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Flow dynamics around a stationary flat plate near a free surface is investigated using time-resolved two-dimensional particle image velocimetry. The study examines variations in angle of attack ($$\theta =0^\circ {-}35^\circ {}$$), Reynolds number ($$Re$$$$\approx$$$$10^3$$$$-$$3$$\times$$$$10^4$$) and plate proximity to the free surface ($$H^*$$). Under symmetric boundary conditions ($$H^*\geqslant {15}$$), increasing$$\theta$$intensifies fluid–plate interaction, resulting in the shedding of leading-edge and trailing-edge vortices (LEV and TEV), each characterised by distinct strengths and sizes. In both symmetric ($$H^*\geqslant {15}$$) and asymmetric ($$H^*=5$$) boundary conditions at$$\theta \lt 5^\circ {}$$, fluid flow follows the contour of the plate, unaffected by Reynolds number. However, at$$H^*=5$$, three flow regimes emerge: the first Coanda effect (CI), regular shedding (RS) and the second Coanda effect (CII), each influenced by$$\theta$$and$$Re$$. The CI regime dominates at lower angles ($$5^\circ {}\leqslant \theta \leqslant 25^\circ {}$$) and$$Re \leqslant 12\,500$$, featuring a Coanda-induced jet-like flow pattern. As the Reynolds number increases, the flow transitions into the RS regime, leading to detachment from the upper surface of the plate. This detachment results in the formation of LEV and TEV in the wake, along with surface deformation, secondary vortices and wavy shear layers beneath the free surface. At$$22\,360\lt Re \leqslant 32\,200$$and$$5^\circ {} \leqslant \theta \leqslant 25^\circ {}$$, in the CII regime, significant surface deformation causes the Coanda effect to reattach the flow to the plate, forming a unique jet-like flow.
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Spontaneous locomotion of a symmetric squirmer
The squirmer is a popular model to analyse the fluid mechanics of a self-propelled object, such as a micro-organism. We demonstrate that some fore–aft symmetric squirmers can spontaneously self-propel above a critical Reynolds number. Specifically, we numerically study the effects of inertia on spherical squirmers characterised by an axially and fore–aft symmetric ‘quadrupolar’ distribution of surface-slip velocity; under creeping-flow conditions, such squirmers generate a pure stresslet flow, the stresslet sign classifying the squirmer as either a ‘pusher’ or ‘puller’. Assuming axial symmetry, and over the examined range of the Reynolds number$$Re$$(defined based upon the magnitude of the quadrupolar squirming), we find that spontaneous symmetry breaking occurs in the puller case above$$Re \approx 14.3$$, with steady swimming emerging from that threshold consistently with a supercritical pitchfork bifurcation and with the swimming speed growing monotonically with$$Re$$.
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- Award ID(s):
- 2002120
- PAR ID:
- 10502834
- Publisher / Repository:
- Cambridge University Press
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 983
- 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.2024.149
