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Direct numerical simulations of spanwise-rotating turbulent channel flow with a parabolic bump on the bottom wall are employed to investigate the effects of rotation on flow separation. Four rotation rates,$$Ro_b := 2\varOmega H/U_b = \pm 0.42$$,$$\pm$$1.0, are compared with the non-rotating scenario. The mild adverse pressure gradient induced by the lee side of the bump allows for a variable pressure-induced separation. The separation region is reduced (increased) when the bump is on the anti-cyclonic (cyclonic) side of the channel, compared with the non-rotating separation. The total drag is reduced in all rotating cases. Through several mechanisms, rotation alters the onset of separation, reattachment and wake recovery. The mean momentum deficit is found to be the key. A physical interpretation of the ratio between the system rotation and mean shear vorticity,$$S:=\varOmega /\varOmega _s$$, provides the mechanisms regarding stability thresholds$$S=-0.5$$and$$-$$1. The rotation effects are explained accordingly, with reference to the dynamics of several flow structures. For anti-cyclonic separation, particularly, the interaction between the Taylor–Görtler vortices and hairpin vortices of wall-bounded turbulence is proven to be responsible for the breakdown of the separating shear layer. A generalized argument is made regarding the essential role of near-wall deceleration and resultant ejection of enhanced hairpin vortices in destabilizing an anti-cyclonic flow. This mechanism is anticipated to have broad impacts on other applications in analogy to rotating shear flows, such as thermal convection and boundary layers over concave walls.
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Optimal wall shapes and flows for steady planar convection
We compute steady planar incompressible flows and wall shapes that maximize the rate of heat transfer ($$Nu$$) between hot and cold walls, for a given rate of viscous dissipation by the flow ($$Pe^2$$), with no-slip boundary conditions at the walls. In the case of no flow, we show theoretically that the optimal walls are flat and horizontal, at the minimum separation distance. We use a decoupled approximation to show that flat walls remain optimal up to a critical non-zero flow magnitude. Beyond this value, our computed optimal flows and wall shapes converge to a set of forms that are invariant except for a$$Pe^{-1/3}$$scaling of horizontal lengths. The corresponding rate of heat transfer$$Nu \sim Pe^{2/3}$$. We show that these scalings result from flows at the interface between the diffusion-dominated and convection-dominated regimes. We also show that the separation distance of the walls remains at its minimum value at large$$Pe$$.
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- Award ID(s):
- 2204900
- PAR ID:
- 10535894
- Publisher / Repository:
- Cambridge Univ Press
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 984
- 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.2024.202
