We investigate the coupling dynamics of interfacial waves in liquid metal batteries and its effects on the battery’s operation safety. Similar to aluminium reduction cells, liquid metal batteries can be highly susceptible to magnetohydrodynamically exited interfacial instabilities. The resulting waves are capable of provoking short-circuits. Owing to the presence of two metal-electrolyte interfaces that may step into resonance, the wave dynamics in liquid metal batteries is particularly complex. In the first part of this paper, we present a potential flow analysis of coupled gravity–capillary interfacial waves. While we are focusing here on liquid metal batteries with circular cross-section, the theory is applicable to arbitrary stably stratified three-layer systems. Analytical expressions for the amplitude ratio and the wave frequencies are derived. It is shown that the wave coupling can be completely described by two independent dimensionless parameters. We further provide a decoupling criterion that suggests that wave coupling will be present in most future liquid metal batteries. In the second part, the theory is validated by comparing it with multiphase direct numerical simulations. An accompanying parameter study is conducted to analyse the system stability for interfaces coupled to varying degrees. Three different coupling regimes are identified involving characteristic coupling dynamics. For strongly coupled interfaces we observe novel instabilities that may have beneficial effects on the operational safety.

We present a combined experimental and theoretical investigation of the dynamics of liquid imbibition through paper. The Washburn equation is widely used to describe the dynamics of capillary flow through paper, but this classical model has limited accuracy, which often makes it difficult to use in developing analytic systems such as paper-based microfluidic devices. We here report that the internal cavity of the cellulose fibres composing paper is significantly responsible for the limited accuracy of the Washburn equation. Our experiments demonstrated that liquid can be absorbed in the internal cavity of the cellulose fibres as well as in the inter-fibre pores formed by the fibre network. We developed a mathematical model for liquid imbibition by considering the flow through the intra-fibre pores based on experimental measurements of the intra-structure of cellulose fibres. The model markedly improves the prediction of the liquid absorption length, compared with the results of the Washburn equation, thus revealing the physics behind the limits of the Washburn equation. This study suggests that the accurate description of capillary imbibition through paper require parameters characterizing the internal pores of the cellulose fibres comprising the paper. Our results not only provide a new insight into porous media flows with different sized pores, but also provide a theoretical background for flow control in paper-based microfluidic systems.

We develop a frame-invariant theory of material spike formation during flow separation over a no-slip boundary in two-dimensional flows with arbitrary time dependence. Based on the exact curvature evolution of near-wall material lines, our theory identifies both fixed and moving flow separation, is effective also over short time intervals, and admits a rigorous instantaneous limit. As a byproduct, we derive explicit formulae for the evolution of material line curvature and the curvature rate for general compressible flows. The material backbone that we identify acts first as the precursor and later as the centrepiece of unsteady Lagrangian flow separation. We also discover a previously undetected spiking point where the backbone of separation connects to the boundary, and derive wall-based analytical formulae for its location. Finally, our theory explains the perception of off-wall separation in unsteady flows and provides conditions under which such a perception is justified. We illustrate our results on several analytical and experimental flows.

Non-parallelism, i.e. the effect of the slow variation of the boundary-layer flow in the chordwise and spanwise directions, in general produces a higher-order correction to the growth rate of instability modes. Here we investigate stationary crossflow vortices, which arise due to the instability of the three-dimensional boundary layer over a swept wing, focusing on a region near the leading edge where non-parallelism plays a leading-order role in their development. In this regime, the vortices align themselves with the local wall shear at leading order, and so have a marginally separated triple-deck structure, consisting of the inviscid main boundary layer, an upper deck and a viscous sublayer. We find that the streamwise (and spanwise) variations of both the base flow and the modal shape must be accounted for. An explicit expression for the growth rate is derived that shows a neutral point occurs in this regime, downstream of which non-parallelism has a stabilising effect. Stationary crossflow vortices thus have a viscous and non-parallel genesis near the leading edge. If an ‘effective pressure minimum’ occurs within this region then the growth rate becomes unbounded, and so the previous analysis is regularised within a localised region around it. A new instability is identified. The mode maintains its three-tiered structure, but the pressure perturbation now plays a passive role. Downstream, the instability evolves into a Cowley, Hocking & Tutty (Phys. Fluids, vol. 28, 1985, pp. 441–443) instability associated with a critical layer located in the lower deck. Finally, we consider the receptivity of the flow in the non-parallel regime: generation of stationary crossflow modes by arrays of chordwise-localised, spanwise-periodic surface roughness elements. The flow responds differently to different Fourier spectral content of the roughness, giving the lower deck a two-part structure. We find that roughness elements with sharper edges generate stronger modes. For roughness elements of fairly moderate height, the resulting nonlinear forcing leads to the so-called super-linearity of receptivity, namely, the amplitude of the generated crossflow mode deviates from the linear dependence on the roughness height even though the perturbation in the boundary layer remains linear.

The influences of non-Oberbeck–Boussinesq (NOB) effects on flow instabilities and bifurcation characteristics of Rayleigh–Bénard convection are examined. The working fluid is air with reference Prandtl number $Pr=0.71$ and contained in two-dimensional rigid cavities of finite aspect ratios. The fluid flow is governed by the low-Mach-number equations, accounting for the NOB effects due to large temperature difference involving flow compressibility and variations of fluid viscosity and thermal conductivity with temperature. The intensity of NOB effects is measured by the dimensionless temperature differential $\unicode[STIX]{x1D716}$. Linear stability analysis of the thermal conduction state is performed. An $\unicode[STIX]{x1D716}^{2}$ scaling of the leading-order corrections of critical Rayleigh number $Ra_{cr}$ and disturbance growth rate $\unicode[STIX]{x1D70E}$ due to NOB effects is identified, which is a consequence of an intrinsic symmetry of the system. The influences of weak NOB effects on flow instabilities are further studied by perturbation expansion of linear stability equations with regard to $\unicode[STIX]{x1D716}$, and then the influence of aspect ratio $A$ is investigated in detail. NOB effects are found to enhance (weaken) flow stability in large (narrow) cavities. Detailed contributions of compressibility, viscosity and buoyancy actions on disturbance kinetic energy growth are identified quantitatively by energy analysis. Besides, a weakly nonlinear theory is developed based on centre-manifold reduction to investigate the NOB influences on bifurcation characteristics near convection onset, and amplitude equations are constructed for both codimension-one and -two cases. Rich bifurcation regimes are observed based on amplitude equations and also confirmed by direct numerical simulation. Weakly nonlinear analysis is useful for organizing and understanding these simulation results.

A theoretical study of the decay of plane gaseous detonations is presented. The analysis concerns the relaxation of weakly overdriven detonations toward the Chapman–Jouguet (CJ) regime when the supporting piston is suddenly arrested. The initial condition concerns propagation velocities ${\mathcal{D}}$ that are not far from that of the CJ wave ${\mathcal{D}}_{CJ}$, $0<({\mathcal{D}}/{\mathcal{D}}_{CJ}-1)\ll 1$. The unsteady inner structure of the detonation wave is taken into account analytically for small heat release, i.e. when the propagation Mach number of the CJ wave $M_{u_{CJ}}$ is small, $0<(M_{u_{CJ}}-1)\ll 1$. Under such conditions the flow is transonic across the inner structure. Then, with small differences between heat capacities (Newtonian limit), the problem reduces to an integral equation for the velocity of the lead shock. This equation governs the detonation dynamics resulting from the coupling of the unsteady inner structure with the self-similar dynamics of the centred rarefaction wave in the burnt gas. The key point of the asymptotic analysis is that the response time of the inner structure is larger than the reaction time. How, and to what extent, the result is relevant for real detonations is discussed in the text. In a preliminary step the steady-state approximation is revisited with particular attention paid to the location of the sonic condition.

We study experimentally the propagation of internal waves in two different three-dimensional (3D) geometries, with a special emphasis on the refractive focusing due to the 3D reflection of obliquely incident internal waves on a slope. Both studies are initiated by ray tracing calculations to determine the appropriate experimental parameters. First, we consider a 3D geometry, the classical set-up to get simple, two-dimensional (2D) parallelogram-shaped attractors in which waves are forced in a direction perpendicular to a sloping bottom. Here, however, the forcing is of reduced extent in the along-slope, transverse direction. We show how the refractive focusing mechanism explains the formation of attractors over the whole width of the tank, even away from the forcing region. Direct numerical simulations confirm the dynamics, emphasize the role of boundary conditions and reveal the phase shifting in the transverse direction. Second, we consider a long and narrow tank having an inclined bottom, to simply reproduce a canal. In this case, the energy is injected in a direction parallel to the slope. Interestingly, the wave energy ends up forming 2D internal wave attractors in planes that are transverse to the initial propagation direction. This focusing mechanism prevents indefinite transmission of most of the internal wave energy along the canal.

We present results on the global and local characterisation of heat transport in homogeneous bubbly flow. Experimental measurements were performed with and without the injection of ${\sim}2.5~\text{mm}$ diameter bubbles (corresponding to bubble Reynolds number $Re_{b}\approx 600$) in a rectangular water column heated from one side and cooled from the other. The gas volume fraction $\unicode[STIX]{x1D6FC}$ was varied in the range 0 %–5 %, and the Rayleigh number $Ra_{H}$ in the range $4.0\times 10^{9}{-}1.2\times 10^{11}$. We find that the global heat transfer is enhanced up to 20 times due to bubble injection. Interestingly, for bubbly flow, for our lowest concentration $\unicode[STIX]{x1D6FC}=0.5\,\%$ onwards, the Nusselt number $\overline{Nu}$ is nearly independent of $Ra_{H}$, and depends solely on the gas volume fraction $\unicode[STIX]{x1D6FC}$. We observe the scaling $\overline{Nu}\,\propto \,\unicode[STIX]{x1D6FC}^{0.45}$, which is suggestive of a diffusive transport mechanism, as found by Alméras et al. (J. Fluid Mech., vol. 776, 2015, pp. 458–474). Through local temperature measurements, we show that the bubbles induce a huge increase in the strength of liquid temperature fluctuations, e.g. by a factor of 200 for $\unicode[STIX]{x1D6FC}=0.9\,\%$. Further, we compare the power spectra of the temperature fluctuations for the single- and two-phase cases. In the single-phase cases, most of the spectral power of the temperature fluctuations is concentrated in the large-scale rolls/motions. However, with the injection of bubbles, we observe intense fluctuations over a wide range of scales, extending up to very high frequencies. Thus, while in the single-phase flow the thermal boundary layers control the heat transport, once the bubbles are injected, the bubble-induced liquid agitation governs the process from a very small bubble concentration onwards. Our findings demonstrate that the mixing induced by high Reynolds number bubbles ($Re_{b}\approx 600$) offers a powerful mechanism for heat transport enhancement in natural convection systems.

We experimentally investigate the sedimentation of a non-wetting drop confined between two parallel walls. The whole system is immersed in a bath of liquid of low viscosity and a lubricating film may be dynamically formed between the drop and the walls of the cell. Depending on the thickness of the film and on the viscosity ratio between the droplet and the surrounding liquid, viscous dissipation localizes either in the lubrication layer or in the bulk of the drop. The velocity of the droplet is non-trivial as the thickness of the lubricating layer may depend on the interplay between interfacial tension and viscous dissipation. Interestingly, thin films whose nanometric thickness is set by long range intermolecular interactions may lubricate efficiently the motion of highly viscous droplets. We derive asymptotic models that successfully capture the settling velocity of the drop in the different regimes observed experimentally. The effect of partial wetting is finally illustrated by a sharp increase of the velocity of the drops that we attribute to a wetting transition.

We study experimentally the effects of spanwise confinement on turbulent miscible fountains issuing from a round source of radius $r_{0}$. A dense saline solution is ejected vertically upwards into a fresh-water environment between two parallel plates, separated by a gap of width $W$, which provide restraint in the spanwise direction. The resulting fountain, if sufficiently forced, rapidly attaches to the side plates as it rises and is therefore ‘confined’. We report on experiments for five confinement ratios $W/r_{0}$, spanning from strongly confined ($W/r_{0}\rightarrow 2$) to weakly confined ($W/r_{0}\approx 24$), and for source Froude numbers $Fr_{0}$ ranging between $0.5\leqslant Fr_{0}\leqslant 96$. Four distinct flow regimes are observed across which the relative importance of confinement, as manifested by the formation and growth of quasi-two-dimensional structures, varies. The onset of each regime is established as a function of both $W/r_{0}$ and $Fr_{0}$. From our analysis of the time-averaged rise heights, we introduce a ‘confined’ Froude number $Fr_{c}\equiv Fr_{0}(W/r_{0})^{-5/4}$, which encompasses the effects of confinement and acts as the governing parameter for confined fountains. First-order statistics extracted from the flow visualisation, such as the time-averaged rise height and lateral excursions, lend further insight into the flow and support the proposed classification into regimes. For highly confined fountains, the flow becomes quasi-two-dimensional and, akin to quasi-two-dimensional jets and plumes, flaps (or meanders). The characteristic frequency of this flapping motion, identified through an ‘eddy counting’ approach, is non-dimensionalised to a Strouhal number of $St=0.12{-}0.16$, consistent with frequencies found in quasi-two-dimensional jets and plumes.

The present study investigates the role of hydroelasticity and nonlinearity in the fundamental problem of the interaction between non-breaking water waves and an elastic wall. To this end, two interaction scenarios are considered: the interaction of a rigid wall supported by springs and a pulse-type wave, and the interaction of an elastic deformable wall and an incident wave group. Both of these scenarios are numerically simulated in a computational domain representing a two-dimensional wave flume. The simplicity of the domain enables one to perform highly efficient simulations using the high-order spectral method (HOSM). Wave generation at the flume entrance and the wave–wall interaction at the flume end are simulated by means of the additional potential concept. In this way, the efficiency that characterizes the original HOSM is preserved for the present non-periodic problems. The investigation of the first scenario reveals the influence of the wall’s dynamical response on the hydrodynamic values. The results show that the maximum wave run-up and wave force are prominently fluctuating around the values corresponding to a fixed wall as a function of the wall’s eigenfrequency, revealing regions of relaxation and amplification. The second scenario studies the effect of the nonlinear evolution of the incident wave group. The high-order wave harmonics generated during the group evolution are found to be significant for predicting extreme hydrodynamic and structural values, and may result in resonant interactions in which hydroelasticity appears to play an important role.

Surface water waves are considered propagating over highly variable non-smooth topographies. For this three-dimensional problem a Dirichlet-to-Neumann (DtN) operator is constructed reducing the numerical modelling and evolution to the two-dimensional free surface. The corresponding discrete Fourier integral operator is defined through a matrix decomposition. The topographic component of the decomposition requires special care, and a Galerkin method is provided accordingly. One-dimensional numerical simulations, along the free surface, validate the DtN formulation in the presence of a large-amplitude rapidly varying topography. An alternative conformal-mapping-based method is used for benchmarking. A two-dimensional simulation in the presence of a Luneburg lens (a particular submerged mound) illustrates the accurate performance of the three-dimensional DtN operator.

An exponential horn geometry is introduced in order to establish cellular detonations with a constant mean lateral mass divergence, propagating at quasi-steady speeds below the Chapman–Jouguet value. The experiments were conducted in $2\text{C}_{2}\text{H}_{2}+5\text{O}_{2}+21\text{Ar}$ and $\text{C}_{3}\text{H}_{8}+5\text{O}_{2}$. Numerical simulations were also performed for weakly unstable cellular detonations to test the validity of the exponential horn geometry. The experiments and simulations demonstrated that such quasi-steady state detonations can be realized, hence permitting us to obtain the relations between the detonation speed and mean lateral flow divergence for cellular detonations in an unambiguous manner. The experimentally obtained speed ($D$) dependencies on divergence ($K$) were compared with the predictions for steady detonations with lateral flow divergence obtained with the real thermo-chemical data of the mixtures. For the $2\text{C}_{2}\text{H}_{2}+5\text{O}_{2}+21\text{Ar}$ system, reasonable agreement was found between the experiments and steady wave prediction, particularly for the critical divergence leading to failure. Observations of the reaction zone structure in these detonations indicated that all the gas reacted very close to the front, as the transverse waves were reactive. The experiments obtained in the much more unstable detonations in $\text{C}_{3}\text{H}_{8}+5\text{O}_{2}$ showed significant differences between the experimentally derived $D(K)$ curve and the prediction of steady wave propagation. The latter was found to significantly under-predict the detonability of cellular detonations. The transverse waves in this mixture were found to be non-reactive, hence permitting the shedding of non-reacted pockets, which burn via turbulent flames on their surface. It is believed that the large differences between experiment and the inviscid model in this class of cellular structures is due to the importance of diffusive processes in the burn-out of the non-reacted pockets. The empirical tuning of a global one-step chemical model to describe the macro-scale kinetics in cellular detonations revealed that the effective activation energy was lower by 14 % in $2\text{C}_{2}\text{H}_{2}+5\text{O}_{2}+21\text{Ar}$ and 54 % in the more unstable $\text{C}_{3}\text{H}_{8}+5\text{O}_{2}$ system. This confirms previous observations that diffusive processes in highly unstable detonations are responsible for reducing the thermal ignition character of the gases processed by the detonation front.

Inkjet technology is a commendable tool in many applications including graphics printing, bioengineering and micro-electromechanical systems (MEMS). Droplet stability is a key factor influencing inkjet performance. The stability can be analysed using dimensionless numbers that usually combine thermophysical properties and system dimensions. In this paper, a drop-on-demand (DOD) inkjet experimental system is established. A numerical model is developed to investigate the influence of the operating conditions on droplet stability, including nozzle dimensions, driving parameters (the pulse amplitude and width used to drive droplet formation) and fluid properties. The results indicate that the stability can be improved by decreasing the pulse amplitude and width, decreasing the fluid density and viscosity or increasing the nozzle diameter and fluid surface tension. Based on case analysis and modelling, a dimensionless number ($Z$), the reciprocal of the Ohnesorge number, is numerically determined for a stable droplet to lie in a range between 4 and 8. To explicitly combine the driving parameters, a new stability criterion, $Pj$, is further proposed. A general rule taking into account both $Pj$ and $Z$ is proposed for choosing appropriate driving parameters to eject stable droplets for a known nozzle and fluid, which is further validated by experiments.

The dynamics of multiple alternating oceanic jets has been studied in the presence of a simple bottom topography with constant slope in the zonal direction. A baroclinic quasi-geostrophic model forced with a horizontally uniform and vertically sheared background flow generates mesoscale eddies and jets that are tilted from the zonal direction and drift with constant speed. The governing dynamical equations are rewritten in a tilted frame of reference moving with the jets, and the cross-jet time-mean profiles of the linear and nonlinear stress terms are analysed. Here, the linear stress terms are present because of the zonally asymmetric topography. It is demonstrated that the linear dynamics controls the drift mechanism. Also, it is found that the drifting jets are directly forced by the imposed vertical shear, whereas the eddies oppose the jets, although this is limited to continuously forced dissipative systems. This role of the eddies is opposite to the one in the classical baroclinic model of stationary, zonally symmetric multiple jets. This is expected to be more generic in the ocean, which is zonally asymmetric nearly everywhere.

Direct numerical simulations of particle-laden flows in a spatially developing turbulent thermal boundary layer over an isothermally heated wall have been performed with realistic fully developed turbulent inflow boundary conditions. To the authors’ best knowledge, this is the first time the effects of inertial solid particles on turbulent flow and heat transfer in a flat-plate turbulent boundary layer have been investigated, using a two-way coupled Eulerian–Lagrangian method. Results indicate that the presence of particles increases the mean streamwise velocity and temperature gradients of the fluid in the near-wall region. As a result, the skin-friction drag and heat transfer are significantly enhanced in the particle-laden flows with respect to the single-phase flow. The near-wall sweep and ejection motions are suppressed by the particles and hence the Reynolds shear stress and wall-normal turbulent heat flux are attenuated, which leads to reductions in the production of the turbulent kinetic energy and temperature fluctuations. In addition, the coherence and spacing of the near-wall velocity and temperature streaky structures are distinctly increased, while the turbulent vortical structures appear to be disorganized under the effect of the particles. Moreover, the intensity of the streamwise vortices decreases monotonically with increasing particle inertia.

The present work studies the effect of passive exit flexibility on a two-dimensional starting jet. The exit flexibility is introduced by attaching two flexible (deformable) flaps at the jet exit of a high aspect ratio rectangular duct with the flaps initially being parallel to the channel walls. A controlled piston motion is used to generate the starting jet, which is composed of a rapid acceleration to a constant velocity ($U_{p}$) that is maintained for a given duration of time, after which it is brought to rest impulsively. The parameters which are varied include the flexural rigidity ($EI$) of the flaps, flap length ($L_{f}$) and piston speed ($U_{p}$), with measurements of the flap kinematics and flow field in each case. The flaps initially bulge due to the acceleration of the piston from rest, with this bulge growing in size and moving downstream as the flow develops, culminating in a large opening at the flap exit. Subsequently, the flaps return to their initial parallel position and remain there as long as the piston is in motion. Once the piston stops, the flaps collapse inwards due to fluid deceleration causing additional flow out of the flap region in the form of a jet that adds to the net amount of fluid pushed by the piston. We find that the flap kinematics is affected by the flap $EI$ and $L_{f}$ besides $U_{p}$. We define a non-dimensional flexural rigidity $EI^{\ast }=EI_{eq}/(1/2\unicode[STIX]{x1D70C}U_{p}^{2}L_{f}^{2}d)$, where $EI_{eq}$ is an equivalent flexural rigidity which takes the self-weight of the flaps into account ($d=\text{channel width}$; $\unicode[STIX]{x1D70C}=$ fluid density). We find that across different $EI_{eq}$, $L_{f}$, and piston speeds, the maximum opening of the flap tip and the time taken to reach this maximum opening in terms of $L/L_{f}$ (where $L=\text{fluid slug length}$) fall on a single curve for all the cases studied, when plotted with $EI^{\ast }$. Particle image velocimetry measurements show that the motion of the flaps results in the formation of additional pairs of vortices when compared to the single vortex pair formed in the absence of flaps. The total final circulation coming out of the flap region remains nearly the same as that of the rigid exit case. However, the final fluid impulse is always found to be higher in the flap cases, with the fluid impulse in most flap cases being approximately two times the fluid impulse of the rigid exit case. This increase in impulse is shown to be linked to the fact that the centroids of vorticity get spread out more in the lateral direction due to the opening of the flaps. The increased impulse and the higher time rate of change of impulse, which is linked with force, suggest that introduction of flexible flaps can help improve thrust performance when looked at from a propulsion point of view.

Turbulent wall-bounded flows exhibit a wide range of regimes with significant interaction between scales. The fluid dynamics associated with single-phase channel flows is predominantly characterized by the Reynolds number. Meanwhile, vastly different behaviour exists in particle-laden channel flows, even at a fixed Reynolds number. Vertical turbulent channel flows seeded with a low concentration of inertial particles are known to exhibit segregation in the particle distribution without significant modification to the underlying turbulent kinetic energy (TKE). At moderate (but still low) concentrations, enhancement or attenuation of fluid-phase TKE results from increased dissipation and wakes past individual particles. Recent studies have shown that denser suspensions significantly alter the two-phase dynamics, where the majority of TKE is generated by interphase coupling (i.e.  drag) between the carrier gas and clusters of particles that fall near the channel wall. In the present study, a series of simulations of vertical particle-laden channel flows with increasing mass loading is conducted to analyse the transition from the dilute limit where classical mean-shear production is primarily responsible for generating fluid-phase TKE to high-mass-loading suspensions dominated by drag production. Eulerian–Lagrangian simulations are performed for a wide range of particle loadings at two values of the Stokes number, and the corresponding two-phase energy balances are reported to identify the mechanisms responsible for the observed transition.

In the present study the wake flow past an isolated propeller operating in oblique flow conditions is investigated experimentally. In particular, the investigation concerns a systematic topological comparison of the wake behaviour in axisymmetric and in oblique inflow conditions, for three inclination angles, and is focused on an analysis of the underlying mechanisms of wake evolution and instability. To this end, the experiment has been designed to investigate the dynamics of propeller vortical structures over a wide spatial extent covering the wake region from the propeller disk up to 4.5 diameters in the streamwise direction. Detailed flow measurements have been undertaken by particle image velocimetry (PIV), using a multicamera configuration with three cameras arranged side by side. This allowed simultaneous acquisition of a large flow extent at a spatial resolution adequate to resolve the smallest vortical structures involved in the process of propeller wake instability. The analysis has been based on both phase-locked averaged and instantaneous flow fields. The study extends the knowledge on the subject of propeller wake dynamics, highlighting the major hydrodynamic effects that non-axisymmetric propeller operating conditions exert on the mechanisms of wake evolution, instability and breakdown, such as asymmetric destabilization of the tip vortices on the leeward and windward sides of the wake, and the interference between the tip and the junction vortices, as well as the cause–effect relation between the breakdown of the blade trailing wake and the instability of the tip and hub vortices.

A significant amount of the fuel consumed by marine vehicles is expended to overcome skin-friction drag resulting from turbulent boundary layer flows. Hence, a substantial reduction in this frictional drag would notably reduce cost and environmental impact. Superhydrophobic surfaces (SHSs), which entrap a layer of air underwater, have shown promise in reducing drag in small-scale applications and/or in laminar flow conditions. Recently, the efficacy of these surfaces in reducing drag resulting from turbulent flows has been shown. In this work we examine four different, mechanically durable, large-scale SHSs. When evaluated in fully developed turbulent flow, in the height-based Reynolds number range of 10 000 to 30 000, significant drag reduction was observed on some of the surfaces, dependent on their exact morphology. We then discuss how neither the roughness of the SHSs, nor the conventional contact angle goniometry method of evaluating the non-wettability of SHSs at ambient pressure, can predict their drag reduction under turbulent flow conditions. Instead, we propose a new characterization parameter, based on the contact angle hysteresis at higher pressure, which aids in the rational design of randomly rough, friction-reducing SHSs. Overall, we find that both the contact angle hysteresis at higher pressure, and the non-dimensionalized surface roughness, must be minimized to achieve meaningful turbulent drag reduction. Further, we show that even SHSs that are considered hydrodynamically smooth can cause significant drag increase if these two parameters are not sufficiently minimized.