This study examines the two-dimensional interaction of two unequal co-rotating viscous vortices in uniform background shear. Numerical simulations are performed for vortex pairs having various circulation ratios $\varLambda _0 = \varGamma _{1,0}/\varGamma _{2,0} = (\omega _{1,0}/\omega _{2,0})(a^2_{1,0}/a^2_{2,0}) \leqslant 1$, corresponding to different initial characteristic radii $a_{i,0}$ and peak vorticities $\omega _{i,0}$ of each vortex $i=1,2$, in shears of various strengths $\zeta _0 = \omega _S/\omega _{2,0}$, where $\omega _S$ is the constant vorticity of the shear. Two primary flow regimes are observed: separations ($\zeta _0 < \zeta _{sep} < 0$), in which the vortices move apart continuously, and henditions ($\zeta _0 > \zeta _{sep}$), in which the interaction results in a single vortex (where $\zeta _{sep}$ is the adverse shear strength beyond which separation occurs). Vortex motion and values of $\zeta _{sep}(\varLambda _0)$ are well-predicted by a point-vortex model for unequal vortices. In vortex-dominated henditions, shear varies the peak–peak distance $b$, and vortex deformation. The main convective interaction begins when core detrainment of one vortex is established, and proceeds similarly to the no-shear ($\zeta _0 = 0$) case: merger occurs if the second vortex also detrains, engendering mutual entrainment; otherwise straining out occurs. Detrainment requires persistence of straining of both sufficient magnitude, as indicated by relative straining above a consistent critical value, $(S/\omega )_i > (S/\omega )_{cr}$, where $S$ is the strain rate magnitude at the vorticity peak, and conducive direction. Hendition outcomes are assessed in terms of an enhancement factor $\varepsilon \equiv \varGamma _{end}/\varGamma _{2,start}$. Although $\varepsilon$ generally varies with $\zeta _0$, $(a^2_{1,0} /a^2_{2,0} )$ and $(\omega _{1,0}/\omega _{2,0})$ in a complicated manner, this variation is well-characterized by the pair's starting enstrophy ratio, $Z_2/Z_1$. Within a transition region between merger and straining out (approximately $1.65 < Z_2/Z_1 < 1.9$), shear of either sense may increase $\varepsilon$.

The use of thin liquid films has expanded beyond lubrication and coatings, and into applications in actuators and adaptive optical elements. In contrast to their predecessors, whose dynamics can be typically captured by modelling infinite or periodic films, these applications are characterized by a finite amount of liquid in an impermeable domain. The global mass conservation constraint, together with common boundary conditions (e.g. pinning), create quantitatively and qualitatively different dynamics than those of infinite films. Mathematically, this manifests itself as a non-self-adjoint problem. This work presents a combined theoretical and experimental study for this problem. We provide a time-dependent closed-form analytical solution for the linearized non-self-adjoint system that arises from these boundary conditions. We highlight that, in contrast to self-adjoint problems, here, special care should be given to deriving the adjoint problem to reconstruct the solution based on the eigenfunctions properly. We compare these solutions with those obtained for permeable and periodic boundary conditions, representing common models for self-adjoint thin-film problems. We show that, while the initial dynamics is nearly identical, the boundary conditions eventually affect the film deformation as well as its response time. To experimentally illustrate the dynamics and to validate the theoretical model, we fabricated an experimental set-up that subjects a thin liquid film to a prescribed normal force distribution through dielectrophoresis, and used high-frame-rate digital holography to measure the film deformation in real time. The experiments agree well with the model and confirm that confined films exhibit a different behaviour which could not be predicted by existing models.

Wake interaction of two rotationally oscillating cylinders in side-by-side configuration is studied experimentally at a Reynolds number of 150. Five spacing ratios, $T/D$ (ratio of centre-to-centre spacing to cylinder diameter), are considered, namely, 1.4, 1.8, 2.5, 4.0 and 7.5. Both in-phase and antiphase forcing are investigated. Oscillation amplitude is varied from ${\rm \pi} /8$ to ${\rm \pi}$, and forcing frequency, $FR$ (ratio of the oscillation frequency to the vortex-shedding frequency of a stationary cylinder) is varied from 0 to 5. The experimental investigation is done using laser-induced fluorescence, hot film anemometry and particle-image velocimetry (PIV). The interaction between the two cylinders under forcing results in new wake modes and vortex structures and a comprehensive study from the wake visualisations is conducted. Quantitative results are presented in terms of streamwise and cross-stream mean velocity profiles, centreline velocity recovery, peak velocity deficit, wake width, fluctuation intensity, circulation, vorticity contours and drag coefficient. The magnitude of streamwise velocity deficit and cross-stream velocity variation is strongly affected by the presence of second cylinder. The recirculation region behind the cylinders is found to extend further downstream with increase in the forcing. Scaling analysis is carried out to express the peak velocity deficit variation with forcing. It is observed that the relative strength of the vortices shed from inner and outer shear layers depends on the phase of oscillation. An experimental set-up for direct force measurement is designed and the drag force acting on the oscillating cylinders assembly is directly measured and the effect of forcing on the variation of ${C}_{d}$ is studied. An estimate for drag coefficient is also made from the PIV data following a detailed control volume analysis. It is observed that the set of forcing parameters that correspond to maximum and minimum drag also yield extrema in the values of circulation and fluctuation intensity.

The stratified inclined duct (SID) experiment consists of a zero-net-volume exchange flow in a long tilted rectangular duct, which allows the study of realistic stratified shear flows with sustained internal forcing. We present the first three-dimensional direct numerical simulations (DNS) of SID to explore the transitions between increasingly turbulent flow regimes first described by Meyer & Linden (J. Fluid Mech., vol. 753, 2014, pp. 242–253). We develop a numerical set-up that faithfully reproduces the experiments and sustains the flow for arbitrarily long times at minimal computational cost. We recover the four qualitative flow regimes found experimentally in the same regions of parameter space: laminar flow, waves, intermittent turbulence and fully developed turbulence. We find good qualitative and quantitative agreement between DNS and experiments and highlight the added value of DNS to complement experimental diagnostics and increase our understanding of the transition to turbulence, both temporally (laminar/turbulent cycles) and parametrically (as the tilt angle of the duct and the Reynolds number are increased). These results demonstrate that numerical studies of SID – and deeper integration between simulations and experiments – have the potential to lead to a better understanding of stratified turbulence.

Effects of the spanwise wavelength (λ) of a sinusoidal wavy cylinder with elliptic cross-section on wake structures and fluid forces are numerically investigated at a Reynolds number Re = 100. A wide range of the wavelength, $0.43 \le \lambda /{D_m} \le 8.59$, is considered with a wave amplitude of a/Dm = 0.048, where Dm is the hydraulic diameter of the wavy cylinder. Based on vortical structures, Strouhal number (St) and wake closure length (Lc), fluid forces, streamline topologies and spatio-temporal evolutions of the near wake, five distinct flow patterns (I–V) are identified depending on λ/Dm. The drag force reaches its minimum in pattern III, the fluctuating lift force is zero in flow patterns III and IV. Distinct from the classical flow where alternate vortex shedding occurs synchronously over the entire cylinder span, flow pattern IV has alternate vortex shedding over a one half-wavelength of the wavy elliptic cylinder, antiphased with that over the other half-wavelength, thus leading to zero fluctuating lift over one complete wavelength. A thorough comparison of the wakes is made between the wavy elliptic cylinder and wavy circular or square cylinder, distinguishing the underlying flow physics behind the salient behaviours observed.

We study fluctuations of all co-existing energy exchange/transfer/transport processes in stationary periodic turbulence including those that average to zero and are not present in average cascade theories. We use a Helmholtz decomposition of accelerations that leads to a decomposition of all terms in the Kármán–Howarth–Monin–Hill (KHMH) equation (scale-by-scale two-point energy balance) causing it to break into two energy balances, one resulting from the integrated two-point vorticity equation and the other from the integrated two-point pressure equation. The various two-point acceleration terms in the Navier–Stokes difference (NSD) equation for the dynamics of two-point velocity differences have similar alignment tendencies with the two-point velocity difference, implying similar characteristics for the NSD and KHMH equations. We introduce the two-point sweeping concept and show how it articulates with the fluctuating interscale energy transfer as the solenoidal part of the interscale transfer rate does not fluctuate with turbulence dissipation at any scale above the Taylor length but with the sum of the time derivative and the solenoidal interspace transport rate terms. The pressure fluctuations play an important role in the interscale and interspace turbulence transfer/transport dynamics as the irrotational part of the interscale transfer rate is equal to the irrotational part of the interspace transfer rate and is balanced by two-point fluctuating pressure work. We also study the homogeneous/inhomogeneous decomposition of interscale transfer. The statistics of the latter are skewed towards forward cascade events whereas the statistics of the former are not. We also report statistics conditioned on intense forward/backward interscale transfer events.

We present the results of a combined experimental and theoretical investigation of sheet evolution, expansion and retraction, under unsteady fragmentation upon drop impact on a surface of comparable size to that of the drop. We quantify and model the effect of the continuous time-varying – unsteady – shedding of droplets from the sheet via its bounding rim. We present and validate especially developed advanced image processing algorithms that quantify, with high accuracy, the key quantities involved in such unsteady fragmentation, from sheet, to rim, to ligaments, to droplet properties. With these high precision measurements, we show the important effect of continuous unsteady droplet shedding on the sheet dynamics. We combine experiments and theory to derive and validate governing equations of the sheet that incorporate such continuous shedding – associated with continuous loss of momentum and mass – from unsteady fragmentation. Combining this theory with the universal unsteady rim dynamics discovered in Wang et al. (Phys. Rev. Lett., vol. 120, 2018, 204503), we show that the governing equation of the sheet can be reduced to a continuous-shedding, non-Galilean Taylor–Culick law, from which we deduce new analytical expressions for the time evolution of the sheet radius. We show the robustness of the predictions to changes of fluid properties, including surface tension and moderate fluid viscosity and elasticity, including use of physiological mucosalivary fluid. We also reconcile prior literature's inconsistent experimental results on the sheet dynamics upon drop impact.

Instability measurements of an axisymmetric, laminar separation bubble were made over a sharp cone-cylinder-flare with a $12^{\circ }$ flare angle under hypersonic quiet flow. Two distinct instabilities were identified: Mack's second mode (which peaked between 190 and 290 kHz) and the shear-layer instability in the same frequency band as Mack's first mode (observed between 50 and 150 kHz). Both instabilities were measured with surface pressure sensors and were captured with high-speed schlieren. Linear stability analysis results agreed well with these measured instabilities in terms of both peak frequencies and amplification rates. Lower-frequency fluctuations were also noted in the schlieren data. Bicoherence analysis revealed nonlinear phase-locking between the shear-layer and second-mode instabilities. For the first time in axisymmetric, low-disturbance flow, naturally generated intermittent turbulent spots were observed in the reattached boundary layer. These spots appeared to evolve from shear-layer-instability wave packets convecting downstream. This work presents novel experimental evidence of the hypersonic shear-layer instability contributing directly to transition onset for an axisymmetric model.

Large-eddy simulation on a grid consisting of 5 billion points was utilized to study the properties of turbulence at the core of the tip and hub vortices shed by a marine propeller across working conditions. Turbulence at the core of the tip vortices was found to be initially isotropic, moving towards a ‘cigar-shaped’ axisymmetric state as instability grows, dominated by turbulent fluctuations of the velocity component directed in the radial direction of the cylindrical reference frame centred at the wake axis. The break-up of the coherence of the tip vortices is instead characterized by turbulence recovering an isotropic state. This process is accelerated by growing load conditions of the propeller. In contrast, during instability of the hub vortex, turbulence at its core develops a ‘pancake-shaped’ axisymmetric state, dominated by the fluctuations of the radial and azimuthal velocities. However, at higher propeller loads turbulence at the core of the hub vortex keeps close to isotropy, thanks to a faster instability. Within both tip and hub vortices the deviations from Boussinesq's hypothesis were found very significant, providing evidence of the unsuitability of conventional turbulence modelling. At the core of the tip vortices they become especially large at their break-up and for increasing load conditions of the propeller, equivalent to more intense structures. In contrast, at the core of the hub vortex they were verified to be decreasing functions of the propeller load.

Attenuation and even freeze-out (amplitude growth stagnation) of the perturbation amplitude growth of a shocked SF$_6$–air interface are first realized in shock-tube experiments through reflected rarefaction waves, which produce reverse baroclinic vorticity offsetting the vorticity deposited by the shock. A theoretical model is constructed to predict the perturbation growth after the impact of rarefaction waves, and seven possibilities of amplitude growth are analysed. Experimentally, a planar air–helium interface is used to produce reflected rarefaction waves. Through changing the perturbation wavelength and the time interval of two impacts, five experiments with specific initial conditions are carried out, and three different possibilities of perturbation growth attenuation are realized.

Turbulent shear flows are abundant in geophysical and astrophysical systems and in engineering-technology applications. They are often riddled with large-scale secondary flows that drastically modify the characteristics of the primary stream, preventing or enhancing mixing, mass and heat transfer. Using experiments and numerical simulations, we study the possibility of modifying these secondary flows by using superhydrophobic surface treatments that reduce the local shear. We focus on the canonical problem of Taylor–Couette flow, the flow between two coaxial and independently rotating cylinders, which has robust secondary structures called Taylor rolls that persist even at significant levels of turbulence. We generate these structures by rotating only the inner cylinder of the system, and show that an axially spaced superhydrophobic treatment can weaken the rolls through a mismatching surface heterogeneity, as long as the roll size can be fixed. The minimum hydrophobicity of the treatment required for this flow control is rationalized, and its effectiveness beyond the Reynolds numbers studied here is also discussed.

A steady granular flow experiment was performed in a confined annular shear cell to examine how the wall friction coefficient $\mu _w$ degrades from the intrinsic sliding friction coefficient $f$ between the grains and the container wall. Two existing models are invoked to examine the decay trend of $\mu _w/f$ in view of the ratio of shear velocity to the square root of granular temperature $\chi$ (Artoni & Richard, Phys. Rev. Lett., vol. 115, 2015, 158001) and the ratio of grain angular and slip velocities $\varOmega$ (Yang & Huang, Granul. Matt., vol. 18, issue 4, 2016, p. 77), respectively. As both models correlate $\mu _w/f$ to different flow properties, a hidden relation is speculated between $\chi$ and $\varOmega$, or equivalently, between the granular temperature and the grain rotation speed. We used experiment data to confirm and reveal this hidden relation. From there, a unified $\mu _w/f-\chi$ model is proposed with physical meanings for the model coefficients and to show general agreement with the measured trend. Hence we may conclude that both the fluctuations in grain translations and their mean rotation are the crucial yet equivalent mechanisms to degrade $\mu _w/f$.