Influence of slow rotation on the stability of a thermocapillary incompressible liquid flow in an infinite layer under zero-gravity conditions for small Prandtl number

Shvarts, K. G.

doi:10.1088/0169-5983/44/3/031416

Cited by 13 publications

(4 citation statements)

References 13 publications

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“…where e l = −Re(θ * u ∂ b ∂x ) = −Re(θ * u) represents a production term related to the imposed longitudinal gradient of temperature, e v = −Re(θ * w ∂ b ∂z ) = −Re(θ * w dT b dz ) represents a production term related to the vertical gradient of temperature, and e d = Pr Re[θ * ( d 2 θ dz 2 − k 2 θ )] is a dissipation term linked to heat diffusion. Similarly to (27), we can also obtain an equation for the total fluctuating thermal energy E = V e dv:…”

Section: -20mentioning

confidence: 99%

“…Aristov and Frik [24] considered the effect of rotation on large-scale turbulence in a thin rotating fluid layer with a horizontal temperature gradient. Shvarts and Boudlal [25][26][27] carried out several stability studies in which the effect of rotation was examined. These studies investigated the effect of rotation on the stability of the advective flow and the behavior of finite-amplitude perturbations beyond the instability threshold for layers with solid boundaries [25] and with a free upper boundary [26] and finally in the case of thermocapillary convection for layers with two free boundaries in zero gravity.…”

Section: Introductionmentioning

confidence: 99%

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Effect of rotation on the stability of side-heated buoyant convection between infinite horizontal walls

Medelfef¹,

Henry²,

Bouabdallah³

et al. 2017

Phys. Rev. Fluids

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This paper deals with buoyant convection generated by a horizontal gradient of temperature in an infinite fluid layer, which is known as Hadley circulation, and studies the effects induced by applying a rotation around the vertical axis. First, the basic flow profile with rotation is derived and the influence of the rotation is depicted: The original longitudinal velocity profile is decreased in intensity when rotation is applied and its structure is progressively changed, whereas a transverse velocity component is created, which increases with the rotation intensity, overcomes the longitudinal velocity, and eventually decreases. Different asymptotic behaviors for these profiles have also been highlighted. The stability of these flows is then studied. The effects of the Prandtl number, the Taylor number, and the thermal boundary conditions are highlighted for the three types of instability occurring in such a situation (shear, oscillatory, and Rayleigh instabilities). It is observed that they are all stabilized by the rotation and that the increase of the critical thresholds is accompanied by a spinning of the wave vector corresponding to a progressive change of the orientation of the marginal perturbation rolls. Energy budgets are finally used to analyze the instability mechanisms.

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Section: -20mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Effect of rotation on the stability of side-heated buoyant convection between infinite horizontal walls

Medelfef¹,

Henry²,

Bouabdallah³

et al. 2017

Phys. Rev. Fluids

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“…Jou et al (1997) found that the Coriolis force can suppress the onset of Bénard-Marangoni convection and stabilize the system in a thin infinite liquid layer. Shvarts (2012) studied the effects of rotation and Bi on the Marangoni convection stability. Takagi et al (2014) investigated the combined effects of pool rotation and applied magnetics field on HTWs.…”

Section: Introductionmentioning

confidence: 99%

Effect of pool rotation on three-dimensional flow in a shallow annular pool of silicon melt with bidirectional temperature gradients

Zhang¹,

Peng²,

Wang³

et al. 2016

Fluid Dyn. Res.

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In order to understand the effect of pool rotation on silicon melt flow with the bidirectional temperature gradients, we conducted a series of unsteady threedimensional (3D) numerical simulations in a shallow annular pool. The bidirectional temperature gradients are produced by the temperature difference between outer and inner walls as well as a constant heat flux at the bottom. Results show that when Marangoni number is small, a 3D steady flow is common without pool rotation. But it bifurcates to a 3D oscillatory flow at a low rotation Reynolds number. Subsequently, the flow becomes steady and axisymmetric at a high rotation Reynolds number. When the Marangoni number is large, pool rotation can effectively suppress the temperature fluctuation on the free surface, meanwhile, it improves the flow stability. The critical heat flux density diagrams are mapped, and the effects of radial and vertical temperature gradients on the flow are discussed. Additionally, the transition process from the flow dominated by the radial temperature gradient to the one dominated by the vertical temperature gradient is presented.

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“…Gelfgat 14 also reported the destabilization effect of weak rotation. Recently, Shvarts 15 analytically investigated the stability of thermocapillary flow in a slowly rotating liquid layer in microgravity. He concluded that rotation destabilizes the flow within a certain range of Taylor numbers, but after a critical value of the Taylor number, the rotation has a stabilizing effect.…”

Section: Introductionmentioning

confidence: 99%

Rotating and thermocapillary-buoyancy-driven flow in a cylindrical enclosure with a partly free surface

Liao

2014

Physics of Fluids

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In order to understand the characteristics of the complex flow driven by the combined thermocapillary-buoyancy effect and differential rotation of a cylindrical pool and a disk on the free surface, a series of unsteady three-dimensional numerical simulations were performed. Results indicate that the flow is axisymmetric and steady at a small temperature difference and low rotation rates. The basic meridional flow structures are composed of toroidal circulations. With an increase of the rotation rate and/or temperature difference, the basic flow transits to a three-dimensional oscillatory flow. Without rotation, the unstable thermocapillary-buoyancy flow is characterized by pulsating spoke patterns with the periodic growth and decay of temperature and velocity oscillations. When the disk and/or cylinder rotate, the oscillatory flow behaves as temperature and velocity fluctuation waves traveling in the azimuthal direction. The wave propagation velocity and direction, fluctuation amplitude, and wave number depend on the interaction of the thermocapillary, buoyancy, centrifugal and Coriolis forces. The critical conditions for the flow transition are determined. It is found that the critical thermocapillary Reynolds number initially increases before decreasing with the increase of the disk rotation rate, but the rotation of cylinder always retards the flow instability. In addition, the mechanisms of the flow instabilities are discussed and briefly summarized.

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Influence of slow rotation on the stability of a thermocapillary incompressible liquid flow in an infinite layer under zero-gravity conditions for small Prandtl number

Cited by 13 publications

References 13 publications

Effect of rotation on the stability of side-heated buoyant convection between infinite horizontal walls

Effect of rotation on the stability of side-heated buoyant convection between infinite horizontal walls

Effect of pool rotation on three-dimensional flow in a shallow annular pool of silicon melt with bidirectional temperature gradients

Rotating and thermocapillary-buoyancy-driven flow in a cylindrical enclosure with a partly free surface

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