The impact of buoyancy on the mean velocity, temperature, and scalar concentration profiles in the lower atmosphere is typically investigated within the framework of Monin-Obukhov similarity theory (MOST). MOST is the theoretical foundation for parametrizing surface-atmosphere exchanges in nearly all weather, climate, and hydrological models. According to MOST, the classic logarithmic profiles of mean velocity and temperature break down as the buoyancy effects become important. However, recent studies on turbulent Rayleigh-Bénard convection and natural convection along vertical walls suggest that the mean temperature in the near-surface region still follows a logarithmic profile. Motivated by these new results, we study the mean potential temperature profile in sheared and unstably stratified atmospheric boundary layers using direct numerical simulations and field observations. We find that the mean potential temperature profile remains logarithmic across a wide range of stability parameters, which characterizes the relative importance of buoyancy versus shear effects. Compared to MOST, our results suggest that the buoyancy force does not modify the logarithmic nature of the mean potential temperature profile, but instead modulates its slope, which is no longer universal and differs from $1/\kappa$, where $\kappa$ is the von Kármán constant. This study provides another perspective on scalar turbulence in the atmospheric boundary layer.

Using a closed set of boundary layer equations [E. S. C. Ching et al., Phys. Rev. Research 1, 033037 (2019)] for turbulent Rayleigh-Bénard convection, we derive analytical results for the dependence of the heat flux, measured by the Nusselt number $\left(\text{Nu}\right)$, on the Reynolds $\left(\text{Re}\right)$ and Prandtl $\left(\text{Pr}\right)$ numbers and two parameters that measure fluctuations in the regime where the horizontal pressure gradient is negligible. This regime is expected to be reached at sufficiently high Rayleigh numbers for a fluid of any given Prandtl number. In the high-$\text{Pr}$ limit, $\text{Nu}=F_1\left(k_1\right){\text{Re}}^{1/2}{\text{Pr}}^{1/3}$ and, in the low-$\text{Pr}$ limit, $\text{Nu}$ tends to ${\pi }^{-1/2}{\text{Re}}^{1/2}{\text{Pr}}^{1/2}$, where $F_1\left(k_1\right)$ has a weak dependence on the parameter $k_1$ in the eddy viscosity that measures velocity fluctuations. These theoretical results further reveal a close resemblance of the scaling dependencies of heat flux in steady forced convection and turbulent Rayleigh-Bénard convection and this finding solves a puzzle in our present understanding of heat transfer in turbulent Rayleigh-Bénard convection.

Electroconvective (EC) instability and its influence on surface morphological perturbations (Morph) are important in many applications, including electrodialysis, batteries, and fuel cells. In this work, we study the effects of a two-dimensional channel flow on the EC and Morph instabilities using two approaches. In the bulk analysis, we derive the asymptotic solutions for small and large wave numbers by neglecting the space charge layer and imposing a second kind electroosmosis slip velocity boundary condition on the electroneutral bulk region. In the full analysis, the instability of the entire region of the liquid electrolyte is analyzed using the ultraspherical spectral method. Both studies show that the flow significantly affects the EC instability. The imposed flow distorts the concentration field, causing a sheltering effect which hinders the ion transport from low- to high-concentration regions, and therefore suppresses the EC instability below a certain wave number. In combination with the viscous stabilization of the high wave number modes by the space charge layer, a sufficiently strong imposed flow can fully suppress the EC instability. The increment in the critical voltage for the instability onset is roughly proportional to the square root of the product of imposed velocity and double layer thickness. The imposed flow has a smaller effect on the Morph instability, except that it may remove the morphological modes resulting from the EC instability and thereby change the wave number of the most unstable mode.

A liquid hanging from a liquid-filled tube can spread spontaneously on rough hydrophilic surfaces while it cannot on smooth hydrophilic surfaces, a difference resulting from the competition between the capillary suction pressures provided by the tube and by the surface roughness. In order to pattern liquids on solid surfaces utilizing such wetting characteristics, we investigate the dynamics of a spontaneous liquid spreading from a tube onto a nanostructured superhydrophilic microlane surrounded by a superhydrophobic background. We find distinct regimes of liquid film propagation dynamics to arise depending on the lane width and the liquid column height in the tube. We theoretically analyze the spreading rates of films, which change power laws in the course of spreading, and corroborate the theory with experiments. The spontaneous liquid patterning process reported in this work can provide a viable venue for such applications as electronic circuit printing and biochip fabrication.

When an object suspended in fluid moves past a soft substrate it experiences an additional lift force due to the deformability of the substrate. In this work we find this lift force analytically for a general deformable substrate in the limit of small deformations. In particular we employ Lorentz's reciprocal theorem to obtain a general integral relation between the lift force and the linear response function of the soft substrate. We apply these results to an elastic layer, and discuss the behavior of the lift force as a function of Poisson's ratio and the thickness of the layer, obtaining analytic results for thin and thick layers. Then we generalize the theory to a linear viscoelastic response of the substrate. For oscillatory relative motion between the surfaces we find that the resulting lift force is a superposition of steady and oscillating modes whose amplitude and phase contain information about the elastic and viscous components of the material response. Our theory makes transparent the connection between the elastohydrodynamic lift force and the underlying response of the substrate and can be used to characterize the mechanical properties of an arbitrary soft material without solid-to-solid contact via lift force measurements.

This work reports an experimental investigation of a liquid-solid fluidized bed involving inertial particles at a large Reynolds number. Owing to optical techniques and index matching, the statistics of the velocity fluctuations of both the particles and the liquid are measured for a wide range of the particle volume fraction ${\alpha }_p$. The dynamics of the fluctuations suggests that the flow possesses the following three properties: (1) The liquid volume involves a wake region in which vertical fluctuations are negative and an interstitial region where they are positive. (2) The statistics of the horizontal fluctuations are similar to vertical ones, except that they are symmetric. (3) Local instant particle fluctuations are proportional to liquid ones. Assuming these properties are true allows us to derive a model for the probability density functions (PDFs) of the two components of the velocity fluctuations of the two phases. This model involves a single reference PDF that is independent of ${\alpha }_p$ and one weighting parameter for each phase. The weighting parameter of the liquid phase is an affine function of ${\alpha }_p$, which characterizes the volume of the wakes relative to that of the interstices. That of the particle phase depends on the preferential concentration of the particles, which tend to avoid the wakes at low ${\alpha }_p$. This model accurately describes the experimental PDFs up to the third-order moment and reproduces all their peculiar features: the skewness of the vertical fluctuations which reverses at a given volume fraction, the presence of exponential tails corresponding to rare intense events, and the symmetry between low and large volume fractions.

Lower respiratory tract infections originate from multiple aerosol sources, varying from droplets erupting from bursting bubbles in a toilet or those produced by human speech. A key component of the aerosol-based infection pathway—from source to potential host—is the survival of the pathogen during aerosolization. Due to their finite-time instability, pinch-off processes occurring during aerosolization have the potential to rapidly accelerate the fluid into focused regions of these droplets, stress objects therein, and if powerful enough, disrupt biological life. However, the extent that a pathogen will be exposed to damaging hydrodynamic stressors during the aerosolization process is unknown. Here we compute the probability that particulates will be exposed to a hydrodynamic stressor during the generation of droplets that range in size from one to 100 microns. For example, particulates in water droplets less than 5 $\mu \mathrm{m}$ have a 50% chance of being subjected to an energy dissipation rate in excess of ${10}^{11}$ $\mathrm{W}/{\mathrm{m}}^3$, hydrodynamic stresses in excess of ${10}^4$ Pa, and strain rates in excess of ${10}^7$ ${\mathrm{s}}^{-1}$, values known to damage certain biological cells. Using a combination of numerical simulations and self-similar dynamics, we show how the exposure within a droplet can be generally predicted from its size, surface tension, and density, even across different aerosolization mechanisms. Collectively, these results introduce aerosol agitation as a potential factor in pathogen transmission and implicate the pinch-off singularity flow as setting the distribution of hydrodynamic stressors experienced within the droplet.

We numerically study the impact-induced hardening in dense suspensions. We employ the lattice Boltzmann method and perform simulations of dense suspensions under impacts, which incorporate the contact between suspended particles with the free surface of the suspension. Our simulation for a free-falling impactor on a dense suspension reproduces experimental results, where rebound takes place for frictional particles at high-speed impact and high volume fraction shortly after the impact before subsequently sinking. We found that the shear stress of the suspension is not affected by the impact, which clearly distinguishes the impact-induced hardening from the discontinuous shear thickening. Instead, we found the existence of a localized region with distinctively high value of normal stress corresponding to the dynamically jammed region. Our simulation indicates that the frictional interaction between suspended particles is important for the impact-induced hardening to maintain the dynamically jammed region. Furthermore, persistent homology analysis successfully elucidates the topological structure of force chains.

We use linear stability analysis to demonstrate how to stabilize multilayer radial Hele-Shaw and porous media flows with a time-dependent injection rate. Sufficient conditions for an injection rate that maintains a stable flow are analytically derived for flows with an arbitrary number of fluid layers. We show numerically that the maximum injection rate for a stable flow decreases proportional to $t^{-1/3}$ for $t\gg 1$ regardless of the number of fluid layers. However, the constant of proportionality depends on the number of layers and increases at a rate that is proportional to the number of interfaces to the two-thirds power. Therefore, flows with more fluid layers can be stable with faster time-dependent injection rates than comparable flows with fewer fluid layers, even when the additional layers are very thin. We also show that for unstable flows, which may be required to inject a given amount of fluid in a fixed amount of time, an increasing injection rate is less unstable than a constant or decreasing injection rate, and that the inclusion of more fluid layers can overcome poor injection strategies.

The unsteady wake of a wall-mounted rectangular prism at large incident (yaw) angles is investigated numerically at Reynolds number of 250. The incident angles considered here ranged between $0^{\circ }$ and ${45}^{\circ }$, which altered the wake dynamics substantially. A symmetric steady wake at small angles transforms into an asymmetric unsteady wake with complex structures at large angles. Approaching ${40}^{\circ }$, the wake appears weakly unsteady with small amplitude fluctuations in velocity and forces. At ${45}^{\circ }$, however, the wake is dominated by unsteady formation of helical structures with a dominant Strouhal number of ${\mathrm{St}}_v=0.14$ that are formed by the interaction of tip vortices on the front and windward edges of the prism. There also exists an embedded low-frequency mechanism that corresponds to the formation and suppression of unsteady helical structures in the wake. This mechanism creates a low-frequency signature in the wake at ${\mathrm{St}}_l=0.011$. A skeleton model is developed and proposed for the wake that characterizes coherent structures at large incident angles. Furthermore, a more representative length scale is proposed based on the projected width of the prism. The range of Reynolds number based on this new scale varies between 208 and 885 with increasing incident angle.

The force experienced by an object moving in a granular medium is a necessary input to describe locomotion problems in such a context. Towards this objective, resistive force theory (RFT) has been developed for granular flows inspired by previous developments in the case of viscous flows. In viscous fluids, a reciprocal motion does not lead to a net propulsion due to the kinematics reversibility of viscous flows that is included in the RFT. We show that, in a granular medium, a reciprocal motion allows for propulsion. We investigate the specific mechanisms underlying this propulsion and discuss how they differ from that of viscous flows. Understanding these phenomena permit both the accurate description of locomotion in sand and the refinement of the RFT for granular materials. These achievements provide opportunities towards the development of robots that are able to progress inside granular media and are suitable for controlling industrial processes.

Small conical-shaped jets may emanate from a liquid bath a short while after a small drop has hit a liquid pool. Here we perform Particle Image Velocimetry (PIV) measurements of the liquid flow inside upward jets after drop impact and show that fluid elements inside the jets may decelerate up to 5–20 times the gravitational acceleration. The measurements show that both the shape of the jet and the velocity profile are self-similar. A theoretical model including surface tension, fluid inertia and gravity correctly predicts the self-similar velocity profile and shape of the jet, allowing us to provide the first quantitative explanation of the shape and dynamics of the emanating jets.

The influence of heating on the shape and the dynamics of a droplet on a liquid substrate has been investigated. The problem is studied numerically in the framework of longwave amplitude equations. The effect of gravity is taken into account. We show that the thermocapillary stresses produce a significant deformation of droplet's interfaces. Heating the droplet from above can create an oscillatory instability generating periodic and quasiperiodic oscillations, change of the droplet shape, and the droplet's decomposition. Heating from below can lead to the substrate layer's rupture due to its monotonic instability.

We theoretically investigate the role of solutal free convection on the diffusion of a buoyant solute at the microfluidic scales, $\simeq 5$–$500\mu \mathrm{m}$. We first consider a horizontal microfluidic slit, one half of which is initially filled with a binary solution (solute and solvent) and the other half with pure solvent. The buoyant forces generate a gravity current that couples to the diffusion of the solute. We perform numerical resolutions of the 2D model describing the transport of the solute in the slit. This study allows us to highlight different regimes as a function of a single parameter, the Rayleigh number Ra which compares gravity-induced advection to solute diffusion. We then derive asymptotic analytical solutions to quantify the width of the mixing zone as a function of time in each regime and establish a diagram that makes it possible to identify the range of Ra and times for which buoyancy does not impact diffusion. In a second step, we present numerical resolutions of the same model but for a 3D microfluidic channel with a square cross section. We observe the same regimes as in the 2D case and focus on the dispersion regime at long timescales. We then derive the expression of the 1D dispersion coefficient for a channel with a rectangular section and analyze the role of the transverse flow in the particular case of a square section. Finally, we show that the impact of this transverse flow on the solute transport can be neglected for most of the microfluidic experimental configurations.

A minimal form of quasilinear approximation (QLA), recently proposed with a stochastic forcing and proper orthogonal decomposition modes [Hwang and Ekchardt, J. Fluid Mech. 894, A23 (2020)], has been extended by employing a resolvent framework. A particular effort is made to reach an extremely high Reynolds number by carefully controlling the approximation without loss of the general scaling properties in the spectra, while setting out the main limitations and accuracy of the proposed QLA with possibility of further improvement. The QLA is subsequently applied to turbulent channel flow up to ${\text{Re}}_{\tau }={10}^6$ (${\text{Re}}_{\tau }$ is the friction Reynolds number). While confirming that the logarithmic wall-normal dependence in streamwise and spanwise turbulence intensities robustly appears, it reveals some nontrivial difference from the scaling of the classical attached eddy model based on inviscid flow assumption. First, the spanwise wave number spectra do not show any clearly visible inverse-law behavior due to the viscous wall effect prevailing in a significant portion of the lower part of the logarithmic layer. Second, the near-wall peak streamwise and spanwise turbulence intensities are found to deviate from $ln{\text{Re}}_{\tau }$ scaling for ${\text{Re}}_{\tau }\gtrsim {10}^4$. Importantly, the near-wall streamwise turbulence intensity is inversely proportional to $1/U_{cl}^{+}$ ($U_{cl}^{+}$ is the inner-scaled channel centreline velocity), consistent with the scaling obtained from an asymptotic analysis of the Navier-Stokes equations [Monkewitz and Nagib, J. Fluid Mech. 783, 474 (2015)]. The same behavior was also observed for the streamwise turbulence intensity in the logarithmic region, as was predicted with the asymptotic analysis. Finally, the streamwise turbulence intensity in the logarithmic region is found to become greater than the near-wall one at ${\text{Re}}_{\tau }\simeq O\left({10}^5\right)$. It is shown that this behavior originates from the near-wall spectra associated with large-scale inactive motions, the intensity of which gradually decays as ${\text{Re}}_{\tau }\to \infty$.

A hypersonic shock wave/turbulent boundary layer interaction (STBLI) is investigated using direct numerical simulation (DNS). The geometry is an $8^{\circ }$ compression ramp, and the flow conditions upstream of the interaction are Mach 7.2 and ${\text{Re}}_{\theta }=3500$. Consistent with experiments at similar conditions, the flow is found to be attached in the mean, although the DNS shows that the probability of observing reversed flow on an instantaneous basis is significant. Due to the high Mach number of the flow combined with a low deflection angle, the shock angle is shallow and the shock is immersed in the boundary layer for a streamwise distance equal to several incoming boundary layer thicknesses downstream of the compression corner. The instantaneous flow structure observed in the DNS is in good qualitative agreement with filtered Rayleigh scattering images obtained experimentally that are available in the literature. The behavior of the turbulence is described based on the evolution of the Reynolds stresses, the anisotropy tensor, the wall pressure spectra, and the turbulence kinetic energy budget through the interaction. The various Reynolds stress components are found to be amplified by factors of 1.8–2.5. The heat transfer through the interaction is also investigated, as well as the relationship between the velocity and temperature fields. At the corner and for a significant distance downstream of the corner, the Reynolds analogy factor lies above values typically observed in zero-pressure-gradient hypersonic boundary layers. A common heat-transfer–pressure scaling describes the behavior observed in the DNS more accurately but with some departures near the corner. In the present attached STBLI, the strong Reynolds analogy, including the assumption of a constant turbulent Prandtl number around unity, is satisfied reasonably well in the interaction, although there are significant departures in the near-wall region.

This study examines the effects of angle of attack on the characteristics of the laminar separation bubble (LSB), its associated low-frequency flow oscillation (LFO), and the flow field about a NACA-0012 airfoil at Reynolds number of $5\times {10}^4$ and $9\times {10}^4$, Mach number of 0.4, and several angles of attack near stall. In the range of the investigated angles of attack, statistics of the flow field suggest the existence of three distinct angle-of-attack regimes. At angles of attack lower than the stall angle of attack, the mean flow field is attached, a short bubble is formed, and the flow field is not much affected by the LFO. At angles of attack higher than the stall angle of attack and lower than the angle of attack of maximum LFO, the flow field undergoes a transition process in which the LFO develops until the flow field reaches a quasiperiodic switching between separated and attached flow and the LSB switches between short and long bubble. At angles of attack higher than the angle of attack of maximum LFO, the mean flow field is massively separated, an open bubble is formed, and the LFO gradually loses momentum and becomes unable to reattach the flow until the airfoil approaches the angle of a full stall. These angle-of-attack regimes have, to the best of the authors' knowledge, not been reported in the literature before.

A liquid droplet, immersed into a Newtonian fluid, can be propelled solely by internal flow. In a simple model, this flow is generated by a collection of point forces, which represent externally actuated devices or model autonomous swimmers. We work out the general framework to compute the self-propulsion of the droplet as a function of the actuating forces and their positions within the droplet. A single point force, $\mathbf{F}$, with general orientation and position, ${\mathbf{r}}_0$, gives rise to both translational and rotational motion of the droplet. We show that the translational mobility is anisotropic and the rotational mobility can be nonmonotonic as a function of $|{\mathbf{r}}_0|$, depending on the viscosity contrast. Due to the linearity of the Stokes equation, superposition can be used to discuss more complex arrays of point forces. We analyze force dipoles, such as a stresslet, a simple model of a biflagellate swimmer and a rotlet, representing a helical swimmer, driven by an external magnetic field. For a general force distribution with arbitrary high multipole moments the propulsion properties of the droplet depend only on a few low order multipoles: up to the quadrupole for translational and up to a special octopole for rotational motion. The coupled motion of droplet and device is discussed for a few exemplary cases. We show in particular that a biflagellate swimmer, modeled as a stresslet, achieves a steady comoving state, where the position of the device relative to the droplet remains fixed. There are two fixed points, symmetric with respect to the center of the droplet. A tiny external force selects one of them and allows one to switch between forward and backward motion.

We study the flow and thermal stratification of a closed domain subjected to different combinations of line and distributed surface heating and cooling. Our observations are drawn from a set of direct numerical simulations in which the ratio of the strength of the distributed sources to the localized sources $\mathrm{\Gamma }$ is varied and shown to play a decisive role in determining the system's statistically steady state. Domains of sufficient horizontal extent that are heated from below and cooled from above in equal amounts by two line sources ($\mathrm{\Gamma }=0$) produce a stable two-layer stratification. The planar plumes generated by each line source are connected by a large-scale circulation over the full depth of the domain and induce secondary circulations within each layer. As the distributed component of the heating, and therefore $\mathrm{\Gamma }$, increases, the buoyancy difference between the layers decreases, before being destroyed when $\mathrm{\Gamma }>1$. For increasing $\mathrm{\Gamma }\in [0,1]$, we observe an increasing tilt of the interface between the layers and the eventual disappearance of the secondary circulation cells. The mean buoyancy transport between the two layers of the stable stratification is dominated by the plumes for all $\mathrm{\Gamma }<1$ because the buoyancy flux associated with interfacial mixing is negligible. Building on existing approaches that typically assume uniform buoyancy within each layer, we develop a model that admits a lateral buoyancy gradient. The model predictions of the buoyancy difference between the layers, the tilt of the interface, and the large-scale circulation strength exhibit a reasonably good agreement with the direct numerical simulation data.