Effect of rotation on the stability of advective flow in a horizontal liquid layer with solid boundaries at small Prandtl numbers

Chikulaev, D. G.; Shvarts, K. G.

doi:10.1134/s0015462815020052

Cited by 9 publications

(4 citation statements)

References 3 publications

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“…This solution was later published again in [43,44]. The Ostroumov -Birikh family, which describes one-directional fluid flows, turned out to be very useful in solving the problem of convective hydrodynamical stability [45][46][47]. In the scientific works [27,28,[45][46][47][48][49][50][51][52], various modifications and generalizations of the class of exact Ostroumov -Birikh solutions are presented.…”

Section: Introductionmentioning

confidence: 99%

An Inhomogeneous Steady-State Convection of a Vertical Vortex Fluid

Berestova¹,

Prosviryakov²

2023

Nelin. Dinam.

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An exact solution of the Oberbeck – Boussinesq equations for the description of the steady-state Bénard – Rayleigh convection in an infinitely extensive horizontal layer is presented. This exact solution describes the large-scale motion of a vertical vortex flow outside the field of the Coriolis force. The large-scale fluid flow is considered in the approximation of a thin layer with nondeformable (flat) boundaries. This assumption allows us to describe the large-scale fluid motion as shear motion. Two velocity vector components, called horizontal components, are taken into account. Consequently, the third component of the velocity vector (the vertical velocity) is zero. The shear flow of the vertical vortex flow is described by linear forms from the horizontal coordinates for velocity, temperature and pressure fields. The topology of the steady flow of a viscous incompressible fluid is defined by coefficients of linear forms which have a dependence on the vertical (transverse) coordinate. The functions unknown in advance are exactly defined from the system of ordinary differential equations of order fifteen. The coefficients of the forms are polynomials. The spectral properties of the polynomials in the domain of definition of the solution are investigated. The analysis of distribution of the zeroes of hydrodynamical fields has allowed a definition of the stratification of the physical fields. The paper presents a detailed study of the existence of steady reverse flows in the convective fluid flow of Bénard – Rayleigh – Couette type.

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Section: Introductionmentioning

confidence: 99%

An Inhomogeneous Steady-State Convection of a Vertical Vortex Fluid

Berestova¹,

Prosviryakov²

2023

Nelin. Dinam.

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“…However, experiments [8] show that this condition is often violated. This paper examines the influence of the Navier slip condition [9] and of the nonzero pressure gradient on the features of the velocity field, temperature field, and pressure field topologies during fluid flow in a flat horizontal layer [10][11][12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Unidirectional Marangoni–Poiseuille flows of a viscous incompressible fluid with the Navier boundary condition

Burmasheva

Prosviryakov

2019

MECHANICS, RESOURCE AND DIAGNOSTICS OF MATERIALS AND STRUCTURES (MRDMS-2019): Proceedings of the 13th International Conference

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The paper obtains an exact solution describing the shear convection of a swirling viscous incompressible fluid in a horizontal layer taking into account the Marangoni condition, the Navier condition and the non-uniform pressure distribution on one of the layer boundaries. It is shown that this exact solution is able to describe the appearance of the stratification of a velocity field and thermal force fields.

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“…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. Furthermore, Chikulaev and Shvarts [28] studied the effect of rotation on the stability of the horizontally heated fluid layer with solid boundaries at small Prandtl numbers (typical values for liquid metals) and Knutova and Shvarts [29] examined the effect of rotation on the thermocapillary flow under microgravity conditions. In all these previous studies, however, the instability modes are either transverse (with k x = 0 and k y = 0) or longitudinal (with k x = 0 and k y = 0) rolls, which are, as will be shown in this paper, not the most unstable modes.…”

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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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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Effect of rotation on the stability of advective flow in a horizontal liquid layer with solid boundaries at small Prandtl numbers

Cited by 9 publications

References 3 publications

An Inhomogeneous Steady-State Convection of a Vertical Vortex Fluid

An Inhomogeneous Steady-State Convection of a Vertical Vortex Fluid

Unidirectional Marangoni–Poiseuille flows of a viscous incompressible fluid with the Navier boundary condition

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

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