aided by the differential convection of the irrotational shearing flow outside the vortex core.…”

Section: Introductionmentioning

confidence: 99%

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Instability of a dusty vortex

Shuai

Roy

et al. 2022

J. Fluid Mech.

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We investigate the effect of inertial particles dispersed in a circular patch of finite radius on the stability of a two-dimensional Rankine vortex in semi-dilute dusty flows. Unlike the particle-free case where no unstable modes exist, we show that the feedback force from the particles triggers a novel instability. The mechanisms driving the instability are characterized using linear stability analysis for weakly inertial particles and further validated against Eulerian–Lagrangian simulations. We show that the particle-laden vortex is always unstable if the mass loading $M>0$ . Surprisingly, even non-inertial particles destabilize the vortex by a mechanism analogous to the centrifugal Rayleigh–Taylor instability in radially stratified vortex with density jump. We identify a critical mass loading above which an eigenmode $m$ becomes unstable. This critical mass loading drops to zero as $m$ increases. When particles are inertial, modes that fall below the critical mass loading become unstable, whereas modes above it remain unstable but with lower growth rates compared with the non-inertial case. Comparison with Eulerian–Lagrangian simulations shows that growth rates computed from simulations match well the theoretical predictions. Past the linear stage, we observe the emergence of high-wavenumber modes that turn into spiralling arms of concentrated particles emanating out of the core, while regions of particle-free flow are sucked inward. The vorticity field displays a similar pattern which leads to the breakdown of the initial Rankine structure. This novel instability for a dusty vortex highlights how the feedback force from the disperse phase can induce the breakdown of an otherwise resilient vortical structure.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Instability of a dusty vortex

Shuai

Roy

et al. 2022

J. Fluid Mech.

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Linear stability of a rotating liquid column revisited

2022

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We revisit the somewhat classical problem of the linear stability of a rigidly rotating liquid column in this article. Although the literature pertaining to this problem dates back to 1959, the relation between inviscid and viscous stability criteria has not yet been clarified. While the viscous criterion for stability, given by $We < n^2 + k^2 -1$ , is both necessary and sufficient, this relation has only been shown to be sufficient in the inviscid case. Here, $We = \rho \varOmega ^2 a^3 / \gamma$ is the Weber number and measures the relative magnitudes of the centrifugal and surface tension forces, with $\varOmega$ being the angular velocity of the rigidly rotating column, $a$ the column radius, $\rho$ the density of the fluid and $\gamma$ the surface tension coefficient; $k$ and $n$ denote the axial and azimuthal wavenumbers of the imposed perturbation. We show that the subtle difference between the inviscid and viscous criteria arises from the surprisingly complicated picture of inviscid stability in the $We$ – $k$ plane. For all $n > 1$ , the viscously unstable region, corresponding to $We > n^2 + k^2-1$ , contains an infinite hierarchy of inviscidly stable islands ending in cusps, with a dominant leading island. Only the dominant island, now infinite in extent along the $We$ axis, persists for $n=1$ . This picture may be understood, based on the underlying eigenspectrum, as arising from the cascade of coalescences between a retrograde mode, that is the continuation of the cograde surface-tension-driven mode across the zero Doppler frequency point, and successive retrograde Coriolis modes constituting an infinite hierarchy.

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Linear instability analysis of a viscoelastic jet in a co-flowing gas stream

Ding

et al. 2022

J. Fluid Mech.

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The instability characteristic of a viscoelastic jet in a co-flowing gas stream is studied comprehensively. The important role of the non-uniform basic velocity in the instability analysis of viscoelastic jets is clarified, which first induces an unrelaxed elastic tension, and then produces a coupling term between the elastic tension and perturbation velocity. The elastic tension promotes the instability of the jet, while the coupling term exhibits a stabilizing effect, which is essentially related to the nonlinear constitutive relation of viscoelastic fluids and the non-uniform basic velocity. The competition between these two factors leads to the non-monotonic effect of fluid elasticity on the disturbance growth rate, which can be divided into two different regimes characterized by the Weissenberg number with values smaller or larger than unity. In different regimes, the structure of the eigenspectrum is also significantly different. Furthermore, three instability mechanisms are identified using the energy budget analysis, corresponding to the predominance of the surface tension, elastic tension and shear and pressure of the external gas, respectively. By analysing the variations of the growth rate and phase speed of the disturbances, the general features of viscoelastic jet instability are obtained. Finally, the transitions of instability modes in parameter spaces are investigated theoretically and the transition boundaries among them are provided. This study provides guidance for understanding the underlying mechanism of instability of a viscoelastic jet surrounded by a co-flowing gas stream and the transition criterion of different instability modes.

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Inertio–elastic instability of a vortex column

Cited by 5 publications

References 68 publications

Instability of a dusty vortex

Instability of a dusty vortex

Linear stability of a rotating liquid column revisited

Linear instability analysis of a viscoelastic jet in a co-flowing gas stream

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