We consider the flow induced by a sphere, contained in an otherwise quiescent body of fluid, that is suddenly imparted with angular momentum. This classical problem is known to exhibit a finite-time singularity in the boundary-layer equations, due to the viscous boundary layer, induced by the sudden rotation, colliding at the sphere's equator. We consider this flow from the perspective of the post-collision dynamics, showing that the collision gives rises to a radial jet headed by a swirling toroidal starting vortex pair. The starting vortex propagates away from the sphere and, in doing so, loses angular momentum. The jet, in turn, develops an absolute instability which propagates back towards the sphere's equator. The starting vortex pair detaches from the jet and expands as a coherent (non-swirling) toroidal vortex pair. We also present results of some new experiments which show good qualitative agreement with our computational results.

The unsteady flow due to a sphere, immersed in a quiescent fluid, and suddenly rotated, is a paradigm for the development of unsteady boundary layers and their collision. Such a collision arises when the boundary layers on the surface of the sphere are advected towards the equator, where they collide, serving to generate a radial jet. We present the first particle image velocimetry measurements of this collision process, the resulting starting vortex and development of the radial jet. Coupled with new computations, we demonstrate that the post-collision steady flow detaches smoothly from the sphere’s surface, in qualitative agreement with the analysis of Stewartson (Grenzschichtforschung/Boundary Layer Research (ed. H. Görtler), Springer, 1958, pp. 60–70), with no evidence of a recirculation zone, contrary to the conjectured structure of Smith & Duck (Q. J. Mech. Appl. Maths, vol. 20, 1977, pp. 143–156).

A numerical study on the effect of surface slip on the flow in a constricted channel is presented, with the aim of exploring the use of surface slip to control flow separation. Our focus is on two-dimensional flow in a channel over a bump, with a fixed aspect ratio, upon which a Robin-type slip boundary condition is imposed. When the channel walls are fully no-slip, such a flow is known to develop a region of separation behind the bump, at sufficiently large Reynolds numbers. The effect of slip on the separation bubble dynamics occurring behind the bump is investigated, for Reynolds numbers $2000$ and $4000$ . It is shown that surface slip (i) attenuates the intensity of separation as it diminishes the minimum of the streamwise velocity within the recirculation region; (ii) delays the onset of flow separation, shifting it downstream, along the bump, and (iii) reduces the dimensions of the separation bubble behind the bump, allowing the flow to reattach sooner. Ultimately, slip inhibits separation, with both the points of separation and reattachment coalescing, for a slip length $\lambda$ of approximately $0.2$ .

The main concern of this paper is to investigate the effects on the stability behavior of wall suction or injection for external boundary-layer flow over a heated, porous plate for a fluid with temperature-dependent viscosity. The wall suction or injection are applied to the flow by a simple modification for the no-penetration condition and the current boundary conditions on the flat plate. Liquid-type viscosities are found to entrain both the velocity and temperature profiles closer to the plate with increasing both temperature sensitivity and suction intensity, whereas gas-type viscosities are found to exhibit the reverse effect with increasing flow injection and decreasing temperature dependence. We present then the linear stability analysis and find that increasing both the temperature dependence (from gas-to liquid-type behavior) and suction intensity of the fluid leads to increasing critical Reynolds number to a point of maximum stability. We note also that increasing both the Prandtl number (Pr) and flow suction in the liquid-type behavior results in an increased critical Reynolds number. The magnitudes of the perturbation eigenfunctions are considered before utilising them to obtain solutions to an energy balance integral. We find that the eigenfunction profiles are imitative of the narrowing of their mean flow counterparts when increasing either the temperature dependence or the flow suction. Our results are then confirmed by the energy analysis, where we find a significant reduction in the energy produced by the disturbance with increasing suction intensity and ultimately leads to a more stable flow. Overall, there is a strong destabilizing effect with increasing injection and the temperature-dependent viscosity over a heated plate. In summary, the findings indicate that increasing the wall suction and temperature dependence results in significantly more stable flows. It is worth noting that application and extension of this study are considered in the context of chemical vapor deposition reactors.

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A linear stability investigation is undertaken on the two-dimensional flow that develops in a channel whose walls are coated with a superhydrophobic material. The surfaces are modeled as classical slip surfaces, exploiting a linear Navier slip condition imposed on the channel walls. Both symmetric and asymmetric slip walls are considered, whereby the linearized stability of the flow is determined via an Orr–Sommerfeld normal-mode approach. In both instances, the application of slip establishes a significant stabilizing effect and increases the critical Reynolds number associated with the onset of linearly unstable behavior. Indeed, for sufficiently large slip lengths, the upper and lower branches of the neutral stability curve coalesce. Consequently, the flow becomes linearly stable to all disturbances for all wavelengths and Reynolds numbers.

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