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.

What is the shape formed by a body that is melting or dissolving into an ambient fluid? We present a theoretical analysis of the dynamics of melting or dissolving bodies in the common situation where the transfer of heat or solute at the surface creates a thin thermal or solutal convective boundary layer along its surface. By conducting a general analysis of a mathematical model describing the shape evolution of such bodies (Pegler & Davies Wykes, J. Fluid Mech., vol. 900, 2020, A35), we reveal new phenomena relating to the emergence of fundamental similarity solutions, asymptotic transitions, tip structure and the conditions for the development of sharp versus blunted tips. A universal regime diagram is developed showing asymptotic transitions between two different classes of similarity solutions. With $t$ time, the tip of initially rectangular bodies is found to descend as $t^{4/3}$ at early times, but transitions to the considerable faster power of $t^4$ at long times, for example. Surprisingly, the tips of certain shapes, including initially rectangular bodies, sharpen continuously, whilst those of others, including initially conic bodies, blunt for all times. For the former case, the tip curvature grows rapidly as $t^{12}$, forming a needle-like shape. More general initial shapes can produce multiple transitions between sharpening and blunting. These results provide foundational understanding of buoyancy-driven fluid sculpting that underlies numerous natural and industrial applications.

Dispersion of droplets in an emulsion is commonly seen in several chemical, pharmaceutical and petroleum industries. Electric field has been shown to affect the stability of these dispersions. We study the dynamics of a pair of leaky dielectric droplets in a leaky dielectric liquid in the presence of an externally applied electric field. A pair of droplets may coalesce or repel each other in the presence of an electric field. Interactions between a pair of drops have been shown to be governed by the ratio $\varepsilon _r/\sigma _r$, where $\varepsilon _r$ and $\sigma _r$ are the ratios of drop to ambient fluid electric permittivities and conductivities, respectively. When inertia is neglected, the droplets approach each other if $\varepsilon _r/\sigma _r > 1$, whereas droplets repel when $\varepsilon _r/\sigma _r < 1$. However, inclusion of inertia permits interesting transient behaviour, where the droplets may attract due to the electrostatic dipole–dipole attraction even for $\varepsilon _r/\sigma _r < 1$. The approach velocity then is governed by the electrostatic forces and varies as $1/h^4$, where $h$ is the separation distance between the droplets, in contrast to being hydrodynamically driven as predicted in the Stokes flow limit by Baygents et al. (J. Fluid Mech., vol. 368, 1998, pp. 359–375). For compound droplets, interactions between droplets are essentially governed by the electrical properties of the outer droplet and the ambient fluid. However, transient dynamics may also result in the breakup of a compound droplet and lead to formation of single droplets.

The incompressible $\mu (I)$-rheology has been used to study subaerial granular flows with remarkable success. For subaquatic granular flows, drag between grains and the pore fluid is substantially higher and the physical behaviour is more complex. High drag forces constrain the rearrangement of grains and dilatancy, leading to a considerable buildup of pore pressure. Its transient and dynamic description is the key to modelling subaquatic granular flows but out of the scope of incompressible models. In this work, we advance from the incompressible $\mu (I)$-rheology to the compressible $\mu (J)$, $\phi (J)$-rheology to account for pore pressure, dilatancy and the scaling laws under subaquatic conditions. The model is supplemented with critical state theory to yield the correct properties in the quasi-static limit. The pore fluid is described by an additional set of conservation equations and the interaction with grains is described by a drag model. This new implementation enables us to include most of the physical processes relevant for submerged granular flows in a highly transparent manner. Both the incompressible and compressible rheologies are implemented into OpenFOAM, and various simulations at low and high Stokes numbers are conducted with both frameworks. We found a good agreement of the $\mu (J)$, $\phi (J)$-rheology with low-Stokes-number experiments, which incompressible models fail to describe. The combination of granular rheology, pore pressure and drag model leads to complex phenomena such as apparent cohesion, remoulding, hydroplaning and turbidity currents. The simulations give remarkable insights into these phenomena and increase our understanding of subaquatic mass transports.

The application of cavitation-induced shock waves generated at low driving frequencies, known as power ultrasound, is essential for a wide range of fields, such as sonochemistry, lithotripsy, nanomaterials, emulsions and casting, to name but a few. In this paper, we present measurements of the shock wave pressures emitted by cavitating bubbles in water, under ultrasonic excitation produced by an immersed probe oscillating at 24 kHz. A broad-spectrum fibre-optic hydrophone calibrated in the range of 1–30 MHz was used for this purpose. Spectral analysis of the data reveals a consistent resonance peak at a very narrow range of frequencies (3.27–3.43 MHz). Results were confirmed using real-time analysis of high-speed recordings. By eliminating other possible sources, we propose that this new peak might be associated with shock wave emissions from collapsing bubbles. Spatial maps obtained by collating individual shock wave pressures highlight the effect of pressure shielding with increasing input power, attributed to a cloud of bubbles surrounding the probe. This work contributes towards the elucidation of the key properties of cavitation-driven shock waves and the underlying mechanisms, essential in controlling the effectiveness of the external processing conditions on various physical, chemical and biological systems.

Non-decaying bores are generated in a laboratory using a dam-break system with different reservoir length and depth ratios at the dam-break gate. The experimental data show the dependency of inundation depth, run-up height and flood duration on the reservoir length and the bore strength at the beach toe. Employing the method of characteristics, the relationship between the reservoir length and the bore characteristics at beach toe is obtained. Numerical simulations are carried out for a series of dam-break generated bores, extending the range of physical parameters used in the laboratory experiments. The accuracy of the numerical results is confirmed by the experimental data. Predictive formulae are then obtained for the inundation depth, run-up height and flood duration in terms of the bore characteristics at beach toe and beach slope. Finally, the minimum bore lengths at beach toe necessary to produce the maximum inundation depths and the flooding plateau are identified in the parameter space. These relations can be employed to design dam-break experiments for generating bores with a target length or duration.

New experimental results on turbulent boundary layers (TBLs) with wall suction show that it is possible to experimentally realise a turbulent asymptotic suction boundary layer (TASBL), i.e. a boundary layer which becomes independent of the streamwise location and with the suction rate as the only control parameter. Turbulent asymptotic suction boundary layers show a mean-velocity profile with a large logarithmic region and without a clear wake region. If outer-scaling is adopted, using the free stream velocity and the boundary layer thickness as characteristic velocity and length scale, respectively, a single log-law describes the logarithmic region of all the measured TASBLs independently from the suction rate. Streamwise velocity profiles were measured with different hot-wire probe sizes, in order to account for and correct for probe-filtering effects. It emerges that wall suction is responsible for strong damping of the velocity fluctuations, with a decrease of the near-wall peak of the velocity-variance profile ranging from $50\,\%$ to $65\,\%$ when compared with a canonical zero-pressure gradient TBL at comparable Reynolds number. The analysis of the power spectral density maps suggests that the decrease in the turbulent activity can be explained by increased stability of the near-wall streaks.

The stratified inner-shelf response to surf-zone-generated transient rip currents (TRC) is examined using idealized simulations with uniform initial thermal stratification $\mathrm {d}{T_0}/\mathrm {d}{z}$, with initial temperature T0 and vertical coordinate z, or initial squared buoyancy frequency $N_0^2$, varying from unstratified to highly stratified ($0.75^\circ \text {C}\ \text {m}^{-1}$). The TRC-induced depth-integrated cross-shore eddy kinetic energy flux is independent of $\mathrm {d}{T_0}/\mathrm {d}{z}$ and decays to near zero within $4L_{SZ}$ (surf-zone width $L_{SZ}=100$ m). Cross-shore inhomogeneous TRC mixing causes shoreward broadening isotherms, driving a near-field inner-shelf overturning circulation and a far-field geostrophic along-shore velocity that strengthen with $\mathrm {d}{T_0}/\mathrm {d}{z}$. TRC mixing mostly (90 %) increases background potential energy (BPE) and also available (APE, 10 %) potential energy, driving inner-shelf mean circulation. The specific BPE zero-crossing depth $d_{s}$ collapses the near-field $3$-layer cross-shore velocity, using an intrusive gravity current scaling $(d_{s} N_0)$. The approximately steady exchange flow exports low-stratification fluid ($N/N_0\approx 1/2$) at a depth $z/d_{s}\approx -1$, re-supplying the TRC region with stratified fluid from above/below, similar to localized mixing laboratory experiments. Offshore of $\approx 5L_{SZ}$, a self-similar far-field intrusion with characteristic isotherm slope $d_{s}/L_{R}$ (Rossby deformation radius $L_{R}\sim d_{s} f/N_0$) is in approximate geostrophic balance with the non-dimensional along-shore velocity. Inner-shelf near-field and far-field horizontal length scales vary as $x/d_{s}$ and $x/L_{R}$, respectively. The length scale $d_{s}$ is related to the work performed by TRC mixing using an idealized well-mixed wedge geometry. Idealized analytical scalings are qualitatively consistent with modelled BPE and APE distributions. Thus, the self-similar stratified inner-shelf response to TRC-driven mixing depends on key dimensional parameters $N_0$ and $d_{s}$.

This paper develops second-order theory for narrow-banded surface gravity wavepackets experiencing a sudden depth transition based on a Stokes and multiple-scales expansion. As a wavepacket travels over a sudden depth transition, additional wavepackets are generated that propagate freely obeying the linear dispersion relation and arise at both first and second order in wave steepness in a Stokes expansion. In the region near the top of the depth transition, the resulting transient processes play a crucial role. At second order in wave steepness, free and bound waves coexist with different phases. Their different speeds of travel result in a local peak a certain distance after the depth transition. This distance depends on the water depth $h_s$ relative to the carrier wavelength on the shallower side $\lambda _{0s}$. We validate our theory through comparison with fully nonlinear numerical simulations. Experimental validation is provided in a companion paper (Li et al, J. Fluid Mech., 2021, 915, A72). We conjecture that the combination of the local transient peak at second order and the magnitude of the linear free waves provides the explanation for the rogue waves observed after a sudden depth transition reported in a significant number of papers and reviewed in Trulsen etal (J. Fluid Mech., vol. 882, 2020, R2).

Surface gravity wavepackets in intermediate water depth experiencing an abrupt depth decrease are investigated experimentally. The experiments provide validation for the second-order (in steepness) theory for narrow-banded surface gravity wavepackets experiencing a sudden depth transition derived in a companion paper (Li et al., J. Fluid Mech., 2021, 915, A71). We observe the generation of free second-order sub- and superharmonic wavepackets due to the sudden depth transition, in addition to changes to the main (first-order) wavepacket and its second-order bound waves. Locally, just after the step, this leads to the superposition of different wavepacket components. Thereafter, separation occurs because of the different group speeds of the free second-order sub- and superharmonic wavepackets compared with the main packet. Experiments show that the local superposition of waves can lead to significant amplification of wave crests near the top of a step, as predicted by theory. In addition to a step, we also experimentally examine more gradual depth changes in the form of 1 : 1 and 1 : 3 slopes to explore the limits of the theory's validity. Although we find small differences in amplitude and phase comparing these steep slopes with a step, these experiments suggest that the theoretical model derived in Part 1 for wavepackets travelling over a step is applicable to slopes steeper than $1\,{:}\,3$.

We examine the effect on near-wall turbulence of displacing the apparent, virtual origins perceived by different components of the overlying flow. This mechanism is commonly reported for drag-altering textured surfaces of small size. For the particular case of riblets, Luchini et al. (J. Fluid Mech., vol. 228, 1991, pp. 87–109) proposed that their effect on the overlying flow could be reduced to an offset between the origins perceived by the streamwise and spanwise velocities, with the latter being the origin perceived by turbulence. Later results, particularly in the context of superhydrophobic surfaces, suggest that this effect is not determined by the apparent origins of the tangential velocities alone, but also by the one for the wall-normal velocity. To investigate this, the present paper focuses on direct simulations of turbulent channels imposing different virtual origins for all three velocity components using Robin, slip-like boundary conditions, and also using opposition control. Our simulation results support that the relevant parameter is the offset between the virtual origins perceived by the mean flow and turbulence. When using Robin, slip-like boundary conditions, the virtual origin for the mean flow is determined by the streamwise slip length. Meanwhile, the virtual origin for turbulence results from the combined effect of the wall-normal and spanwise slip lengths. The slip experienced by the streamwise velocity fluctuations, in turn, has a negligible effect on the virtual origin for turbulence, and hence the drag, at least in the regime of drag reduction. This suggests that the origin perceived by the quasi-streamwise vortices, which induce the cross-flow velocities at the surface, is key in determining the virtual origin for turbulence, while that perceived by the near-wall streaks, which are associated with the streamwise velocity fluctuations, plays a secondary role. In this framework, the changes in turbulent quantities typically reported in the flow-control literature are shown to be merely a result of the choice of origin, and are absent when using as origin the one experienced by turbulence. Other than this shift in origin, we demonstrate that turbulence thus remains essentially smooth-wall-like. A simple expression can predict the virtual origin for turbulence in this regime. The effect can also be reproduced a priori by introducing the virtual origins into a smooth-wall eddy-viscosity framework.

Recently, in Zhang et al. (Phys. Rev. Lett., vol. 124, 2020, 084505), it was found that, in rapidly rotating turbulent Rayleigh–Bénard convection in slender cylindrical containers (with diameter-to-height aspect ratio $\varGamma =1/2$) filled with a small-Prandtl-number fluid (${Pr}\approx 0.8$), the large-scale circulation is suppressed and a boundary zonal flow (BZF) develops near the sidewall, characterized by a bimodal probability density function of the temperature, cyclonic fluid motion and anticyclonic drift of the flow pattern (with respect to the rotating frame). This BZF carries a disproportionate amount (${>}60\,\%$) of the total heat transport for ${Pr} < 1$, but decreases rather abruptly for larger ${Pr}$ to approximately $35\,\%$. In this work, we show that the BZF is robust and appears in rapidly rotating turbulent Rayleigh–Bénard convection in containers of different $\varGamma$ and over a broad range of ${Pr}$ and ${Ra}$. Direct numerical simulations for Prandtl number $0.1 \leq {\textit {Pr}} \leq 12.3$, Rayleigh number $10^7 \leq {Ra} \leq 5\times 10^{9}$, inverse Ekman number $10^{5} \leq 1/{\textit {Ek}} \leq 10^{7}$ and $\varGamma = 1/3$, 1/2, 3/4, 1 and 2 show that the BZF width $\delta _0$ scales with the Rayleigh number ${Ra}$ and Ekman number ${\textit {Ek}}$ as $\delta _0/H \sim \varGamma ^{0} Pr^{\{-1/4, 0\}} {Ra}^{1/4} {\textit {Ek}}^{2/3}$ ($\{{\textit {Pr}}<1, {\textit {Pr}}>1\}$) and with the drift frequency scales as $\omega /\varOmega \sim \varGamma ^{0} Pr^{-4/3} {Ra}\,{\textit {Ek}}^{5/3}$, where $H$ is the cell height and $\varOmega$ the angular rotation rate. The mode number of the BZF is 1 for $\varGamma \lesssim 1$ and $2 \varGamma$ for $\varGamma = \{1,2\}$ independent of ${Ra}$ and ${Pr}$. The BZF is quite reminiscent of wall mode states in rotating convection.

In geo- and astrophysics, low Prandtl number convective flows often interact with magnetic fields. Although a static magnetic field acts as a stabilizing force on such flow fields, we find that self-organized convective flow structures reach an optimal state where the heat transport significantly increases and convective velocities reach the theoretical free-fall limit, i.e. the maximum possible velocity a fluid parcel can achieve when its potential buoyant energy is fully converted into kinetic energy. Our measurements show that the application of a static magnetic field leads to an anisotropic, highly ordered flow structure and a decrease of the turbulent fluctuations. When the magnetic field strength is increased beyond the optimum state, Hartmann braking becomes dominant and leads to a reduction of the heat and momentum transport. The results are relevant for the understanding of magneto-hydrodynamic convective flows in planetary cores and stellar interiors in regions with strong toroidal magnetic fields oriented perpendicular to temperature gradients.

Place a droplet of mineral oil on water and the oil will spread to cover the water surface in a thin film. In this paper we study the everted problem: an aqueous droplet deposited onto a deep layer of silicone oil. As it is energetically favourable for the oil phase to spread to cover the droplet surface completely, the droplet is ultimately engulfed in the oil layer. We present a detailed study of engulfment dynamics, from the instant the droplet impacts the oil surface until it finally sediments into the less dense oil. We study a broad range of droplet sizes (micrometric to millimetric) and oil kinematic viscosities ($10^2$–$10^5$ cSt), corresponding to a viscosity-dominated parameter regime. We find that droplet engulfment involves the rapid submersion of the droplet driven by capillary forces in the oil surface, followed by the much slower peeling of the droplet from the interface, to which it is adhered via a thin cloaking layer of oil formed during the earlier stage. The later peeling stage is driven by a combination of geometric constraints at the apparent contact line and gravity pulling on the droplet. Gravitational effects are therefore essential to complete engulfment, even for micrometric droplets. Furthermore, the opposing effects of geometry and gravity result in the longest engulfment times for droplets of intermediate size. Experiments at fixed droplet size reveal a power law dependence of engulfment time on oil kinematic viscosity, which we argue reflects the dynamical formation of the oil cloaking layer.