Advective flow in a rotating liquid film

Aristov, S. N.; Shvarts, K. G.

doi:10.1134/s0021894416010211

Cited by 14 publications

(5 citation statements)

References 3 publications

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“…In this classification, special emphasis must be placed on the use of classes of exact solutions. Historically, the class of exact solutions is understood to mean a given structure of the velocity field, which is a some combination of functions of a simpler form than the general solution of the Navier-Stokes equations, although the calculated solutions can be threedimensional in coordinates and depend on time (Ovsiannikov 1956, Lin 1958, Rajagopal and Gupta 1981, Sidorov 1981, Goldshtik et al 1989, Wang 1989, 1990, Hamdan 1998, Meleshko 2004, Aristov and Shvarts 2006, 2011:…”

Section: Reviewmentioning

confidence: 99%

Towards understanding the algorithms for solving the Navier–Stokes equations

Ershkov¹,

Prosviryakov²,

Burmasheva³

et al. 2021

Fluid Dyn. Res.

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In this paper, we present a review of featured works in the field of hydrodynamics with the main aim to clarify the ways of understanding the algorithms for solving the Navier-Stokes equations. Discussing the existing algorithms, approaches and analytical or semi-analytical methods, we especially note that important problems of stability for the exact solutions should be explored accordingly relate to this respect, e.g. exploring the case of non-stationary helical flows of the Navier-Stokes equations for incompressible fluids with variable (spatially dependent) coefficient of proportionality α between velocity and the curl field of the flow. Meanwhile, the system of Navier-Stokes equations (including continuity equation) has been successfully explored previously with respect to the existence of analytical way for presentation of non-stationary helical flows of the aforementioned type. Conditions for the stability criteria of the exact solution for such the type of flows are obtained herein in the current research, for which non-stationary helical flow with invariant Bernoulli-function is considered.

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Section: Reviewmentioning

confidence: 99%

Towards understanding the algorithms for solving the Navier–Stokes equations

Ershkov¹,

Prosviryakov²,

Burmasheva³

et al. 2021

Fluid Dyn. Res.

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“…They found that the critical wave number also increases with increasing rotational intensity. The stability of an advective flow in a rotating horizontal layer was studied in Julien et al (1996); Schwarz (2005); Aristov and Shvarts (2016); Aristov and Schwarz (2006); Novi et al (2019).…”

Section: Introductionmentioning

confidence: 99%

Pattern Formation in Miscible Rotating Hele-Shaw Flows Induced by a Neutralization Reaction

Utochkin

Siraev

Bratsun

2021

Microgravity Sci. Technol.

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We study the centrifugal buoyancy-driven chemoconvection in a Hele-Shaw cell that uniformly rotates around e perpendicular axis. The slot is considered thin enough to neglect the influence of the Coriolis force. The initial configuration of the system consists of two aqueous reacting solutions separated by a concentric boundary. The acid solution fills the center of the cavity, while the base solution is in the periphery. Bringing liquids into contact initiates a neutralization reaction to form a salt. We show that reaction-diffusion processes produce a potential well near the reaction front, which determines the pattern formation of the system. For some ratios of initial concentrations, there appears a periodic sequence of chemoconvective vortices in the well, while for others, when the well collapses, a shock-like density wave occurs. When the density of the acid solution is higher, the Rayleigh-Taylor instability develops in the system. We found that an increase in the rotation speed leads to a gradual disruption of the structure periodicity. It can even result in the ejection of some vortices from the potential well. We show that the density wave is extremely sensitive to the magnitude of the centrifugal force, occurring only at some critical value. Finally, we obtained a stability map of the system by performing direct numerical simulations for increasing the centrifugal Rayleigh number and the dimensionless distance of the initial contact surface between the solutions from the axis of rotation.

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“…Для невращающихся жидкостей при учете конвекции точными решениями для переопределенной системы уравнений Обербека-Буссинеска точными решениями является класс Остроумова-Бириха и его модификации и обобщения [40][41][42][43][44][45][46][47][48][49][50][51][52]. В статьях [53][54][55][56][57][58][59][60][61][62][63][64] рассмотрены приложения точного решения Остроумова-Бириха к вращающейся жидкости. Все течения, о которых шла речь выше, зависят от распределения давления.…”

Section: Introductionunclassified