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We explored the settling dynamics of vertically aligned particles in a quiescent, stratified two-layer fluid using particle tracking velocimetry. Glass spheres of$$d=4\,{\rm mm}$$diameter were released at frequencies of 4, 6 and 8 Hz near the free surface, traversing through an upper ethanol layer ($$H_1$$), whereHis height or layer thickess, varying from$$10d$$to$$40d$$and a lower oil layer. Results reveal pronounced lateral particle motion in the ethanol layer, attributed to a higher Galileo number ($$Ga = 976$$, ratio of buoyancy–gravity to viscous effects), compared with the less active behaviour in the oil layer ($$Ga = 16$$). The ensemble vertical velocity of particles exhibited a minimum just past the density interface, becoming more pronounced with increasing$$H_1$$, and suggesting that enhanced entrainment from ethanol to oil resulted in an additional buoyancy force. This produced distinct patterns of particle acceleration near the density interface, which were marked by significant deceleration, indicating substantial resistance to particle motion. An increased drag coefficient occurred for$$H_1/d = 40$$compared with a single particle settling in oil; drag reduced as the particle-release frequency ($$\,f_p$$) increased, likely due to enhanced particle interactions at closer proximity. Particle pair dispersions, lateral ($$R^2_L$$) and vertical ($$R^2_z$$), were modulated by$$H_1$$, initial separation$$r_0$$and$$f_p$$. The$$R^2_L$$dispersion displayed ballistic scaling initially, Taylor scaling for$$r_0 < H_1$$and Richardson scaling for$$r_0 > H_1$$. In contrast,$$R^2_z$$followed a$$R^2_z \sim t^{5.5}$$scaling under$$r_0 < H_1$$. Both$$R^2_L$$and$$R^2_z$$plateaued at a distance from the interface, depending on$$H_1$$and$$f_p$$.
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Fixed-flux Rayleigh–Bénard convection in doubly periodic domains: generation of large-scale shear
This work studies two-dimensional fixed-flux Rayleigh–Bénard convection with periodic boundary conditions in both horizontal and vertical directions and analyses its dynamics using numerical continuation, secondary instability analysis and direct numerical simulation. The fixed-flux constraint leads to time-independent elevator modes with a well-defined amplitude. Secondary instability of these modes leads to tilted elevator modes accompanied by horizontal shear flow. For$$Pr=1$$, where$$Pr$$is the Prandtl number, a subsequent subcritical Hopf bifurcation leads to hysteresis behaviour between this state and a time-dependent direction-reversing state, followed by a global bifurcation leading to modulated travelling waves without flow reversal. Single-mode equations reproduce this moderate Rayleigh number behaviour well. At high Rayleigh numbers, chaotic behaviour dominated by modulated travelling waves appears. These transitions are characteristic of high wavenumber elevator modes since the vertical wavenumber of the secondary instability is linearly proportional to the horizontal wavenumber of the elevator mode. At a low$$Pr$$, relaxation oscillations between the conduction state and the elevator mode appear, followed by quasi-periodic and chaotic behaviour as the Rayleigh number increases. In the high$$Pr$$regime, the large-scale shear weakens, and the flow shows bursting behaviour that can lead to significantly increased heat transport or even intermittent stable stratification.
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- PAR ID:
- 10539003
- Publisher / Repository:
- Cambridge University Press
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 979
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2023.1057
