This work investigates the statistical response of short and long laminar separation bubbles to external flow parameters, such as Reynolds number, free-stream turbulence intensity and streamwise pressure gradient, known to govern bubble formation and characteristics. A parametric experimental campaign has been performed using particle image velocimetry on a flat plate to provide a comprehensive database for the characterization of separation-induced transition in both short and long separation bubbles. The proper orthogonal decomposition (POD) was applied to the data set of all dividing streamlines commonly used to identify a laminar separation bubble. This provides an optimal state-space basis for the data-driven classification of the state of a laminar separation bubble, with the leading modes capturing the change in length and height of the laminar separation bubble in response to changes in the flow parameters. When projected onto the POD subspace constituted by the first three leading modes, the normalized data from the present study and the results from prior investigations not used in the modal analysis collapse on the same trajectory in the low-dimensional space. The present POD basis can be therefore adopted for the description of the general response of the time-mean shape of a laminar separation bubble to changes in the main influencing parameters. A well-defined pattern was observed in the case of short laminar separation bubbles in the reduced-order space defined by the first three POD coefficients, whereas a higher dispersion in the long-bubble regime indicates an increased sensitivity of long bubbles to the external flow characteristics.

Turbine–wake and farm–atmosphere interactions influence wind farm power production. For large offshore farms, the farm–atmosphere interaction is usually the more significant effect. This study proposes an analytical model of the ‘momentum availability factor’ to predict the impact of farm–atmosphere interactions. It models the effects of net advection, pressure gradient forcing and turbulent entrainment, using steady quasi-one-dimensional flow assumptions. Turbulent entrainment is modelled by assuming self-similar vertical shear stress profiles. We used the model with the ‘two-scale momentum theory’ to predict the power of large finite-sized farms. The model compared well with existing results of large-eddy simulations of finite wind farms in conventionally neutral boundary layers. The model captured most of the effects of atmospheric boundary layer (ABL) height on farm performance by considering the undisturbed vertical shear stress profile of the ABL as an input. In particular, the model predicted the power of staggered wind farms with a typical error of 5 % or less. The developed model provides a novel way of predicting instantly the power of large wind farms, including the farm blockage effects. A further simplification of the model to predict analytically the ‘wind extractability factor’ is also presented. This study provides a novel framework for modelling farm–atmosphere interactions. Future studies can use the framework to better model large wind farms.

In microfluidic systems, analyte/reagent mixing is essential to achieve rapid chemical/biochemical reactions. The low Reynolds number (Re) flow, however, makes passive mixing difficult and necessitates the use of some external stimulus to cause disturbance in the system. Here, we report how a periodic thermocapillary effect may interact with strategically patterned wall wettability and boost the mixing dynamics in a micro-confined ternary-liquid film system. Approximate, yet without compromise on the physics involved, analytical solutions to the energy and Navier–Stokes equations under creeping flow conditions are obtained to comprehend the thermal and hydrodynamic characteristics of the thermo-capillarity. In the binary fluid limit, our model is validated with the findings of Pendse & Esmaeeli (Intl J. Therm. Sci., vol. 49, 2010, pp. 1147–1155), and good agreement is found. The flow characteristics in the ternary-liquid system due to discrete wall temperatures is also demonstrated via finite-element-based numerical simulations, and agreement with the semi-analytical solution is noted. The qualitative study of the flow pattern reveals that enhanced mixing is obtained as a result of vortical motion created by the interplay of the periodic thermo-capillarity-driven interfacial flow and wall slip. The observation is further consolidated from the numerical simulation of the species transport equation. The species distribution so obtained is compared with fully developed laminar flow for the same inlet concentration. Our study further investigates the effects of the fluids’ relative thermal conductivity, wall slip length, relative film thickness and thermal (or slip) phase differences on the mixing efficiency of the proposed arrangement. While wall slip, relative film thickness and relative thermal conductivity regulate mixing in the top and bottom layers, phase difference determines how well the middle fluid layer mixes. Slip at the walls creates vortex distortions to get a strong churning effect. The lower thermal conductivity of the top and bottom fluids weakens the thermocapillary flow; however, the dominance of the patterned slip improves mixing in such cases.

In this work, the dynamics of two-dimensional rotating Janus drops in shear flow is studied numerically using a ternary-fluid diffuse interface method. The rotation of Janus drops is found to be closely related to their deformation. A new deformation parameter $D$ is proposed to assess the significance of the drop deformation. According to the maximum value of $D$ ($D_{max}$), the deformation of rotating Janus drops can be classified into linear deformation ($D_{max}\le 0.2$) and nonlinear deformation ($D_{max}> 0.2$). In particular, $D_{max}$ in the former depends linearly on the Reynolds and capillary numbers, which can be interpreted by a mass–spring model. Furthermore, the rotation period $t_R$ of a Janus drop is found to be more sensitive to the drop deformation than to the aspect ratio of the drop at equilibrium. By introducing a corrected shear rate and an aspect ratio of drop deformation, a rotation model for Janus drops is established based on Jeffery's theory for rigid particles, and it agrees well with our numerical results.

Diapycnal mixing plays a key role in the thermohaline circulation of the deep ocean. Field observations have suggested that this mixing is intensified over the rough topography along the boundaries of the ocean. In this study, we experimentally explore the transport of salinity and tracer in a horizontally stirred, stratified fluid with a steady vertical buoyancy flux. The mechanical mixing occurs either uniformly across the tank or near a sidewall. To compare uniform and boundary mixing, first we explore the steady state dynamics and find that, in both cases, the surfaces of constant density are horizontal. With uniform mixing, vertical transport of buoyancy occurs uniformly throughout the tank while, with boundary mixing, transport is confined to the turbulent region and the interior space remains quiescent and does not mix or have any net movement. We then explore the transient evolution of the stratification when the source of buoyancy is removed from the base of the system. In the boundary mixing case, the resulting divergence of the turbulent diffusive flux in the boundary region leads to a reduction in the buoyancy of the fluid in the boundary region, and a net upflow develops in the boundary region. In turn, this drives a downwelling in the interior. Vertical gradients in the rate of downwelling lead to stretching of isopycnals and, together, these processes enable the interior stratification to evolve. The experiments highlight that, with boundary mixing, the main transport of buoyancy occurs near the boundaries even though the interior is stratified; independent measurements of tracer mixing in the interior show that this fluid may be quiescent and stratified even though there is a large flux being transported in the boundary region. This has important implications for the interpretation of mixing data in the ocean. In a companion paper, (Li and Woods Part 2), we explore the interaction of a net upwelling with such boundary mixing.

Evaporating sessile droplets are critical to many industrial applications and are also ubiquitous in nature. Two predominant evaporation models have emerged in the literature, one-sided and diffusion-limited, with differing assumptions on the evaporation process. Both models are used widely, and their predictions can differ greatly from each other, but the physical mechanisms responsible for these differences are not yet well understood. Here, we develop a lubrication-theory-based model of a thin evaporating sessile droplet, and compare predictions from both evaporation models to elucidate the origins of the differences in their predictions. For the one-sided model, we derive expressions for the droplet lifetime, show that in certain parameter regimes the total evaporation rate is proportional to the droplet surface area, and demonstrate that the contact line is always warmer than the bulk of the droplet. Furthermore, we show that differences in the structures of the evaporation models near the contact line lead to qualitatively different behaviour of the apparent contact angles and interface temperature profiles. The fundamental understanding gained from this work is expected to be helpful in determining which evaporation model is most appropriate for describing experimental observations.

In statistically stationary homogeneous incompressible turbulence, the average energy transfer rate balance which exists at diffusion/dissipation-dominated length scales does not reflect what actually happens locally in space and time. We use a highly resolved direct numerical simulation of forced periodic turbulence to shed some light on the actual fluctuating dynamics which occur at these very small scales and which are rubbed off by averaging. Even though the viscous diffusion in physical space averages to zero and fluctuates less intensely than all other terms (except the energy input rate) in the local (in space–time) two-point energy balance, it fundamentally cannot be neglected. The local unsteadiness and the interspace turbulence transport terms cannot be ignored either in the interscale energy dynamics in spite of the fact that they also average to zero.

The transition to turbulence in a plane Poiseuille flow of dilute polymer solutions is studied by direct numerical simulations of a finitely extensible nonlinear elastic fluid with the Peterlin closure. The range of Reynolds number ($Re$) $2000 \le Re \le 5000$ is studied but with the same level of elasticity in viscoelastic flows. The evolution of a finite-amplitude perturbation and its effects on the transition dynamics are investigated. A viscoelastic flow begins transition at an earlier time than its Newtonian counterparts, but the transition time appears to be insensitive to polymer concentration in the dilute and semi-dilute regimes studied. Increasing polymer concentration, however, decreases the maximum attainable energy growth during the transition process. The critical or minimum perturbation amplitude required to trigger transition is computed. Interestingly, both Newtonian and viscoelastic flows follow almost the same power-law scaling of $Re^\gamma$ with the critical exponent $\gamma \approx -1.25$, which is in close agreement with previous studies. However, a shift downward is observed for viscoelastic flow, suggesting that smaller perturbation amplitudes are required for the transition. A mechanism of the early transition is investigated by the evolution of wall-normal and spanwise velocity fluctuations and flow structure. The early growth of these fluctuations and the formation of quasi-streamwise vortices around low-speed streaks are promoted by polymers, hence causing an early transition. These vortical structures are found to support the critical exponent $\gamma \approx -1.25$. Once the transition process is completed, polymers play a role in dampening the wall-normal and spanwise velocity fluctuations and vortices to attain a drag-reduced state in viscoelastic turbulent flows.

We numerically study the transverse flow-induced vibration (FIV) of elastically coupled tandem cylinders at Reynolds number $100$, using an in-house immersed boundary method-based solver in two-dimensional coordinates. While several previous studies considered tandem cylinders coupled through flow between them, a hitherto unexplored elastic coupling with fluid flow between them significantly influences FIV. We consider a wide range of gap ratio, reduced velocity, an equal mass ratio of both cylinders and zero damping. A systematic comparison between the classic elastically mounted tandem cylinders and elastically coupled cylinders is presented. The latter configuration exhibits two vibration modes, in-phase and out-of-phase, with corresponding natural frequencies approaching the Strouhal frequency of the system. We quantify variation of the following output variables with reduced velocity and gap ratios: cylinders’ displacement; fluid forces; amplitude spectral density of displacement and force signals; phase characteristics; energy harvesting potential; and discuss the wake characteristics using flow separation, pressure distribution, gap flow quantification, and dynamic mode decomposition characterization. The FIV response is classified into several regimes: initial desynchronization with and without gap vortices; final desynchronization; mixed mode; initial branch; lock-in; upper and lower branch; wake-induced vibration; galloping. We draw upon similarities of computed FIV characteristics with those of an isolated cylinder, in which the lower branch exhibits larger a amplitude than the upper branch. The elastically coupled cylinders show a galloping response similar to an isolated D-section cylinder. By invoking the elastic coupling, we demonstrate FIV suppression and augmentation for in-phase and out-of-phase systems. Our calculations show larger energy harvesting potential at reduced cost for elastically coupled cylinders.

Motile bacteria play essential roles in biology that rely on their dynamic behaviours, including their ability to navigate, interact and self-organize. However, bacteria dynamics on fluid interfaces are not well understood. Swimmers adsorbed on fluid interfaces remain highly motile, and fluid interfaces are highly non-ideal domains that alter swimming behaviour. To understand these effects, we study flow fields generated by Pseudomonas aeruginosa PA01 in the pusher mode. Analysis of correlated displacements of tracers and bacteria reveals dipolar flow fields with unexpected asymmetries that differ significantly from their counterparts in bulk fluids. We decompose the flow field into fundamental hydrodynamic modes for swimmers in incompressible fluid interfaces. We find an expected force-doublet mode corresponding to propulsion and drag at the interface plane, and a second dipolar mode, associated with forces exerted by the flagellum on the cell body in the aqueous phase that are countered by Marangoni stresses in the interface. The balance of these modes depends on the bacteria's trapped interfacial configurations. Understanding these flows is broadly important in nature and in the design of biomimetic swimmers.