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Evolution of the Diffusion-Induced Flow over a Disk Submerged in a Stratified Viscous Fluid

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Abstract

The paper presents the results of the mathematically simulated evolution of a 3D diffusion-induced flow over a disk (with diameter d and thickness H = 0.76 d) immersed in a linearly density-stratified incompressible viscous fluid (described by a system of the Navier–Stokes equations in the Boussinesq approximation). The disk rests at the level of the neutral buoyancy (coinciding with its symmetry axis z) and disturbs the homogeneity of the background diffusion flux in the fluid forming a complex system of slow currents (internal gravitational waves). Over time, two thin horizontal convection cells are formed at the upper and lower parts of the disk stretching parallel to the z axis and adjacent to the base cell with thickness d/2. This work is the first to analyze in detail the fundamental mechanism for the formation of each new half-wave near the vertical axis x (passing through the center of the disk) during half the buoyancy period of the fluid Tb. This mechanism is based on gravitational instability. The emergence of this instability is first detected at 0.473Tb at a height of 3.9 d above the center of the disk. The same mechanism is also implemented over the place where the body moves in the horizontal direction. The 3D vortex structure of the flow is visualized by constructing the isosurfaces of the imaginary part of the complex-conjugate eigenvalues of the velocity gradient tensor. In mathematical simulation, we employed a numerical method SMIF that has proved itself over three decades with an explicit hybrid finite-difference scheme for the approximation of the convective terms of the equations (second-order approximation, monotonicity).

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  1. Institute for Computer-Aided Design, Russian Academy of Sciences, Moscow, Russia

    P. V. Matyushin

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  1. P. V. Matyushin
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Correspondence to P. V. Matyushin.

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Translated by I. Pertsovskaya

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Matyushin, P.V. Evolution of the Diffusion-Induced Flow over a Disk Submerged in a Stratified Viscous Fluid. Math Models Comput Simul 11, 479–487 (2019). https://doi.org/10.1134/S2070048219030141

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