The flow speedup generated by windbreaks can be used to increase the power production of wind turbines. However, due to the increased drag imposed by the windbreaks, their use in large wind turbine arrays has been questioned. We use large eddy simulations to show that windbreaks can increase the power production of large wind farms. A crucial finding is that windbreaks in a wind farm should be much lower than in the single-turbine case. In fact, the optimal windbreak for an isolated turbine can reduce wind-farm performance. The optimal windbreak height in a wind farm namely depends on the right balance between the flow speedup over the windbreak and the drag imposed by all windbreaks in the farm. The increased performance is a result of the favorable total pressure flux created by the windbreaks.

In the present paper we study the biphasic co-flow through a Hele-Shaw cell with an abrupt change, either expansion or contraction, in channel width. Assuming gentle variation of the flow in the streamwise direction (valid at small capillary number), we derive the third-order nonlinear differential equation governing the shape of the interface separating the two fluids. The interfacial profiles obtained by solving this nonlinear equation are further used as the initial guess for the interface shape in the rigorous numerical solution of the two-dimensional free-boundary problem by the finite element method. The theoretical results are then compared with the experimental findings showing a good agreement. The amplitude of the capillary ridge emerging upstream from a sudden expansion (for moderate expansion ratios up to 1:3) and leading to narrowing of the thread of the disperse phase is significant, however not large enough to trigger its instability and breakup.

Boundary layer instability beneath internal solitary waves (ISWs) of depression may be a significant source of wave-energy dissipation and drive localized mixing and resuspension in coastal regions. Wave flume experiments were undertaken to measure the dissipation of turbulent kinetic energy in the boundary layer beneath ISWs shoaling over a flat bottom. The rate of dissipation of turbulent kinetic energy $(\varepsilon \sim {10}^{-7}-{10}^{-2}\mathrm{W}\mathrm{k}{\mathrm{g}}^{-1})$ was elevated within the unstable boundary layer region, occurring for waves with momentum thickness-based Reynolds number ${\mathrm{Re}}_{ISW}>\sim 200$. Dissipation was parametrized in terms of wave energy $(\mathrm{RMSE}=10\times {10}^{-4}\mathrm{W}{\mathrm{m}}^{-1})$ and ${\mathrm{Re}}_{ISW}$ $(\mathrm{RMSE}=7\times {10}^{-4}\mathrm{W}{\mathrm{m}}^{-1})$. The dissipation length scale was computed from wave-integrated boundary layer dissipation $L_d=\frac{cE}{D}$ and parametrized as a function of wavelength $\lambda$ and ${\mathrm{Re}}_{ISW}$ as ${L_d}^{*}=100\lambda +2.5\times {10}^{10}\lambda {\mathrm{Re}}_{ISW}^{-3.7}$ $(\mathrm{RMSE}=\sim 50\lambda )$. Unstable waves had a dissipative length scale of $\sim 100\lambda$, in agreement with limited field observations, whereas stable waves propagated significantly further $(>\sim 1000\lambda )$.

The flow generated by a biorthogonally stretched membrane below a steadily rotating flow at infinity is examined. The flow's velocity field is shown to be an exact, self-similar solution of the fully three-dimensional Navier-Stokes equations with the solution governed by a set of four ordinary differential equations. It is demonstrated that dual solutions exist when the membrane is stretched in both directions (except in the radially symmetric case), as well as for a range of parameters where the membrane is stretched in one direction and allowed to shrink in the other. For stretching rates close to the radially stretched symmetric case, four solutions exist, including one which has a large wall-jet velocity profile close to the membrane. The linear stability of each solution is also examined, and it is found that only a single solution is stable (where one exists) for a given stretching and rotation rate.

We present high-precision experimental and numerical studies of the Nusselt number $\mathrm{Nu}$ as functions of the Rayleigh number $\mathrm{Ra}$ in geostrophic rotating convection with the domain aspect ratio $\mathrm{\Gamma }$ varying from 0.4 to 3.8 and the Ekman number $\mathrm{Ek}$ varying from $2.7\times {10}^{-5}$ to $2.0\times {10}^{-7}$. With decreasing $\mathrm{Ra}$ our heat-transport data $\mathrm{Nu}\left(\mathrm{Ra}\right)$ reveal a gradual transition from buoyancy-dominated to geostrophic convection at large $\mathrm{Ek}$, whereas the transition becomes sharp with decreasing $\mathrm{Ek}$. We determine the power-law scaling of $\mathrm{Nu}\sim {\mathrm{Ra}}^{\gamma }$, and find an unexpectedly strong $\mathrm{\Gamma }$ dependence of the scaling exponent $\gamma$. We further show that the boundary flows formed near the lateral wall give rise to pronounced enhancement of $\mathrm{Nu}$ over a broad range of the geostrophic regime, leading to reduction of $\gamma$ in small-$\mathrm{\Gamma }$ cells. A very steep scaling with $\gamma >3$ is observed when the periodic lateral boundary condition is used, which manifests the significant differences between laterally confined and unconfined rotating thermal convection. The present work provides insight into the heat-transport scaling in geostrophic convection.

Droplet evaporation has been intensively investigated in past decades owing to its emerging applications in diverse fields of science and technology. Yet the role of transport mechanisms has been the subject of a heated debate, especially the presence of Marangoni flow in water droplets. This work aims to draw a clear picture of the switching transport mechanisms inside a drying pinned sessile water droplet in both the presence and absence of thermocapillarity by developing a comprehensive model that accounts for all pertinent physics in both phases as well as interfacial phenomena at the interface. The model reveals a hitherto unexplored mixed radial and buoyant flow by shedding light on the transition from buoyancy induced Rayleigh flow to the radial flow causing the coffee ring effect. Predictions of the model excellently match previous experimental results across varying substrate temperatures only in the absence of Marangoni flow. When thermocapillarity is accounted for, strong surface flows shape the liquid velocity field during most of the droplet lifetime and the model starts to overestimate evaporation rates with increasing substrate temperature.

We analyze theoretically and experimentally the triadic resonance instability (TRI) of a plane inertial wave in a rotating fluid. Building on the classical triadic interaction equations between helical modes, we show by numerical integration that the maximum growth rate of the TRI is found for secondary waves that do not propagate in the same vertical plane as the primary wave (the rotation axis is parallel to the vertical). In the inviscid limit, we prove this result analytically, in which case the change in the horizontal propagation direction induced by the TRI evolves from ${60}^{\circ }$ to ${90}^{\circ }$ depending on the frequency of the primary wave. Due to a wave generator with a large spatial extension in the horizontal direction of invariance of the forced wave, we are able to report experimental evidence that the TRI of a plane inertial wave is three dimensional. The wave vectors of the secondary waves produced by the TRI are shown to match the theoretical predictions based on the maximum growth rate criterion. These results reveal that the triadic resonant interactions between inertial waves are very efficient at redistributing energy in the horizontal plane, normal to the rotation axis.

Oscillating foils in synchronized pitch/heave motions can be used to harvest hydrokinetic energy. By understanding the wake structure and its correlation with the foil kinematics, predictive models for how foils can operate in array configurations can be developed. To establish a relationship between foil kinematics and wake characteristics, a wide range of kinematics is explored in a two-foil tandem configuration with interfoil spacing from four to nine chord lengths separation and multiple interfoil phases. Using data from experiments and simulations, an in-depth wake analysis is performed and the mean velocity and the turbulent kinetic energy are quantified in the wake. With this energy quantification, the trailing foil efficiency is modified to account for the mean flow in addition to the energy transported by the coherent leading edge vortices (LEVs) shed from the leading foil. With the mean wake velocity, a predictive wake model is able to distinguish three regimes through analyzing trailing foil efficiency profiles and the strength of the primary LEV shed from the leading foil. Dividing the wake into regimes is an insightful way to narrow the range of foil kinematics and configurations and improve the energy harvesting in a two-tandem foil array.

Cerebrospinal fluid flows around and into the brain, driven by intricate mechanisms, with profound implications for human health. According to the glymphatic hypothesis, in physiological conditions, cerebrospinal fluid flows primarily during sleep and serves to remove metabolic wastes like the amyloid-beta and tau proteins whose accumulation is believed to cause Alzheimer's disease. This paper reviews one research team's recent in vivo experiments and theoretical studies to better understand the fluid dynamics of brain cerebrospinal fluid flow. Driving mechanisms are considered, particularly arterial pulsation. Flow correlates closely with artery motion and changes when artery motion is manipulated. Though there are discrepancies between in vivo observations and predictions from simulations and theoretical studies of the mechanism, realistic boundary conditions bring closer agreement. Vessel shapes are considered, and have elongation that minimizes their hydraulic resistance, perhaps through evolutionary optimization. The pathological condition of stroke is considered. Much tissue damage after stroke is caused by swelling, and there is now strong evidence that early swelling is caused not by fluid from blood, as is commonly thought, but by cerebrospinal fluid. Finally, drug delivery is considered, and demonstrations show the glymphatic system could quickly deliver drugs across the blood-brain barrier. The paper closes with a discussion of future opportunities in the fast-changing field of brain fluid dynamics.

Interfacial instabilities present challenges in common industrial processes involving multiphase flows. One such phenomenon—the Saffman-Taylor instability—involves the formation of fingerlike protrusions when a less viscous fluid displaces a more viscous fluid. Recent studies have shown that complex surfactant-laden interfaces with surface rheological stresses resist interfacial deformation and alter the fluid dynamics of the system. Despite current progress, the impact of surface rheological stresses on the Saffman-Taylor instability is yet unknown. In this work, we demonstrate the stabilizing effect of surface rheology in radial viscous fingering using linear stability analysis. We quantify the growth rates of perturbations to show that surface viscosity slows the growth of the instability and results in thicker fingers. Finally, we highlight the quantitative changes that are predicted to occur when a typical surface viscous surfactant is present.

When a fluid is confined in a thin layer, it undergoes a dramatic change in its dynamical and/or statistical properties, which occurs when the confining scale is of the order of some characteristic scale of the flow. Here we study this dimensional transition in the framework of Rayleigh-Taylor mixing in porous media. By means of extensive direct numerical simulations of the Darcy-Rayleigh-Taylor model, we demonstrate the existence of a transition from three-dimensional (3D) to 2D phenomenology when the horizontal width of the convective structures becomes larger than the confining scale. At variance with the case of turbulent flows, in which the transition is continuous and a coexistence of the 2D and 3D regimes is observed, the transition in porous media is sharp. We investigate the effects of the transition on the evolution of the mixing process and on the fluctuations of the density field. In the 2D regime, we observe a speedup in the growth rate of the mixing layer with an increase of the inhomogeneities of the density field.

Building on the recent theoretical work of Wray et al. [J. Fluid Mech. 884, A45 (2020)] concerning the competitive diffusion-limited evaporation of multiple thin sessile droplets in proximity to each other, we obtain theoretical predictions for the spatially nonuniform densities of the contact-line deposits (often referred to as “coffee stains” or “ring stains”) left on the substrate after such droplets containing suspended solid particles have completely evaporated. Neighboring droplets interact via their vapour fields, which results in a spatially nonuniform “shielding” effect. We give predictions for the deposits from a pair of identical droplets, which show that the deposit is reduced the most where the droplets are closest together, and demonstrate excellent quantitative agreement with experimental results of Pradhan and Panigrahi [Colloids Surf. A Physicochem. Eng. Asp. 482, 562 (2015)]. We also give corresponding predictions for a triplet of identical droplets arranged in an equilateral triangle, which show that the effect of shielding on the deposit is more subtle in this case.

Recent investigations on electrokinetic (EK) flows have indicated turbulentlike flow can be realized by applying strong and high frequency ac electric field to flows with high-conductivity-gradient interface, even though under low bulk flow Reynolds number. Relative to conventionally hydrodynamic turbulence in a high Reynolds number, the ac EK turbulent flow exhibits high randomness with stronger intermittency [Wang et al., Phys. Rev. E 93, 013106 (2016)]. The abnormally high intermittency could be attributed to the ascending probability density function of velocity gradients (dominated by small scale velocity structure function) far from the equilibrium state. By evaluating the intermittency of the ac EK turbulent flow with hierarchical structures, we astonishingly find the intermittency factor of hierarchical structures in SL94 law, i.e., $\beta$ factor, which is commonly believed to be between 0 and 1, exhibits larger value than 1 in the ac EK turbulent flow. This result indicates the different hierarchical relations of flow structures in ac EK turbulence flow from that in the conventional hydrodynamic turbulence, as further illustrated by the probability density function of velocity structures among different spatial scales.

The linear global stability of a downward flow of liquid metal in a vertical duct under strong wall heating and a transverse magnetic field is examined numerically. The two-dimensional steady-state magnetohydrodynamic (MHD) mixed convection with an upward reverse flow is first computed by the finite-element method. Then linear global stability equations of the MHD mixed convection are derived and solved by the spatial discretization of the Taylor-Hood finite element and an implicitly restarted Arnoldi algorithm for the resulted generalized eigenvalue problem. Elevator and oscillatory unstable modes are revealed through the eigenspetrum computation of linear global stability equations. The elevator mode is found to be always unstable and independent of the basic flow profile, though a large magnetic field may suppress its growth rate. The unstable oscillatory mode is directly related to the basic upward reverse flow and first occurs at the specific flow structure which has an upward reverse flow near the heating wall and a downward flow near the opposite wall. The critical curves of the Grashof number with respect to the Hartmann number for the three-dimensional oscillatory mode are plotted and reveal that larger Hartmann numbers have larger critical Grashof numbers. Energy budget analyses are also performed and show that the shear Kelvin-Helmholtz instability due to the existence of an inflection point is the key instability mechanism of the three-dimensional oscillatory mode. The appearance of the unstable oscillatory mode may be regarded as an alternative physical explanation of the high-amplitude, low-frequency pulsations of temperature in the experiments and related numerical simulations.

The Lagrangian and Eulerian acceleration properties of fluid particles in homogeneous turbulence with uniform shear and uniform stable stratification are studied using direct numerical simulations. The Richardson number is varied from $\mathrm{Ri}=0$, corresponding to unstratified shear flow, to $\mathrm{Ri}=1$, corresponding to strongly stratified shear flow. The probability density functions (pdfs) of both Lagrangian and Eulerian accelerations have a stretched-exponential shape and they show a strong and similar influence on the Richardson number. The extreme values of the Eulerian acceleration are stronger than those observed for the Lagrangian acceleration. Geometrical statistics explain that the magnitude of the Eulerian acceleration is larger than its Lagrangian counterpart due to the mutual cancellation of the Eulerian and convective acceleration, as both vectors statistically show an antiparallel preference. A wavelet-based scale-dependent decomposition of the Lagrangian and Eulerian accelerations is performed. The tails of the acceleration pdfs grow heavier for smaller scales of turbulent motion. Hence the flatness increases with decreasing scale, indicating stronger intermittency at smaller scales. The joint pdfs of the Lagrangian and Eulerian accelerations indicate a trend to stronger correlations with increasing Richardson number and at larger scales of the turbulent motion. A consideration of the terms in the Navier-Stokes equation shows that the Lagrangian acceleration is mainly determined by the pressure-gradient term, while the Eulerian acceleration is dominated by the nonlinear convection term. A similar analysis is performed for the Lagrangian and Eulerian time rates of change of both fluctuating density and vorticity. The Eulerian time rates of change are observed to have extreme values substantially larger than those of their Lagrangian counterparts due to the advection terms in the advection-diffusion equation for fluctuating density and in the vorticity equation, respectively. The Lagrangian time rate of change of fluctuating vorticity is mainly determined by the vortex stretching and tilting term in the vorticity equation. Since the advection-diffusion equation for fluctuating density lacks a quadratic term, the Lagrangian time rate of change pdfs of fluctuating density show a more Gaussian shape, in particular, for large Richardson numbers. Hence, the Lagrangian acceleration and time rates of change of fluctuating density and vorticity reflect the dominant physics of the underlying governing equations, while the Eulerian acceleration and time rates of change are mainly determined by advection.

The dynamics of molecular mixing and the energy transfer process in the Rayleigh-Taylor instability (RTI) are studied through the collection of simultaneous density-velocity measurements. These experiments provide simultaneous density-velocity field measurements, in contrast to previous point measurements. Statistically stationary experiments are performed in a “convective-type” gas tunnel facility, with density contrast achieved through the injection of helium into the bottom stream. Three experiments at Atwood number $\approx 0.1$ are captured at three outer scale Reynolds numbers $\mathrm{Re}=520,2260$, and 4050. Particle image velocimetry and laser induced fluorescence are employed simultaneously. Statistics of the density and velocity show self-similar collapse of RTI profiles at large Reynolds number $\mathrm{Re}>2000$. Flat velocity profiles indicate homogeneous turbulence characteristics in the core of the mixing region. Significant anisotropy develops in the flow, with horizontal velocity fluctuations being only 60% of the vertical velocity fluctuations. The turbulent mass flux is found to be asymmetric about the centerline, with increased peak towards the spike. Measurements of the molecular mixing show that mixing is maximized at the core of the flow and increases with increased Reynolds number. The transport equation of density-specific-volume correlation $b$ shows that it is mostly produced in the core of the mixing region, and that the spatial evolution of its profile is the result of transport by bulk motion of the bubble and spike. Energy transfer from gravitational potential energy to turbulent kinetic energy and viscous dissipation is observed to occur in the experiment with a ratio of dissipated energy to potential energy released of 38%. The analysis of the turbulent kinetic energy transport equation budget reveals that production is the primary mechanism towards the growth of turbulent kinetic energy in the core of the flow, and is asymmetrically slightly skewed towards the spike. However, it is through the transport that the strong advection at the edges of the mixing region is maintained.

Hydrodynamic interactions are important in biophysics research because they influence both the collective and the individual behavior of micro-organisms and self-propelled particles. For instance, hydrodynamic interactions at the microswimmer level determine the attraction or repulsion between individuals, and hence the rise of collective behavior. Meanwhile, hydrodynamic interactions between swimming appendages (e.g., cilia and flagella) influence the emergence of swimming gaits, synchronized bundles, and metachronal waves, and hence the propulsive capacity of the individual swimmer. In this study we address the issue of hydrodynamic interactions between slender filaments separated by a distance larger than their contour length $(d>L)$ by means of asymptotic calculations and numerical simulations. We first derive analytical expressions for the extended resistance matrix of two arbitrarily shaped rigid filaments, as a series expansion in inverse powers of $d/L>1$. The coefficients in our asymptotic series expansion are then evaluated using two well-established methods for slender filaments, resistive-force theory (RFT) and slender-body theory (SBT), and our asymptotic theory is verified using numerical simulations based on SBT for the case of two parallel helical filaments. The theory is able to capture the qualitative features of the interactions in the regime $d/L>1$, which opens the path to a deeper physical understanding of hydrodynamically governed phenomena such as interfilament synchronization and multiflagellar propulsion. To demonstrate the usefulness of our results, we next apply our theory to the case of two helical filaments rotating side-by-side, where we quantify the dependence of all forces and torques on the distance and phase difference between the helices. Using our understanding of pairwise interactions, we then provide physical intuition for the case of a circular array of rotating helices. Our theoretical results will be useful for the study of hydrodynamic effects that emerge between interacting bacterial flagella, nodal cilia, and slender microswimmers, both artificial and biological.

While wall modeling enables significant reduction in computational cost compared to wall-resolved large eddy simulations (LESs), it often fails to capture laminar-to-turbulence transition processes realistically. This issue arises in part because wall models typically assume that the near-wall flow is in a statistically quasiequilibrium turbulent state and hence incorrectly prescribe turbulent wall stresses in regions that are still laminar during transition. In this work we propose an approach in which the application of the wall model is retained within the turbulent regions of transitional flow where even nascent spots exhibit high-Reynolds-number characteristics, but the wall model is not applied in laminar regions. The local distinction between turbulent and laminar regions is performed using a self-organized map (SOM) [see Z. Wu et al., Phys. Rev. Fluids 4, 023902 (2019)], an unsupervised machine learning classifier. We demonstrate the capability of wall-modeled LES with SOM-based turbulent/nonturbulent classification (WMSOM) in predicting both bypass and orderly transitions in channel flow at target Reynolds numbers of ${\text{Re}}_{\tau }=130$ and 200, respectively. Predictions of bypass transition initiated from localized initial disturbances agree well with direct numerical simulation. For orderly transition, we simulate K- and H-type transitions, due to the interaction of two- and three-dimensional instability waves. We show good predictions for both scenarios, with a slight delay in the transition time. The WMSOM approach offers a significant reduction in computational cost compared to wall-resolved LES.

A separation length scaling method for shock/turbulent boundary layer interactions (STBLIs) is considered. A modification of the scaling method of Souverein et al. [J. Fluid Mech. 714, 505 (2013)] is introduced to account for heat transfer effects. As a further generalization of the model, a control volume analysis applied to a cylinder-with-flare geometry demonstrates that this axisymmetric geometry scales with the same parameters as the two-dimensional interactions. The current modified scaling is evaluated for a large range of STBLI conditions. A database of STBLI flows at Mach 2–3 has been collected from the available literature and includes both reflected shock and compression ramp data with various wall heat transfer conditions. A new Large Eddy Simulation database of Mach 7 and Mach 10 cold wall compression ramp flows with parametrically varying ramp angle is also utilized. In addition, the Mach 10 compression ramp experiments of Elfstrom [J. Fluid Mech. 53, 113 (1972)] as well as the Mach 10 cylinder-with-flare experiments of Coleman (Ph.D. thesis, University of London, 1973) and Brooks et al. (AIAA Paper No. 2017-3325, 2017) are included in the evaluation. It is shown that this new generalized scaling method results in a linear collapse of all incipiently separated STBLI data. No collapse is observed for fully separated interactions. Arguments for the physical mechanisms affecting the separation length scaling for the two STBLI regimes, incipient and fully separated, that are consistent with the data trends are presented. Namely, for incipient cases, the distribution of momentum in the incoming boundary layer is key to separation length scaling. In contrast, for fully separated cases, we postulate that the presence and strength of inviscid vortical structures significantly affects the separation length. Furthermore, we postulate how the distinct flow dynamics of the boundary layer and of the inviscid vortical structures mechanisms found in STBLI interplay and become dominant over the other.