Motion of a sphere in a viscous density stratified fluid
نویسندگان
چکیده
We examine the translation of a sphere in stably stratified ambient limit small Reynolds ($Re \ll 1$) and viscous Richardson numbers ($Ri_v 1$); here, $Re = \frac{\rho Ua}{\mu}$ $Ri_v \frac{\gamma a^3 g}{\mu U}$ with $a$ being radius, $U$ speed, $\rho$ $\mu$ density viscosity ambient, $g$ acceleration due to gravity, $\gamma$ gradient (assumed constant) characterizing stratification. In contrast most earlier efforts, our study considers convection dominant corresponding $Pe \frac{Ua}{D} \gg 1$, $D$ diffusivity stratifying agent. characterize detail velocity fields around particle what we term Stokes stratification regime, defined by Ri_v^{\frac{1}{3}} dominance buoyancy over inertial forces. Buoyancy forces associated perturbed fundamentally alter viscously dominated fluid motion at large distances. At distances order screening length, that scales as $aRi_v^{-\frac{1}{3}}$, transforms from familiar fore-aft symmetric Stokesian form asymmetric pattern recirculating cells primarily horizontal within; except vicinity rear stagnation streamline. larger distances, is vanishingly within (a) an axisymmetric wake whose vertical extent grows $O(r_t^{\frac{2}{5}})$, $r_t$ distance plane perpendicular (b) buoyant reverse jet behind narrows inverse square root downstream.
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ژورنال
عنوان ژورنال: Journal of Fluid Mechanics
سال: 2022
ISSN: ['0022-1120', '1469-7645']
DOI: https://doi.org/10.1017/jfm.2022.760