Evolution of the diffusion-induced flow over a sphere submerged in a continuously stratified fluid

Baidulov, V. G.; Matyushin, P. V.; Chashechkin, Yu. D.

doi:10.1134/s001546280702010x

Cited by 26 publications

(14 citation statements)

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“…Thus, in particular, the stratified media bounded by solid surfaces of any shape (topography) do not approach the state of rest even in the absence of disturbing forces. The interruption of molecular flow on impermeable boundaries leads to the formation specific currents induced by diffusion, including boundary layers, large slow eddies, and dissipative gravitational waves (nonstationary currents induced by diffusion on a sphere are computed in [7]). The infinitesimal periodic currents coexisting with two fine-structure components of different kinds in viscous continuously stratified and rotating media become more complicated [8].…”

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confidence: 99%

Hierarchy of the models of classical mechanics of inhomogeneous fluids

Chashechkin

2011

Phys Oceanogr

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The methods of perturbation theory and integral representations are used to analyze the general properties of a system of equations of the mechanics of inhomogeneous fluids including the equations of momentum, mass, and temperature transfer. We also consider various submodels of this system, including the reduced systems in which some kinetic coefficients are equal to zero and degenerate systems in which the variations of density or some other variables are neglected. We analyze both regularly perturbed and singularly perturbed solutions of the system. In the case of reduction or degeneration of solutions, the order of the system decreases. In this case, regularly perturbed solutions are preserved (with certain modifications) but the number of singularly perturbed components participating in the formation of the boundary layers on contact surfaces and their analogs in the bulk of the fluid, i.e., the elongated high-gradient interlayers, decreases. The interaction between all components of the currents is nonlinear, despite the fact that their characteristic scales are different.Together with the experimental and numerical methods, the analytic methods remain one of the basic tools in the investigation of the nature of currents in fluids. In the course of their development, the information variables capable of the reliable characterization of the physical properties of the media and the parameters of currents were selected and the fundamental equations aimed at the description of the mechanics and thermodynamics of fluids were deduced [1, 2]. However, the analysis of the behavior of the entire system and the properties of separate equations, as well as the construction of partial solutions encounter serious difficulties due to the presence of multiscale processes and the nonlinearity of equations and the corresponding boundary and initial conditions. Numerous important results in the theory of slow (as compared with the sound velocity) currents in low-viscous weakly stratified fluids were obtained by the methods of perturbation theory [1,2].Parallel with the fundamental equations, the researchers extensively use constitutive models (various versions of turbulence theory in the hydroaerodynamics of the environment [3] and the theories of boundary layer in the engineering hydromechanics [4]) whose symmetry differs from the symmetry of the fundamental equations [5]. The fact that the constitutive models are not closed stimulated the development of more detailed investigations of the fundamental system of equations and its subsystems. In [6], the analysis of the mechanisms of adaptation of physical fields to rapidly varying external conditions is performed under the assumption of existence of stationary dynamic states of inhomogeneous rotating fluids including the state of rest. The transient wave processes are analyzed in the linear approximation, and the effect of dissipative factors (viscosity, thermal diffusivity, and diffusion) is neglected [6].

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confidence: 99%

Hierarchy of the models of classical mechanics of inhomogeneous fluids

Chashechkin

2011

Phys Oceanogr

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“…Mathematical problems arising in this work and require further study in the internal boundary layers, containing the singular points of saddle type, there are also problems of hydrodynamics. Similar problems have been studied in [20], [25].…”

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confidence: 81%

The asymptotic solutions for boundary value problem to a convective diffusion equation with chemical reaction near a cylinder

Maksimova

Akhmetov

2013

Lat. Am. j. solids struct.

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“…It is known that it is impossible to construct a homogeneous monotonic difference scheme of higher order than the first order of the approximation for equation (9). A monotonic scheme of higher order can therefore only be constructed either on the basis of second-order homogeneous scheme using smoothing operators, or on the basis of the hybrid schemes using different switch conditions from one scheme to another (depending on the nature of the solution), possibly with the use of smoothing.…”

Section: Numerical Methods Smifmentioning

confidence: 98%

“…Let us investigate the class of the difference scheme which can be written in the form of the two-parameter family which depends on the parameters and in the following manner: (10) In this case the first differential approximation for equation (9) has the form , xx x t f u h uf f (11) where h u C C and 1 5 . 0…”

Section: Numerical Methods Smifmentioning

confidence: 99%

“…Thus the classifications of the viscous fluid flow regimes around a sphere have been refined [1][2][3][4][5][6][7]. In the case of a resting sphere in a continuously stratified viscous fluid it was shown (for the first time) that the interruption of the molecular flow (by the resting sphere) not only generates the axisymmetrical flow on the sphere surface (from the equator to the poles) but also creates the short unsteady internal waves [8][9]. The original classification of the 2D stratified viscous fluid flow regimes around a square cylinder has been obtained at Re < 200, 0.1 < Fr < 100 [10].…”

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confidence: 99%

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Mathematical modeling of the incompressible fluid flows

Gushchin¹,

Matyushin²

2014

AIP Conference Proceedings

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The aim of the present paper is the demonstration of the opportunities of the mathematical modeling of the separated flows of the river and the sea water around blunt bodies on the basis of the Navier-Stokes equations (NSE) in the Boussinesq approximation. In the river water only the wakes of the obstacles are observed. In the sea water along with wakes the internal waves (IWs) are generated. The 3D homogeneous (river) and density stratified (sea) incompressible viscous fluid flows around a sphere and a square cylinder have been investigated by means of the direct numerical simulation on supercomputers and the visualization of the 3D vortex structures in the wake. For solving of NSE the Splitting on physical factors Method for Incompressible Fluid flows (SMIF) with hybrid explicit finite difference scheme (second-order accuracy in space, minimum scheme viscosity and dispersion, capable for work in wide range of the Reynolds (Re) and the internal Froude (Fr) numbers and monotonous) has been developed and successfully applied. The different transitions in sphere wakes (2D-3D, laminar-turbulent and others) with increasing of Re (1 < Re < 500000) and decreasing of Fr (0.005 < Fr < 100) have been investigated in details. Thus the classifications of the viscous fluid flow regimes around a sphere have been refined. The original classification of the 2D stratified viscous fluid flow regimes around a square cylinder has been obtained at Re < 200, 0.1 < Fr < 100. At Fr =0.1, Re = 50 the formation process of the two symmetric wavy hanging (soaring) sheets of density (starting from two hanging vortices) is demonstrated. It was found also that the values of the maximum phase difference along the circular cylinder axis are approximately equal to 0.1-0.2 Tf (for mode A, 191 < Re ≤ 300) and 0.015-0.030 Tf (for mode B, 300 ≤ Re ≤ 400), where the time Tf is the period of the flow.

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Evolution of the diffusion-induced flow over a sphere submerged in a continuously stratified fluid

Cited by 26 publications

References 6 publications

Hierarchy of the models of classical mechanics of inhomogeneous fluids

Hierarchy of the models of classical mechanics of inhomogeneous fluids

The asymptotic solutions for boundary value problem to a convective diffusion equation with chemical reaction near a cylinder

Mathematical modeling of the incompressible fluid flows

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