The linear instability and breakdown to turbulence induced by an isolated roughness element in a boundary layer at Mach $2. 5$, over an isothermal flat plate with laminar adiabatic wall temperature, have been analysed by means of direct numerical simulations, aided by spatial BiGlobal and three-dimensional parabolized (PSE-3D) stability analyses. It is important to understand transition in this flow regime since the process can be slower than in incompressible flow and is crucial to prediction of local heat loads on next-generation flight vehicles. The results show that the roughness element, with a height of the order of the boundary layer displacement thickness, generates a highly unstable wake, which is composed of a low-velocity streak surrounded by a three-dimensional high-shear layer and is able to sustain the rapid growth of a number of instability modes. The most unstable of these modes are associated with varicose or sinuous deformations of the low-velocity streak; they are a consequence of the instability developing in the three-dimensional shear layer as a whole (the varicose mode) or in the lateral shear layers (the sinuous mode). The most unstable wake mode is of the varicose type and grows on average ${\sim }17\hspace{0.167em} \% $ faster than the most unstable sinuous mode and ${\sim }30$ times faster than the most unstable boundary layer mode occurring in the absence of a roughness element. Due to the high growth-rates registered in the presence of the roughness element, an amplification factor of $N= 9$ is reached within ${\sim }50$ roughness heights from the roughness trailing edge. The independently performed Navier–Stokes, spatial BiGlobal and PSE-3D stability results are in excellent agreement with each other, validating the use of simplified theories for roughness-induced transition involving wake instabilities. Following the linear stages of the laminar–turbulent transition process, the roll-up of the three-dimensional shear layer leads to the formation of a wedge of turbulence, which spreads laterally at a rate similar to that observed in the case of compressible turbulent spots for the same Mach number.

We introduce, in spherical geometry, experiments on electro-hydrodynamic driven Rayleigh–Bénard convection that have been performed for both temperature-independent (‘GeoFlow I’) and temperature-dependent fluid viscosity properties (‘GeoFlow II’) with a measured viscosity contrast up to 1.5. To set up a self-gravitating force field, we use a high-voltage potential between the inner and outer boundaries and a dielectric insulating liquid; the experiments were performed under microgravity conditions on the International Space Station. We further run numerical simulations in three-dimensional spherical geometry to reproduce the results obtained in the ‘GeoFlow’ experiments. We use Wollaston prism shearing interferometry for flow visualization – an optical method producing fringe pattern images. The flow patterns differ between our two experiments. In ‘GeoFlow I’, we see a sheet-like thermal flow. In this case convection patterns have been successfully reproduced by three-dimensional numerical simulations using two different and independently developed codes. In contrast, in ‘GeoFlow II’, we obtain plume-like structures. Interestingly, numerical simulations do not yield this type of solution for the low viscosity contrast realized in the experiment. However, using a viscosity contrast of two orders of magnitude or higher, we can reproduce the patterns obtained in the ‘GeoFlow II’ experiment, from which we conclude that nonlinear effects shift the effective viscosity ratio.

A numerical and experimental study of radiometric forces on vanes of different thickness is presented for the flow regime where the radiometric force is near its maximum. For single- and multi-vane geometries, it is shown that radiometric force decreases by only ∼10–15 % when the vane thickness-to-height ratio increases fourfold from 0.5 to 2. For a single-vane geometry, the shear force on the lateral side of the vane is attributed to a vortex flow generated by the interaction of cold chamber walls and heated walls of the vane. In that case, it always acts to reduce the total radiometric force governed by the pressure difference between the hot and the cold sides of the vane. For a multi-vane geometry, represented by a perforated vane, the shear force becomes positive for larger thickness-to-height ratios and lower pressures, primarily due to strong vane-driven transpiration flow through the gaps.

The dynamics of a flexible filament sedimenting in a viscous fluid are explored analytically and numerically. Compared with the well-studied case of sedimenting rigid rods, the introduction of filament compliance is shown to cause a significant alteration in the long-time sedimentation orientation and filament geometry. A model is developed by balancing viscous, elastic and gravitational forces in a slender-body theory for zero-Reynolds-number flows, and the filament dynamics are characterized by a dimensionless elasto-gravitation number. Filaments of both non-uniform and uniform cross-sectional thickness are considered. In the weakly flexible regime, a multiple-scale asymptotic expansion is used to obtain expressions for filament translations, rotations and shapes. These are shown to match excellently with full numerical simulations. Furthermore, we show that trajectories of sedimenting flexible filaments, unlike their rigid counterparts, are restricted to a cloud whose envelope is determined by the elasto-gravitation number. In the highly flexible regime we show that a filament sedimenting along its long axis is susceptible to a buckling instability. A linear stability analysis provides a dispersion relation, illustrating clearly the competing effects of the compressive stress and the restoring elastic force in the buckling process. The instability travels as a wave along the filament opposite the direction of gravity as it grows and the predicted growth rates are shown to compare favourably with numerical simulations. The linear eigenmodes of the governing equation are also studied, which agree well with the finite-amplitude buckled shapes arising in simulations.

Direct numerical simulations are used to investigate the individual dynamics of large spherical particles suspended in a developed homogeneous turbulent flow. A definition of the direction of the particle motion relative to the surrounding flow is introduced and used to construct the mean fluid velocity profile around the particle. This leads to an estimate of the particle slipping velocity and its associated Reynolds number. The flow modifications due to the particle are then studied. The particle is responsible for a shadowing effect that occurs in the wake up to distances of the order of its diameter: the particle calms turbulent fluctuations and reduces the energy dissipation rate compared to its average value in the bulk. Dimensional arguments are presented to draw an analogy between particle effects on turbulence and wall flows. Evidence is obtained for the presence of a logarithmic sublayer at distances between the thickness of the viscous boundary layer and the particle diameter ${D}_{p} $. Finally, asymptotic arguments are used to relate the viscous sublayer quantities to the particle size and the properties of the outer turbulence. It is shown in particular that the skin-friction Reynolds number behaves as $R{e}_{\tau } \propto {({D}_{p} / \eta )}^{4/ 3} $.

The drag of a rigid object is expected to increase with flow velocity. For wide ranges of velocities commonly encountered, the drag increases as the square of the relative velocity of the fluid. This strong dependence of the load on the velocity accounts for specific survival strategies adopted by passive living systems such as plants in wind or algae in marine environments: through elastic reconfiguration, the drag on plants is reduced when compared to a rigid configuration and the velocity exponent for the drag is typically found to be between 1 and 1.5. In this work, a membrane configuration is presented that exhibits a drag force that is almost independent of the free-stream velocity. This surprising result is shown to be remarkably robust as it is experimentally observed for a range of geometries. This study opens the way for the design of devices subjected to a drag that is independent of the flow velocity. This possibility constitutes a key point in various fields involving flexible structures that are towed or subjected to wind.

Through theory and numerical simulations in an axisymmetric geometry, we examine evolution of a symmetric intrusion released from a cylindrical lock in stratified fluid as it depends upon the ambient interface thickness, $h$, and the lock aspect ratio ${R}_{c} / H$, in which ${R}_{c} $ is the lock radius and $H$ is the ambient depth. Whereas self-similarity and shallow-water theory predicts that intrusions, once established, should decelerate shortly after release from the lock, we find that the intrusions rapidly accelerate and then enter a constant-speed regime that extend between $2{R}_{c} $ and $5{R}_{c} $ from the gate, depending upon the relative interface thickness ${\delta }_{h} \equiv h/ H$. This result is consistent with previously performed laboratory experiments. Scaling arguments predict that the distance, ${R}_{a} $, over which the lock fluid first accelerates increases linearly with ${R}_{c} $ if ${R}_{c} / H\ll 1$ and ${R}_{a} / H$ approaches a constant for high aspect ratios. Likewise in the constant-speed regime, the speed relative to the rectilinear speed, $U/ {U}_{\infty } $, increases linearly with ${R}_{c} / H$ if the aspect ratio is small and is of order unity if ${R}_{c} / H\gg 1$. Beyond the constant-speed regime, the intrusion front decelerates rapidly, with power-law exponent as large as $0. 7$ if the relative ambient interface thickness, ${\delta }_{h} \lesssim 0. 2$. For intrusions in uniformly stratified fluid (${\delta }_{h} = 1$), the power-law exponent is close to $0. 2$. Except in special cases, the exponents differ significantly from the $1/ 2$ power predicted from self-similarity and the $1/ 3$ power predicted for intrusions from partial-depth lock releases.

Two new families of exact coherent states are found in plane Poiseuille flow. They are obtained from the stationary and the travelling-wave mirror-symmetric solutions in plane Couette flow by a homotopy continuation. They are characterized by the mirror symmetry inherited from those continued solutions in plane Couette flow. The first family arises from a saddle-node bifurcation and the second family bifurcates by breaking the top–bottom symmetry of the first family. We find that both families exist below the minimum saddle-node-point Reynolds number known to date (Waleffe, Phys. Fluids, vol. 15, 2003, pp. 1517–1534).

In a recent study on a coupled laser system, Thévenin et al. (Phys. Rev. Lett., vol. 107, 2011, 104101) reported the first experimental evidence of phase trapping, a partially synchronous state characterized by frequency locking without phase locking. To determine whether this state can arise in a hydrodynamic system, we reanalyse the data from our recent experiment on a periodically forced self-excited low-density jet (J. Fluid Mech., vol. 726, 2013, pp. 624–655). We find that this jet exhibits the full range of phase dynamics predicted by model oscillators with weak nonlinearity. These dynamics include (i) phase trapping between phase drifting and phase locking when the jet is forced far from its natural frequency and (ii) phase slipping during phase drifting when it is forced close to its natural frequency. This raises the possibility that similar phase dynamics can be found in other similarly self-excited flows. It also strengthens the validity of using low-dimensional nonlinear dynamical systems based on a universal amplitude equation to model such flows, many of which are of industrial importance.

The nonlinear triad interaction of two opposing gravity waves with almost identical frequencies and one much longer acoustic-gravity wave is studied for non-resonance, as well as for exact resonance conditions. For non-resonance conditions the previously known results for a ‘bound’ acoustic-gravity wave are recovered. For resonance, or near-resonance conditions, where all three waves are ‘free waves’, the interaction is recurrent and the amplitude of the free acoustic-gravity wave turns out to be much larger than that known for the bound wave. The results for the recurrent evolution are given analytically, in terms of Jacobian elliptic functions and elliptic integrals.

Time-resolved stereoscopic PIV was used to investigate the curvature-induced structures downstream of a $90{{}^\circ} $ bend at Reynolds numbers between $20\times 1{0}^{3} $ and $115\times 1{0}^{3} $. Data were taken at three downstream locations to investigate the evolution of the structures. Snapshot proper orthogonal decomposition (POD) analysis shows that the most energetic structure is not the well-known Dean motion but a bimodal single cell structure with alternating direction of rotation, called the ‘swirl switching’ mode. The strengths of the Dean motion and the swirl-switching structures are similar, indicating that the difference in energy is related to their duration of occurrence, where the Dean motion is associated with a comparatively rapid transition between the two states in the swirl switching mode.