A fully three-dimensional linear stability analysis is carried out to investigate the unstable bifurcations of a compressible viscous fluid past a sphere. A time-stepper technique is used to compute both equilibrium states and leading eigenmodes. In agreement with previous studies, the numerical results reveal a regular bifurcation under the action of a steady mode and a supercritical Hopf bifurcation that causes the onset of unsteadiness but also illustrate the limitations of previous linear approaches, based on parallel and axisymmetric base flow assumptions, or weakly nonlinear theories. The evolution of the unstable bifurcations is investigated up to low-supersonic speeds. For increasing Mach numbers, the thresholds move towards higher Reynolds numbers. The unsteady fluctuations are weakened and an axisymmetrization of the base flow occurs. For a sufficiently high Reynolds number, the regular bifurcation disappears and the flow directly passes from an unsteady planar-symmetric solution to a stationary axisymmetric stable one when the Mach number is increased. A stability map is drawn by tracking the bifurcation boundaries for different Reynolds and Mach numbers. When supersonic conditions are reached, the flow becomes globally stable and switches to a noise-amplifier system. A continuous Gaussian white noise forcing is applied in front of the shock to examine the convective nature of the flow. A Fourier analysis and a dynamic mode decomposition show a modal response that recalls that of the incompressible unsteady cases. Although transition in the wake does not occur for the chosen Reynolds number and forcing amplitude, this suggests a link between subsonic and supersonic dynamics.

Using a physics-based approach, we infer the impact of the coherence of atmospheric turbulence on the power fluctuations of wind farms. Application of the random-sweeping hypothesis reveals correlations characterized by advection and turbulent diffusion of coherent motions. Those contribute to local peaks and troughs in the power spectrum of the combined units at frequencies corresponding to the advection time between turbines, which diminish in magnitude at high frequencies. Experimental inspection supports the results from the random-sweeping hypothesis in predicting spectral characteristics, although the magnitude of the coherence spectrum appears to be over-predicted. This deviation is attributed to the presence of turbine wakes, and appears to be a function of the turbulence approaching the first turbine in a pair.

We investigate experimentally and theoretically the stability and collapse of holes in liquid layers on bounded substrates with various wettabilities. It is shown that for a liquid layer with a thickness of the order of the capillary length, a stable hole exists when the hole diameter is bigger than a critical value $d_{c}$. Consequently, a further increase of the liquid volume causes the hole to collapse. It is found that $d_{c}$ increases with the size of the container, but its dependence on the contact angle is very weak. The experimental results are compared with theory, and good agreement is obtained. Moreover, we present investigations of the dynamics of the hole and the evolution of the liquid film profile after the collapse. The diameter of the hole during collapse and the minimum thickness of the liquid film shortly after the collapse obey different power laws with time. Simple theoretical models are developed which indicate that the collapse of the hole is triggered by surface tension and the subsequent closure process results from inertia, whereas the growth of the liquid column after hole closure results from the balance between the capillary force and inertia. Corresponding scaling coefficients are determined.

The flickering of buoyant diffusion flames is associated with the periodic shedding of toroidal vortices that are formed under gravity-induced shearing at the flame surface. Numerous experimental investigations have confirmed the scaling, $f\propto D^{-1/2}$, where $f$ is the flickering frequency and $D$ is the diameter of the fuel inlet. However, the connection between the toroidal vortex dynamics and the scaling has not been clearly understood. By incorporating the finding of Gharib et al. (J. Fluid Mech., vol. 360, 1998, pp. 121–140) that the detachment of a continuously growing vortex ring is inevitable and can be dictated by a universal constant that is essentially a non-dimensional circulation of the vortex, we theoretically established the connection between the periodicity of the toroidal vortices and the flickering of a buoyant diffusion flame with small Froude number. The scaling theory for flickering frequency was validated by the existing experimental data of pool flames and jet diffusion flames.

We develop a model of the rapid propagation of water at the contact between elastic glacial ice and a poroelastic subglacial till, motivated by observations of the rapid drainage of supraglacial lakes in Greenland. By treating the ice as an elastic bending beam, the fluid dynamics of contact with the subglacial hydrological network, which is modelled as a saturated poroelastic till, can be examined in detail. The model describes the formation and dynamics of an axisymmetric subglacial cavity, and the spread of pore pressure, in response to injection of fluid. A combination of numerical simulation and asymptotic analysis is used to describe these dynamics for both a rigid and a deformable porous till, and for both laminar and turbulent fluid flow. For constant injection rates and laminar flow, the cavity is isostatic and its spread is controlled by bending of the ice and suction of pore water in the vicinity of the ice–till contact. For a deformable till, this control can be modified: generically, a flexural wave that is initially trapped in advance of the contact point relaxes over time by diffusion of pore pressure ahead of the cavity. While the dynamics are found to be relatively insensitive to the properties of the subglacial till during injection with a constant flux, significant dependence on the till properties is manifest during the subsequent spread of a constant volume. A simple hybrid turbulent–laminar model is presented to account for fast injection rates of water: in this case, self-similar turbulent propagation can initially control the spread of the cavity, but there is a transition to laminar control in the vicinity of the ice–till contact point as the flow slows. Finally, the model results are compared with recent geophysical observations of the rapid drainage of supraglacial lakes in Greenland; the comparison provides qualitative agreement and raises suggestions for future quantitative comparison.

Although boundary-layer flows over convex surfaces are exponentially stable, non-modal mechanisms may enable significant disturbance growth which can make the flow susceptible to secondary instabilities. A parametric investigation of the transient growth and secondary instabilities in flows over convex surfaces is performed. The optimal disturbance in the steady case corresponds to alternating streaks and streamwise vortices of opposite sign that reinforce one another due to lift-up and centrifugal forces, respectively. The process repeats with a constant (naturally appearing) streamwise wavelength which is proportional to the square root of the radius. Unsteady disturbances achieve a higher optimal gain, compared to the steady case, as a result of the opposing effects of the lift-up and centrifugal mechanisms. Linear analysis shows that the curvature has a negligible effect on secondary instabilities. Direct numerical simulations of transient growth with and without secondary instabilities confirm the predictions obtained by the local stability theory. It is found that the presence of a secondary instability is not sufficient, on its own, to ensure transition to turbulence. Only sufficiently long and energetic streaks trigger the breakdown to turbulence.

Experimental evidence is provided to demonstrate that the upstream-travelling waves in two jets screeching in the A1 and A2 modes are not free-stream acoustic waves, but rather waves with support within the jet. Proper orthogonal decomposition is used to educe the coherent fluctuations associated with jet screech from a set of randomly sampled velocity fields. A streamwise Fourier transform is then used to isolate components with positive and negative phase speeds. The component with negative phase speed is shown, by comparison with a vortex-sheet model, to resemble the upstream-travelling jet wave first studied by Tam & Hu (J. Fluid Mech., vol. 201, 1989, pp. 447–483). It is further demonstrated that screech tones are only observed over the frequency range where this upstream-travelling wave is propagative.

Designing effective control for complex three-dimensional flow fields proves to be non-trivial. Often, intuitive control strategies lead to suboptimal control. To navigate the control space, we use a linear parabolized stability analysis to guide the design of a control scheme for a trailing vortex flow field aft of a NACA0012 half-wing at an angle of attack $\unicode[STIX]{x1D6FC}=5^{\circ }$ and a chord-based Reynolds number $Re=1000$. The stability results show that the unstable mode with the smallest growth rate (fifth wake mode) provides a pathway to excite a vortex instability, whereas the principal unstable mode does not. Inspired by this finding, we perform direct numerical simulations that excite each mode with body forces matching the shape function from the stability analysis. Relative to the uncontrolled case, the controlled flows show increased attenuation of circulation and peak streamwise vorticity, with the fifth-mode-based control set-up outperforming the principal-mode-based set-up. From these results, we conclude that a rudimentary linear stability analysis can provide key insights into the underlying physics and help engineers design effective physics-based flow control strategies.

This paper studies the transition to three-dimensional flow in the wake of a cylinder immersed in a free stream, where the cylinder is externally forced to continuously rotate about its axis and to linearly oscillate in the streamwise direction. Floquet stability analysis is used to assess the stability of the nominal two-dimensional flows at a Reynolds number $Re=100$ and rotation rate $\unicode[STIX]{x1D6FC}=\unicode[STIX]{x1D714}D/U=3$ to three-dimensional perturbations, as a function of the amplitude and frequency of the linear oscillations. Two modes of instability are found, distinguished by their spatial structure, temporal behaviour and apparent mechanism. The first mode has a shorter wavelength in the spanwise direction and appears to be linked to a centrifugal instability in the layer of fluid near the rotating body. The second mode has a longer wavelength and is linked to an instability of the vortex cores in the wake that is subharmonic, leading to a period doubling. Either mode can be stable while the other is unstable, depending primarily on the frequency of the oscillation of the cylinder. This indicates that either mode can control the transition to a three-dimensional flow. The results are compared to the fully three-dimensional simulation results of a rotating cylinder elastically mounted and free to oscillate in the streamwise direction from Bourguet & Lo Jacono (J. Fluid Mech., vol. 781, 2015, pp. 127–165), and appear to be able to explain the surprising switching of the observed spanwise wavelength in that flow as a change in the dominant mode, and therefore mechanism, of instability.

The nonlinear evolution of an interface between a perfect conducting liquid and a perfect dielectric gas subject to periodic electrostatic forcing is studied under the long-wave approximation. It is shown that inertial thin films become unstable to finite-wavelength Faraday modes at the onset, prior to the long-wave pillaring instability reported in the lubrication limit. It is further shown that the pillaring-mode instability is subcritical in nature, with the interface approaching either the top or the bottom wall, depending on the liquid–gas holdup. On the other hand, the Faraday modes exhibit subharmonic or harmonic oscillations that nonlinearly saturate to standing waves at low forcing amplitudes. Unlike the pillaring mode, wherein the interface approaches the wall, Faraday modes may exhibit saturated standing waves when the instability is subcritical. At higher forcing amplitudes, the interface may approach either wall, again depending on the liquid–gas holdup. It is also shown that a gravitationally unstable configuration of such thin films, under the long-wave approximation, cannot be stabilized by periodic electrostatic forcing, unlike mechanical Faraday forcing. In this case, it is observed that the interface exhibits oscillatory sliding behaviour, approaching the wall in an ‘earthworm-like’ motion.