Spatial optimal responses to both inlet disturbances and harmonic external forcing for hypersonic flows over a blunt cone at non-zero angles of attack are obtained by efficiently solving the direct–adjoint equations with a parabolic approach. In either case, the most amplified disturbances initially take the form of localised streamwise vortices on the windward side and will undergo a two-stage evolution process when propagating downstream: they first experience a substantial algebraic growth by exploiting the Orr and lift-up mechanisms, and then smoothly transition to a quasi-exponential growth stage driven by the crossflow-instability mechanism, accompanied by an azimuthal advection of the disturbance structure towards the leeward side. The algebraic growth phase is most receptive to the external forcing, whereas the exponential growth stage relies on the disturbance frequency and can be significantly strengthened by increasing the angle of attack. The wavemaker delineating the structural sensitivity region for the optimal gain is shown to lie on the windward side immediately downstream of the inlet, implying a potent control strategy. Additionally, considerable non-modal growth is also observed for broadband high-frequency disturbances residing in the entropy layer.

We revisit the model problem of Squires & Brady (Phys. Fluids, vol. 17, 2005, 073101), where a Brownian probe is dragged through a dilute dispersion of Brownian bath particles. In this problem, the microrheology due to excluded-volume interactions is represented by an effective viscosity, with the nonlinearity in the driving force entering via the dependence of the viscosity increment (relative to the viscosity of a pure solvent) upon the deformation of the dispersion microstructure. Our interest is in the limit of large Péclet numbers, $ P{\kern-1pt}e\gg 1$, where the microstructural deformation adopts the form of a boundary layer about the upstream hemisphere of the probe. We show that the boundary-layer solution breaks down at the equator of the probe and identify a transition region about the equator, connecting the layer to a downstream wake. The microstructural deformation in this region is governed by a universal boundary-value problem in a semi-bounded two-dimensional domain. The equatorial region continues downstream as a transition layer, which separates the wake of the probe from the undisturbed ambient; in that layer, the microstructure is governed by a one-dimensional heat-like equation. Accounting for the combined contributions from the respective asymptotic provinces we find the approximation $ ({1}/{2})[1+ (\ln P{\kern-1pt}e + 1.046)/ P{\kern-1pt}e]$ for the ratio of the large-$ P{\kern-1pt}e$ viscosity increment to the corresponding linear-response increment. Our asymptotic approximation is in excellent agreement with the increment predicted by a finite-difference numerical calculation of the microstructure deformation, tailored to the large-$ P{\kern-1pt}e$ topology.

A typical dielectric-barrier-discharge plasma actuator operating in burst mode generates periodic vortices resembling the starting vortex. This paper presents the three-dimensional (3-D) characteristics and instability mechanism of these vortices. The experimental investigation is carried out using smoke visualisation and time-resolved particle image velocimetry techniques in three orthogonal measurement planes. The size of the vortices decreases with an increase in burst signal frequency, $ f_{b}$, at a constant duty cycle, $ \alpha$. At higher burst frequencies, dipole vortices are formed due to the roll-up of the wall boundary layer. The angle of travel also decreases with an increase in $ f_{b}$. The evolution of $ \lambda _{2}$-criterion clearly demonstrates the vortex merging of co-rotating vortices. The vortex merging occurs at a critical ratio $ a_{c}/l_{c}$ of core size, $ a_{c}$, and separation distance, $ l_{c}$, equal to $ 0.22\pm 0.01$ which is close to $ a_{c}/l_{c} = 0.24\pm 0.01$ reported by Meunier et al. (Phys. Fluids,vol.14, 2002, pp. 2757–2766) for merging of a pair of equal two-dimensional co-rotating vortices. The periodic vortices are self-similar in nature and the vorticity distribution inside their core region follows the Lamb–Oseen vortex model. Cell structures form in the spanwise direction, which develops wave-like behaviour with an increase in burst frequency. Subsequently, these cell-like structures separate from each other, whose size and spacing correlate well with that of vorticity patches. The alternating sign of vorticity indicates that the circular cells have rotational motion in opposite sense with respect to each other. These cells grow downstream and appear in pairs of counter-rotating vortices (vortex dipole) akin to mushroom-like structures. At low values of $ \alpha$ and $ f_{b}$, the periodic vortex is subjected to a very weak strain and centrifugal instability dominates. The vortices are subjected to a higher strain at elevated burst frequencies, leading to the elliptic instability phenomenon similar to that observed in counter-rotating (Leweke & Williamson, J. Fluid Mech. 1998, vol. 360, pp. 85–119) and co-rotating (Meunier & Leweke, J. Fluid Mech.2005, vol. 533, pp. 125–159) vortex pair generated in water. The present experimental results based on the cross-cut visualisation, Galilean streamlines and vorticity decomposition confirm the role of the instability mechanism on the 3-D vortical structures generated by the dielectric-barrier-discharge plasma actuator.

This study explores an interesting fluid–structure interaction scenario: the flow past a flexible filament fixed at two ends. The dynamic performance of the filament under various inclination angles ($\theta$) was numerically investigated using the immersed boundary method. The motion of the filament in the $\theta$–$Lr$ space was categorised into three flapping modes and two stationary modes, where $Lr$ is the ratio of filament length to the distance between its two ends. The flow fields for each mode and their transitions were introduced. A more in-depth analysis was carried out for flapping at a large angle (FLA mode), which is widely present in the $\theta$–$Lr$ space. The maximum width $W$ of the time-averaged shape of the filament has been shown to strongly correlate with the flapping frequency. After non-dimensionalising based on $W$, the flapping frequency shows little variation across different $Lr$ and $\theta$. Moreover, two types of lift variation process were also identified. Finally, the total lift, drag and lift-to-drag ratio of the system were studied. Short filaments, such as those with $Lr\leqslant 1.5$, were shown to significantly increase lift and the lift-to-drag ratio over a wide range of $\theta$ compared with a rigid plate. Flow field analysis concluded that the increases in pressure difference on both sides of the filament, along with the upper part of the flexible filament having a normal direction closer to the $y$ direction, were the primary reasons for the increase in lift and lift-to-drag ratio. This study can provide some guidance for the potential applications of flexible structures.

The stability characteristics of a Mach $5.35$ boundary-layer flow over a flat plate with parametrised two-dimensional sinusoidal surface roughness are investigated. The investigation involves varying the roughness height from $10\,\%$ to $44\,\%$ of the boundary-layer thickness and exploring wavelengths ranging between $0.44$ and $3.56$ times the dominant second-mode wavelength in the region. The introduction of surface roughness leads to notable variations in the mean flow, resulting in separation behind the roughness elements and the propagation of local compression and expansion waves into the free stream. Stability investigations involved the utilisation of wave packet tracking in a linear disturbance simulation (LDS) framework and linear stability theory. The findings revealed significant effects on Mack modes including a reduction in frequency corresponding to maximum amplification with increased roughness height. Proper scaling of the dominant wavelength facilitates a collapse of the growth rate data. In contrast to the commonly reported stabilisation effects for roughness wavelengths significantly larger than the instability mode’s wavelength, the findings primarily revealed destabilisation compared with the smooth-wall case, except for cases with very small roughness wavelengths and large amplitudes approaching the threshold of being classified as porous media. The LDS findings depicted lobed wall pressure amplitude plots, indicating potential undiscovered instability mechanisms or differences compared with the smooth wall. A detailed stability analysis elucidates these LDS findings, establishing a connection between the lobed amplitude structures and substantial changes in local stability characteristics, along with the emergence of Mack’s first, second and third modes.

Parametric oscillations of an interface separating two fluid phases create nonlinear surface waves, called Faraday waves, which organise into simple patterns, such as squares and hexagons, as well as complex structures, such as double hexagonal and superlattice patterns. In this work, we study the influence of surfactant-induced Marangoni stresses on the formation and transition of Faraday-wave patterns. We use a control parameter, $B$, that assesses the relative importance of Marangoni stresses as compared with the surface-wave dynamics. Our results show that the threshold acceleration required to destabilise a surfactant-covered interface through vibration increases with increasing $B$. For a surfactant-free interface, a square-wave pattern is observed. As $B$ is incremented, we report transitions from squares to asymmetric squares, weakly wavy stripes and ultimately to ridges and hills. These hills are a consequence of the bidirectional Marangoni stresses at the neck of the ridges. The mechanisms underlying the pattern transitions and the formation of exotic ridges and hills are discussed.

We present numerical analysis of the lateral movement of a spherical capsule in the steady and pulsatile channel flow of a Newtonian fluid for a wide range of oscillatory frequencies. Each capsule membrane satisfying strain-hardening characteristics is simulated for different Reynolds numbers $Re$ and capillary numbers $Ca$. Our numerical results showed that capsules with high $Ca$ exhibit axial focusing at finite $Re$ similarly to the inertialess case. We observe that the speed of the axial focusing can be substantially accelerated by making the driving pressure gradient oscillate in time. We also confirm the existence of an optimal frequency that maximises the speed of axial focusing, which remains the same found in the absence of inertia. For relatively low $Ca$, however, the capsule exhibits off-centre focusing, resulting in various equilibrium radial positions depending on $Re$. Our numerical results further clarify the existence of a specific $Re$ for which the effect of the flow pulsation to the equilibrium radial position is maximum. The roles of channel size on the lateral movements of the capsule are also addressed. Throughout our analyses, we have quantified the radial position of the capsule in a tube based on an empirical expression. Given that the speed of inertial focusing can be controlled by the oscillatory frequency, the results obtained here can be used for label-free cell alignment/sorting/separation techniques, e.g. for circulating tumour cells in cancer patients or precious haematopoietic cells such as colony-forming cells.