We study numerically the melting of a horizontal layer of a pure solid above a convecting layer of its fluid rotating about the vertical axis. In the rotating regime studied here, with Rayleigh numbers of order $10^{7}$, convection takes the form of columnar vortices, the number and size of which depend upon the Ekman and Prandtl numbers, as well as the geometry – periodic or confined. As the Ekman and Rayleigh numbers vary, the number and average area of vortices vary in inverse proportion, becoming thinner and more numerous with decreasing Ekman number. The vortices transport heat to the phase boundary, thereby controlling its morphology characterized by the number and size of the voids formed in the solid, and the overall melt rate, which increases when the lower boundary is governed by a no-slip rather than a stress-free velocity boundary condition. Moreover, the number and size of voids formed are relatively insensitive to the Stefan number, here inversely proportional to the latent heat of fusion. For small values of the Stefan number, the convection in the fluid reaches a slowly evolving geostrophic state wherein columnar vortices transport nearly all the heat from the lower boundary to melt the solid at an approximately constant rate. In this quasi-steady state, we find that the Nusselt number, characterizing the heat flux, co-varies with the interfacial roughness, for all the flow parameters and Stefan numbers considered here. This confluence of processes should influence the treatment of moving boundary problems, particularly those in astrophysical and geophysical problems where rotational effects are important.

We conduct a theoretical study of a two-phase fluid–structure interaction problem in which air is driven at constant volume flux into a liquid-filled Hele-Shaw channel whose upper boundary is an elastic sheet. A depth-averaged model in the frame of reference of the advancing air–liquid interface is used to investigate the steady and unsteady interface propagation modes via numerical simulation. In slightly collapsed channels, the steadily propagating interface adopts a shape that is similar to the classic Saffman–Taylor finger in rigid Hele-Shaw cells. As the level of initial collapse increases, the induced gradients in channel depth alter the morphology of the propagating finger and promote a variety of instabilities from tip splitting to small-scale fingering on the curved interface, in qualitative agreement with experiments. The model has a complex solution structure with a wide range of stable and unstable, steady and time-periodic modes, many of which have similar driving pressures. We find good quantitative agreement between our model and the experimental data of Ducloué et al. (J. Fluid Mech., vol. 819, 2017, p. 121) for the finger width, sheet profile and finger pressure, provided that corrections to account for the presence of liquid films on the upper and lower walls of the channel are included in the model.

We study the steady force acting on a rigid spherical particle immersed in an ideal gas and impinged by a standing acoustic wave. The acoustic wavelength and particle radius are assumed much larger and smaller, respectively, than the molecular mean-free path. To analyse the system, an asymptotic scheme is constructed, combining an inviscid continuum description in the far field with a free-molecular formulation for the near gas–surface interaction. The computation yields a closed-form expression for the steady acoustic force. The free-molecular solution is compared with a formerly derived result in the continuum regime (Doinkov, Proc. R. Soc. Lond. A, vol. 447, 1994, pp. 447–466), and the latter is found characteristically larger by an order of magnitude at a given ratio between the particle radius and the acoustic wavelength. Markedly, the size of the acoustic force at ballistic flow conditions may become up to four orders of magnitude larger than the typical gravitational force, suggesting the feasibility of nano-particle acoustic levitation.

In rotating stratified flows including in the atmosphere and ocean, inertia-gravity waves (IGWs) often coexist with geostrophically balanced turbulent flows. Advection and refraction by such flows lead to wave scattering, redistributing IGW energy in the position–wavenumber phase space. We give a detailed description of this process by deriving a kinetic equation governing the evolution of the IGW phase-space energy density. The derivation relies on the smallness of the Rossby number characterising the geostrophic flow, which is treated as a random field with known statistics, makes no assumption of spatial scale separation, and neglects wave–wave interactions. It extends previous work restricted to near-inertial waves, barotropic flows or waves much shorter than the flow scales. The kinetic equation describes energy transfers that are restricted to IGWs with the same frequency, as a result of the time scale separation between waves and flow. We formulate the kinetic equation on the constant-frequency surface – a double cone in wavenumber space – using polar spherical coordinates, and we examine the form of the two scattering cross-sections involved, which quantify energy transfers between IGWs with, respectively, the same and opposite directions of vertical propagation. The kinetic equation captures both the horizontal isotropisation and the cascade of energy across scales that result from scattering. We focus our attention on the latter to assess the predictions of the kinetic equation against direct simulations of the three-dimensional Boussinesq equations, finding good agreement.

In this work, we investigate the dynamics of long non-axisymmetric fibres in turbulent channel flow. The experimental facility is the TU Wien Turbulent Water Channel, consisting of a closed water channel (aspect ratio of 10), and the experiments are performed at a shear Reynolds number of 360. Fibres are neutrally buoyant rods that are curved and characterised by a length-to-diameter ratio of 120. Illumination is provided by a laser sheet and the motion of fibres is recorded by four high-speed cameras in a fully developed flow section. We apply multiplicative algebraic reconstruction techniques to the recorded images from four high-speed cameras to identify the three-dimensional location, shape and orientation of the fibres. The fibres are also tracked in time to obtain their three-dimensional vectors of velocity and rotation rate. We investigate the behaviour of the fibres, from the near-wall region to the channel centre, and we produce original statistics on the effect of curvature of the fibres on their orientation and rotation rate. Specifically, we measured the orientation and rotation rate of the fibres, and we can confirm that in the centre, the most homogeneous part of the channel, statistics, although influenced by the curvature, bear similarities to those obtained in previous investigations in homogeneous isotropic turbulence. In addition, we have been able to compare the tumbling rate of our long non-axisymmetric fibres with previous solutions for curved ellipsoids in simple shear flow.

An experimental investigation was carried out in a low-turbulence wind tunnel to study the early development of artificially initiated turbulent spots in a laminar boundary layer over a flat plate. The reproducibility of the experiments allowed us to observe fine structural details that have not been observed previously. Initial velocity disturbances quickly developed into hairpin-like structures that multiplied downstream, which increased the width, length and height of the incipient turbulent spots. Only those disturbances that were greater than a threshold value developed into turbulent spots while the others decayed. The rate of development was also affected by the duration of the initial disturbances. We found that the behaviour of turbulence generation within a turbulent spot is similar to the burst events in the turbulent boundary layer, where ejection events are followed by sweep events.

Studying the effect of different in-stream fluvial turbines siting on river morphodynamics allowed us to witness the onset of a time-averaged, large-scale, alternate distortion of bed elevations, which could not be exclusively related to the turbine rotor blockage. The longitudinal profiles of this two-dimensional bathymetric perturbation resemble those of steady fluvial bars. In this contribution we generalize the problem addressing a spatially impulsive, asymmetric distribution of drag force in the channel cross-section. This is experimentally investigated through the deployment of differently sized grids perpendicular to the flow, and analytically explored as a finite perturbation of an open channel flow over an erodible sediment layer, as described by a coupled flow–sediment shallow water equation. The steady solutions of this fluvial morphodynamic problem, physically represented by alternate bars scaling with the channel width, highlight the importance of the resonant conditions in defining the spatial extent of the bed deformation. The equations further suggest that in very shallow flows any asymmetric obstruction may lead to an upstream propagation of the steady bars, consistent with previous studies on the effects of channel curvature. In broad terms, this study provides the preliminary framework to control the onset of river meandering through imposed finite perturbations of the cross-section. In a more applied sense, it provides a tool to predict non-local scour–deposition patterns associated with the deployment of energy converters or other flow obstructions.

Liquid-infused surfaces (LISs) are a promising technique for reducing friction, fouling and icing in both laminar and turbulent flows. Previous work has demonstrated that these surfaces are susceptible to shear-driven drainage. Here, we report a different failure mode using direct numerical simulations of a turbulent channel flow with liquid-infused longitudinal grooves. When the liquid–liquid surface tension is small and/or grooves are wide, we observe travelling-wave perturbations on the interface with amplitudes larger than the viscous sublayer of the turbulent flow. These capillary waves induce a roughness effect that increases drag. The generation mechanism of these waves is explained using the theory developed by Miles for gravity waves. Energy is transferred from the turbulent flow to the LIS provided that there is a negative curvature of the mean flow at the critical layer. Given the groove width, the Weber number and an estimate of the friction Reynolds number, we provide relations to determine whether a LIS behaves as a smooth or rough surface in a turbulent flow.

We derive equations of motion that describe the dynamics of a fluid confined within an elastic nanotube subject to periodic bending deflections. We use the principle of least action applied to a continuous open system at constant temperature. We solve the equations analytically in two limiting situations: when the tube oscillations are so small that they do not affect the fluid motion, but this one affects the tube dynamics; and when the flow magnitude is so small that it has no influence on the tube dynamics, but this one affects fluid motion. In the first case, we find out that the characteristic bending frequency spectrum of the tube depends not only on the magnitude of flow velocity, as previously stated in the literature, but also on the fluid velocity profile. This could constitute the basis of a strategy for indirect determination of the slip length in carbon nanotubes conveying flow via measurement of the buckling speed. In the second case, we find that tube vibrations can modify the dynamics of the fluid. Particularly, for a fluid subject to a constant pressure gradient, the tube motion induces an oscillatory motion in the fluid with twice the frequency of the tube. Moreover, the amplitude of the oscillatory fluid motion persists at high frequencies. This could constitute a strategy to generate high-frequency flows at nanoscales. Our results open up a panorama to control flow across nanotubes via tube vibrations, which could be complementary to chemical functionalization of nanostructures.

The well-known thermal capillary wave theory, which describes the capillary spectrum of the free surface of a liquid film, does not reveal the transient dynamics of surface waves, e.g. the process through which a smooth surface becomes rough. Here, a Langevin model is proposed that can capture this dynamics, goes beyond the long-wave paradigm which can be inaccurate at the nanoscale, and is validated using molecular dynamics simulations for nanoscale films on both planar and cylindrical substrates. We show that a scaling relation exists for surface roughening of a planar film and the scaling exponents belong to a specific universality class. The capillary spectra of planar films are found to advance towards a static spectrum, with the roughness of the surface $W$ increasing as a power law of time $W\sim t^{1/8}$ before saturation. However, the spectra of an annular film (with outer radius $h_0$) are unbounded for dimensionless wavenumber $qh_0<1$ due to the Rayleigh–Plateau instability.

Instability and transition in the boundary layer on a slender cone ($60^{\circ }$ apex angle) rotating in still fluid are investigated using hot-wire anemometry as well as through linear stability analysis. In contrast to broad cones (including the disk), where a cross-flow instability dominates the transition and different studies report similar transition Reynolds numbers, the reported transition Reynolds numbers on slender cones are scattered. The present experiments provide quantitative experimental datasets and the stability and transition are evaluated based on both the Reynolds number and a Görtler number. The results consistently show that the instability development depends on the Görtler number rather than the Reynolds number and that transition starts at a well-defined Görtler number, whereas the transition Reynolds number depends on the rotational rate. The measured disturbance that first grows in the laminar region has a frequency approximately the same as or twice the rotational rate of the cone, which according to the stability analysis corresponds to the critical frequency of a slightly inclined vortex structure with respect to the cone axis or an axisymmetric vortex structure. These structures are similar to those observed in the flow visualisations of Kobayashi & Izumi (J. Fluid Mech., vol. 127, 1983, pp. 353–364) and considered as being due to a centrifugal instability.

Cylinder stubs of finite length, mounted in a wall-normal manner on a flat plate, exert considerable control on their wake when rotating around their central axis. The present paper investigates these effects with linear stability theory and a direct numerical simulation. Three configurations are considered: evenly spaced corotating roughness elements, as well as positive and negative counter-rotating roughness pairs. Here, ‘positive’ and ‘negative’ are defined in accordance with the induced high- and low-speed streaks, respectively. A primary feature of the rotating-cylinder-induced wake is a ‘dominating inner vortex’ (DIV), which intensifies the lift-up effect and creates high-amplitude streaks. Linear stability analysis shows that the modified streaky flow is capable of effectively stabilizing Tollmien–Schlichting (TS) modes. The mechanism of TS mode stabilization, as found by a perturbation kinetic energy analysis, is attributed to the reduction of the wall-normal perturbation production. On the other hand, an inviscid inflectional instability mode related to the presence of the roughness appears which destabilizes the boundary-layer flow, primarily due to an increase in wall-normal perturbation energy production, but also due to increasing spanwise energy production, depending on the case. The inflectional instability roughness mode is more amplified with thicker cylinders since the induced DIV tends to support longer-living inflection points. Regarding an imaginable laminar–turbulent transition delay, positive rotating thinner roughness pairs would be preferable.

The instantaneous structure of a turbulent boundary layer that has developed beneath freestream turbulence (FST) was investigated with planar particle image velocimetry. Measurements were performed in the streamwise–wall-normal plane at a position $Re_x = U_\infty x / \nu = 2.3 \times 10^6$ downstream of the boundary layer origin. FST was generated with an active grid placed upstream of a boundary layer plate. Three cases were investigated with FST intensity increasing from approximately zero to 12.8 %. It is shown that internal interfaces, separating areas of approximately uniform momentum, are present for all cases and show a dependence on the FST. In particular, the number and length of the uniform-momentum zones (UMZs) decrease with increasing FST. The modal velocities associated with the UMZs are distributed in approximately the same way regardless of the condition of the outer flow, suggesting a degree of resilience of the instantaneous structure to the freestream. Tracking the top edge of the upper-most UMZ revealed that this contour approaches the wall for increasing FST. Finally, it is demonstrated that the observed first-order phenomena in a turbulent boundary layer subjected to FST can be modelled by superimposing an isotropic turbulence field on a turbulent boundary layer field, which supports the hypothesis that the underlying structure of the boundary layer appears to remain largely intact if the naturally occurring fluctuations in the turbulent boundary layer exceed the energy of the FST.

Motivated by design challenges related to aerospace propulsive jets, an experimental investigation has been conducted of the high Mach number jet plume flow field from a round convergent nozzle at under-expanded shock-containing conditions. Hot jets up to a total temperature ratio of 3 were considered. Laser doppler anemometry (LDA) measurements in the jet near field (first 15 nozzle exit diameters) captured the turbulent mixing process in detail, enabling the separate effects of compressibility and static temperature ratio (t) on the development of the velocity and turbulence profiles to be identified. Compressibility dominated in the initial shear layer region, whereas temperature effects controlled the downstream jet merging zone. Analysis of shear layer development demonstrated that, at all temperature ratios, a similar, but significantly stronger, damping effect was observed as in planar shear layers (correlated well by convective Mach number Mc). Consideration of the interaction of compressibility and temperature ratio – which reduce/enhance turbulent mixing respectively – provided for the first time a rational explanation of the observation that increasing jet temperature influenced flow development only up to a static temperature ratio t ~ 1.5, after which further increase has little effect. Measurements of the potential core length (Lp) were analysed to produce an empirical correlation that also illustrated the diminishing effects of heat addition at all jet Mach numbers. The data provide the improved understanding and empirical design techniques essential for developing technologies for jet noise and infra red (IR) signature reduction and represent an important validation test case for computational fluid dynamics (CFD) modelling.

The low-frequency unsteady motions behind a backward-facing step (BFS) in a turbulent flow at $Ma=1.7$ and $Re_\infty =1.3718\times 10^7 \ {\rm m}^{-1}$ are investigated using a well-resolved large-eddy simulation. The instantaneous flow field illustrates the unsteady phenomena of the shock wave/boundary layer interaction (SWBLI) system, including vortex shedding in the shear layer, the flapping motions of the shock and breathing of the separation bubble, streamwise streaks near the wall and arc-shaped vortices in the turbulent boundary layer downstream of the separation bubble. A spectral analysis reveals that the low-frequency behaviour of the system is related to the interaction between shock wave and separated shear layer, while the medium-frequency motions are associated with the shedding of shear layer vortices. Using a three-dimensional dynamic mode decomposition (DMD), we analyse the individual contributions of selected modes to the unsteadiness of the shock and streamwise-elongated vortices around the reattachment region. Görtler-like vortices, which are induced by the centrifugal forces originating from the strong curvature of the streamlines in the reattachment region, are strongly correlated with the low-frequency unsteadiness in the current BFS case. Our DMD analysis and the comparison with an identical but laminar case provide evidence that these unsteady Görtler-like vortices are affected by fluctuations in the incoming boundary layer. Compared with SWBLI in flat plate and ramp configurations, we observe a slightly higher non-dimensional frequency (based on the separation length) of the low-frequency mode.

We consider the hydrodynamic stability of viscoelastic films flowing over inclined structured substrates with rectangular trenches. This topography allows investigating independently the effects of trench unit length, depth, width and inclination angle and complements the earlier work by Pettas et al. (Phys. Rev. Fluids, vol. 4, 2019, 33). We account for material rheology by employing the ePTT model. We perform a parametric study of the steady flow and its linear stability, assuming two-dimensional perturbations along the streamwise direction of arbitrary wavelength via the Floquet–Bloch theory. Our predictions for Newtonian liquids are in excellent agreement with previous results. We demonstrate that even for Newtonian liquids, the trench depth has a non-trivial effect on the flow stability. In viscoelastic solutions, the interaction of fluid elasticity with substrate morphology may have a significant impact on the flow dynamics, leading to either the enhancement or suppression of instabilities. Topography characteristics combined with enough material elasticity stabilize the flow. However, beyond a specific trench depth, this effect saturates by eddy formation inside the cavity. Moreover, the stability is also affected by the aspect ratio and shape of the trenches: flows over substrates with a pillar-like configuration are stabilized significantly. On the other hand, flows are destabilized by material shear-thinning. This study helps identifying the shape of the substrate that maximizes/minimizes the viscoelastic mechanisms. This is impossible when considering substrates with sinusoidal topography, but could be of utmost importance for several technological applications, by providing the potential for instability control through the development of appropriately tailored substrates.

We present data from direct numerical simulations of flow through channels containing large, longitudinal, surface-mounted, rectangular ribs at various spanwise spacings, which lead to secondary flows. It is shown that appropriate modifications to the classical log-law, predicated on a greater wetted surface area than in a plane channel, lead to a log-law-like region in the spanwise-averaged axial mean velocity profiles, even though local profiles may be very different. The secondary flows resulting from the presence of the ribs are examined and their effects discussed. Comparing our results with the literature we conclude that the sense of the secondary flows is largely independent of the particular rib spacing whether normalised by channel depth or rib width. The strength of the secondary flows, however, is shown to depend on the ratio of rib spacing to rib width and on Reynolds number. Topological features of the secondary flow structure are illustrated via a critical point analysis and shown to be characterised in all cases by a free stagnation point above the centre of the rib. Finally, we show that if the domain size is chosen as a ‘minimal channel’ size, rather than a size which allows adequate development of the usual outer layer flow structures, the secondary flows can be affected and this leads inevitably to differences in the near-rib flows so that for ribbed channels, unlike plain channels, it is unwise to use minimal domains to identify details of the near-wall flow.

Vortex breakdown (VB) in unconfined swirling jets occurs as either a bubble form of vortex breakdown (BVB) or a conical form of vortex breakdown (CVB). This computational study examines flow features of these forms for a Reynolds number at which VB is accompanied by a transition to turbulence ($Re = 1000$, based on inflow jet radius and centreline velocity). Large eddy simulations were performed with the inflow condition as the Maxworthy profile which models a laminar, axisymmetric swirling jet, and the effect of varying inflow swirl strength was investigated. BVB was observed at lower swirl strengths than those at which CVB occurs. With increasing swirl, the regular and wide-open types of CVB occur. Spiral coherent structures that develop in the flow were examined using spectral proper orthogonal decomposition. Further, by means of hysteresis studies, it is established that the turbulent BVB and regular CVB are bistable forms. Similarly, it is shown that the two types of CVB are also bistable. The difference in recirculation zone (RZ) sizes between the turbulent BVB and regular CVB is greatly reduced when compared to the laminar counterparts. This is postulated as a reason for misidentification of CVB (RZ approximately conical in shape) as BVB (spheroidal RZ) in some previous studies. The present study highlights the distinct features of turbulent BVB and CVB, which can potentially be used towards improving designs of swirl-stabilized combustors.

A linear stability of a shear-imposed viscous liquid flowing down a vibrating inclined plane is deciphered for disturbances of arbitrary wavenumbers. The main purpose of this study is to expand the model of Woods & Lin (J. Fluid Mech., vol. 294, 1995, pp. 391–407) for a shear-imposed flow (Smith, J. Fluid Mech., vol. 217, 1990, pp. 469–485) when the inclined plane oscillates in streamwise and cross-stream directions, respectively. The time-dependent Orr–Sommerfeld-type boundary value problem is derived and solved numerically based on the Chebyshev spectral collocation method along with Floquet theory. Numerical results corresponding to the cross-stream oscillation disclose that there exist three different types of instabilities, the so-called gravitational, subharmonic and harmonic instabilities, which can be resonated in separate unstable ranges of wavenumber by varying the amplitude of cross-stream oscillation. In fact, the subharmonic and harmonic resonances occur once the forcing amplitude exceeds the respective critical amplitudes for the subharmonic and harmonic instabilities. At low Reynolds number, the subharmonic resonance excited at low forcing amplitude intensifies but attenuates in the presence of imposed shear stress when the forcing amplitude is high. However, the harmonic resonance excited solely at high forcing amplitude intensifies in the presence of imposed shear stress. In contrast, at moderate Reynolds number, the subharmonic resonance excited at low forcing amplitude can be weakened by incorporating an imposed shear stress at the liquid surface. Furthermore, at high Reynolds number, a new instability, the so-called shear instability, arises along with the aforementioned three instabilities and becomes stronger in the presence of imposed shear stress. However, the gravitational and shear instabilities become weaker as soon as the forcing amplitude of cross-stream oscillation increases. On the other hand, numerical results for a streamwise oscillatory flow reveal that there exist three distinct unstable zones separated by stable ranges of Reynolds number. The resonated unstable zone induced by the streamwise oscillation attenuates, but the unstable zone responsible for the gravitational instability enhances in the presence of imposed shear stress. As soon as the Reynolds number is large and the inclination angle is sufficiently small, a new instability, the so-called shear instability, occurs in the finite wavenumber regime along with the resonated and gravitational instabilities. Further, the shear instability also intensifies in the presence of imposed shear stress for a streamwise oscillatory flow.

A stably stratified fluid-filled two-dimensional square cavity is subjected to harmonic horizontal oscillations with frequencies less than the buoyancy frequency. The static linearly stratified state, which is an equilibrium of the unforced system, is not an equilibrium for any non-zero forcing amplitude. As viscous effects are reduced, the horizontally forced flows computed from the Navier–Stokes–Boussinesq equations tend to have piecewise constant or piecewise linear vorticity within the pattern of characteristic lines originating from the corners of the cavity. These flows are well described in the inviscid limit by a perturbation analysis of the unforced equilibrium using the forcing amplitude as the small perturbation parameter. At first order, this perturbation analysis leads to a forced linear inviscid hyperbolic system subject to boundary conditions and spatio-temporal symmetries associated with the horizontal forcing. A Fredholm alternative determines the type of solutions of this system: either the response is uniquely determined by the forcing, or it is resonant and corresponds to an intrinsic mode of the cavity. Both types of responses are investigated in terms of a waveform function satisfying a set of functional equations and are related to the behaviour of the characteristics of the hyperbolic system. In particular, non-retracing (ergodic) characteristics may lead to fractal responses. Models of viscous dissipation are also formulated to adjust the linear inviscid model for viscous effects obtained in the viscous nonlinear simulations.