A sequence of three steady-oscillatory transitions of buoyancy convection of air in a laterally heated cube with perfectly thermally insulated horizontal and spanwise boundaries is studied. The problem is treated by Newton and Arnoldi methods based on Krylov subspace iteration. The finite volume grid is gradually refined from ${100}^3$ to ${256}^3$ finite volumes. It is shown that the primary instability is characterized by two competing eigenmodes, whose temporal development results in two different oscillatory states that differ by their symmetries. Bifurcations due to both modes are subcritical. These modes develop into different oscillatory and then chaotic flow states which, at larger Grashof number, stabilize and arrive to single stable steady flow. With further increase of the Grashof number, this flow loses its stability again. It is argued that, in all the three transitions, the instability onsets as well as reinstatement of stability take place owing to an interaction between a destabilizing centrifugal mechanism and stabilizing effect of thermal stratification.

Reactive-infiltration instability is an inherent nature of a solid dissolution process in a rock fracture. This instability expands the aperture (spacing) of the fracture inhomogeneously and forms preferential dissolution channels (wormholes). The initial aperture and the flow rate play important roles in reshaping the confined geometry because they modify the interplay between flow and reaction that controls the unstable dissolution processes. Here, we perform dissolution experiments in a Hele-Shaw cell to study how the characteristics and pattern transitions are influenced by the initial aperture and the flow rate. We visualize the transitions of dissolution patterns and show that a large aperture usually needs a larger flow rate to form wormholes. We observe the initiating radius at which the dissolving interface shifts from stable to unstable in wormholes due to the decrease of the flow velocity along the radial direction. In the unstable region, the buoyancy-driven convection rolls etch the solid surface into radial stripes with a characteristic wavelength. Decreasing initial aperture or increasing flow rate would suppress the effect of buoyancy-driven convection on the dissolution. Based on the theoretical analysis, we confirm that the initiating radius and the pattern transition can be well represented by the ratio of invading length in the bulk flow direction to the longitudinal direction. Using this concept, we can theoretically estimate the initiating radius and pattern transitions affected by the initial aperture and the flow rate. Finally, a phase diagram of dissolution patterns is established, exhibiting excellent agreement with our experimental results and the existing works. Our work elucidates the mechanism of the initial aperture control on dissolution morphologies in a Hele-Shaw cell, and it provides a benchmark for the investigation of reactive-infiltration instability for permeable media.

Reduced order models (ROMs) that capture flow dynamics are of interest for decreasing computational costs for simulation as well as for model-based control approaches. This work presents a data-driven framework for minimal-dimensional models that effectively capture the dynamics and properties of the flow. We apply this to Kolmogorov flow in a regime consisting of chaotic and intermittent behavior, which is common in many flow processes and is challenging to model. The trajectory of the flow travels near relative periodic orbits (RPOs), interspersed with sporadic bursting events corresponding to excursions between the regions containing the RPOs. The first step in development of the models is use of an undercomplete autoencoder to map from the full state data down to a latent space of dramatically lower dimension. Then models of the discrete-time evolution of the dynamics in the latent space are developed. By analyzing the model performance as a function of latent space dimension, we can estimate the minimum number of dimensions required to capture the system dynamics. To further reduce the dimension of the dynamical model, we factor out a phase variable in the direction of translational invariance for the flow, leading to separate evolution equations for the pattern and phase dynamics. At a model dimension of five for the pattern dynamics, as opposed to the full state dimension of 1024 (i.e., a $32\times 32$ grid), accurate predictions are found for individual trajectories out to about two Lyapunov times, as well as for long-time statistics. Further small improvements in the results occur as dimension is increased to nine, beyond which the statistics of the model and the true system are in very good agreement. The nearly heteroclinic connections between the different RPOs, including the quiescent and bursting timescales, are well captured. We also capture key features of the phase dynamics. Finally, we use the low-dimensional representation to predict future bursting events, finding good success.

Droplets interacting with fiber arrays is ubiquitous in nature, textiles, microelectromechanical devices, and fog harvesting. The phenomena of droplet impact on an equidistant array of fibers is experimentally investigated. Drop tower tests are performed to characterize the droplet dynamics in the absence of the effects of gravity which could deform fibers and bias equilibrium configurations. Results show that contact line dissipation is largely responsible for arresting the droplet. Additionally, the penetration length is affected by fiber flexibility. A model is developed predicting the droplet penetration dynamics which shows good agreement with experiments.

Red blood cells (RBCs) flowing in a microchannel undergo dispersion in the flow direction due to the nonuniform velocity profile while transverse migration due to flow-induced deformations of cells combined with the presence of walls and a parabolic velocity profile tends to focus them along the center line. This results in a dispersion of RBC transit times through a capillary that is directly related to their transverse migration properties. By analogy with the Taylor-Aris problem, we present an experimental method to characterise this phenomenon by injecting pulses of dilute suspensions of red blood cells and measuring the evolution of their length along the channel, and varying mechanical parameters such as RBC deformability and fluid viscosity. A direct comparison of experimental results with a model that incorporates longitudinal advection and transverse migration in the dilute limit shows that this principle provides through a simple dispersion measurement an evaluation of migration characteristics that are directly connected to cell mechanical properties.

Magnetorheological fluids span an astounding range of applications. Investigating such systems provides insight into the relationships between the rheological properties and the imposed flow and magnetic conditions, thus aiding in the processing of the magnetorheological fluids. In this study, we apply an in-house Stokesian dynamics code to investigate the dynamics, microstructures, and rheological properties of magnetorheological fluids under constant magnetic fields with different directions and magnitudes. A spectral Ewald method is applied to improve the computational capability. Constrained two-dimensional and fully three-dimensional simulations are conducted, and the results are compared. A magnetic-thickening phenomenon is observed in both the constrained two-dimensional and fully three-dimensional simulations, when the magnetic field is in the shear-flow-gradient direction. However, a magnetic-thickening phenomenon is observed in the constrained two-dimensional simulation while a magnetic-thinning phenomenon is observed in the fully three-dimensional simulation when the field is in the shear-flow direction.

Bioinspired jet propulsion through periodic jetting and refilling is a promising method to achieve high swimming speed with relatively low body stiffness. By using a fluid-structure interaction model, we demonstrate that it is possible to increase the efficiency of this locomotion mode by using a valve-controlled auxiliary inlet. The inlet is closed during the jetting phase yet opened during the refilling phase. Its primary function is to reduce the speed of the ingoing flow so that it takes much less energy to refill and the corresponding energy waste is mitigated. Our results show that a properly designed auxiliary inlet greatly reduces the cost of transport with very little sacrifice in swimming speed. For example, in a typical case the inclusion of such an inlet reduces the cost of transport by 60%, yet the decrease in forward speed is only 2.3%.

At the millimetric scale and below, many systems in nature and industry are soft or deformable, e.g., in biological settings where beds of hair are common. Yet, liquid entrapment over such structures remains virtually unexplored. Here we study the fluid-structure interactions between linear arrays of flexible hairs and a mobile contact line during liquid-liquid displacement in a Hele-Shaw cell. We show that confinement and elastocapillarity together have a dramatic effect on drainage: upon flooding a channel with oil and displacing with an immiscible water phase, the moving contact line evacuates the interstice between beams while simultaneously deforming the fibers due to interfacial forces. When beams contact neighbors, pores become inaccessible and thus the defending phase is trapped within elastocapillary bundles. Unlike the single phase case, in which viscous dissipation is the sole force deforming the beams, here deformation is pronounced due to the presence of an interface even in the limit of vanishing flow rates. We predict the volume of fluid removed past a highly deformable elastic medium, which deviates significantly from the rigid case.

Direct numerical simulations are performed to evaluate the hydrodynamic forces and torque on finite-length cylinders embedded in a uniform flow for a wide range of aspect ratios ($2\le \chi \le 30$). Both viscous-dominated and moderately inertial regimes are investigated. We start the investigation by comparing the numerical results to the predictions of the Khayat and Cox [J. Fluid Mech. 209, 435 (1989)] slender-body theory. We show that this theory can predict with reasonable accuracy the drag force on the cylinder for a large range of aspect ratios. However, the theory is unable to predict accurately the lift force and torque for moderately long cylinders of $\chi <30$. By performing a careful analysis of the local contributions to the loads, we show that the disagreement with the theory is mainly explained by the contribution of the cylinder ends which are not properly taken into account by the theory. Semiempirical models based on theoretical results for small but finite inertia are then built to provide a better match with the numerical predictions. We show as in the slender-body theory that the relevant Reynolds number is based on the particle length. We also derive a ready-to-use tensorial formulation for the forces and inertial torque. Additionally, we compare the whole model to experimental results of settling cylinder showing better agreement than the slender-body theory.

Understanding extreme events and their probability is key for the study of climate change impacts, risk assessment, adaptation, and the protection of living beings. Extreme heatwaves are, and likely will be in the future, among the deadliest weather events. Forecasting their occurrence probability a few days, weeks, or months in advance is a primary challenge for risk assessment and attribution but also for fundamental studies about processes, dataset and model validation, and climate change studies. In this work we develop a methodology to build forecasting models which are based on convolutional neural networks, trained on extremely long 8000-year climate model outputs. This approach is parallel to weather model forecasting and has complementary scopes. Because the relation between extreme events is intrinsically probabilistic, we emphasize probabilistic forecast and validation. We demonstrate that neural networks have positive predictive skills, with respect to random climatological forecasts, for the occurrence of long-lasting 14-day heatwaves over France, up to 15 days ahead of time for fast dynamical drivers (500 hPa geopotential height fields), and also at much longer lead times for slow physical drivers (soil moisture). This forecast is made seamlessly in time and space, for fast hemispheric and slow local drivers. The method is easily implemented and versatile. We find that the neural network selects extreme heatwaves associated with a north hemisphere wave-number 3 pattern. We argue that this machine learning approach should be key in the future for quantitative process studies, model intercomparisons, and dataset studies. For instance, we find that the 2 meter temperature field does not contain any new useful statistical information for heatwave forecast, when added to the 500 hPa geopotential height and soil moisture fields. The main scientific message is that most of the times, training neural networks for predicting extreme heatwaves occurs in a regime of lack of data. We suggest that this is likely to be the case for most other applications to large-scale atmosphere and climate phenomena. Depending on the information to be learned, training might require dataset lengths as long as several thousands of years, or even more, for optimal forecasting skill. For instance, using 100-year-long training sets, a regime of drastic lack of data, leads to severely lower predictive skills and general inability to extract useful information available in the 500 hPa geopotential height field at a hemispheric scale in contrast to the dataset of several thousand years long. Even with several-thousand-year-long datasets, no convergence is observed in the predictive skills coming from hemispheric geopotential height fields. We discuss perspectives for dealing with the lack of data regime, for instance, rare event simulations and how transfer learning may play a role in this latter task.

We investigate the effects of fiber aspect ratio, roughness, flexibility, and volume fraction on the rheology of concentrated suspensions in a steady shear flow using direct numerical simulations. We model the fibers as inextensible continuous flexible slender bodies with the Euler-Bernoulli beam equation governing their dynamics suspended in an incompressible Newtonian fluid. The fiber dynamics and fluid flow coupling is achieved using the immersed boundary method. In addition, the fiber surface roughness might lead to interfiber contacts, resulting in normal and tangential forces between the fibers, which follow Coulomb's law of friction. The surface roughness is modeled as hemispherical protrusions on the fiber surfaces. Their deformation results in a normal load-dependent friction coefficient. Our simulations accurately predict the experimentally observed shear thinning in fiber suspensions. Furthermore, we find that the suspension viscosity $\eta$ increases with increasing the volume fraction, roughness, fiber rigidity, and aspect ratio. The increase in $\eta$ is the macroscopic manifestation of a similar increase in the microscopic contact contribution to the total stress with these parameters. In addition, we observe positive and negative first $N_1$ and second $N_2$ normal stress differences, respectively, with $|N_2|<|N_1|$, in agreement with previous experiments. Last, we propose a modified Maron-Pierce law to quantify the reduction in the jamming volume fraction by increasing the fiber aspect ratio and roughness. Our results and analysis establish the use of fiber surface tribology to tune the suspension flow behavior.

Adding flexibility to rotating structures has been shown to improve their efficiency and reliability as well as their compliance to external flow perturbations. Here, we experimentally investigate the problem of a propulsive rotor submerged in water with flexible blades in both spanwise and chordwise directions. When we rotate the propeller and set an incoming flow, the blades bend and twist. We report measurements of forces and associated blade deformations. We show that moderate deformation affects the thrust produced by the rotor within a few percent while strong deformation completely inhibit thrust production. We show that the bending angle of the blade can be predicted thanks to a modified Cauchy number, taking into account the angle of attack of the blade, in the limit of small deformations. Finally, we show that there exists a single curve linking the thrust produced by the rotor to the bending deformation.

We investigate the effect of a forest of pillars on a granular layer steadily flowing over a rough inclined plane. We quantify experimentally how the steady flow rate of grains is affected by the interpillars distance for different layer thicknesses and slope angles. We then propose a model based on a depth-average approximation associated with $\mu \left(I\right)$ rheology that considers the additional force exerted by the pillars on the granular layer. This model succeeds in accounting for most of the observed results when taking into account some inertia due to the nonvanishing Froude number of the flow.

Recent experiments in cell biology have probed the impact of artificially induced intracellular flows in the spatiotemporal organization of cells and organisms. In these experiments, mild dynamical heating (a few kelvins) via focused infrared light from a laser leads to long-range, thermoviscous flows of the cytoplasm inside a cell. To extend future use of this method in cell biology, popularized as focused-light-induced cytoplasmic streaming (FLUCS), new quantitative models are needed to link the external light forcing to the produced flows and transport. Here, we present a fully analytical, theoretical model describing the fluid flow induced by the dynamical laser stimulus at all length scales (both near the scan path of the laser beam and in the far field) in two-dimensional confinement. We model the effect of the focused light as a small, local temperature change in the fluid, which causes a small change in both the density and the viscosity of the fluid locally. In turn, this results in a locally compressible fluid flow. We analytically solve for the instantaneous flow field induced by the translation of a heat spot of arbitrary time-dependent amplitude along a scan path of arbitrary length. We show that the leading-order instantaneous flow field results from the thermal expansion of the fluid and is independent of the thermal viscosity coefficient. This leading-order velocity field is proportional to the thermal expansion coefficient and the magnitude of the temperature perturbation, with far-field behavior typically dominated by a source or sink flow and proportional to the rate of change of the heat-spot amplitude. In contrast, and in agreement with experimental measurements, the net displacement of a material point due to a full scan of the heat spot is quadratic in the heat-spot amplitude, as it results from the interplay of thermal expansion and thermal viscosity changes. The corresponding average velocity of material points over a scan is a hydrodynamic source dipole in the far field, with direction dependent on the relative importance of thermal expansion and thermal viscosity changes. Our quantitative findings show excellent agreement with recent experimental results and will enable the design of new controlled experiments to establish the physiological role of physical transport processes inside cells.

This paper investigates quantized thin vortex rings with an internal structure. The quantization scheme of this dynamical system is based on an earlier approach proposed by the author. Both energy spectrum and circulation spectrum are calculated. Examples show that the set of permissible circulation values has a fractal structure. The suggested model allows us to describe the system of isolated vortex rings as well as the vortex rings with interaction. Furthermore, the application to the quantum turbulence theory is discussed. The general expression for the partition function of a turbulent flow is suggested.

Many species of plankton migrate through the water column to avoid predation and acquire resources available only at depth. These vertical migrations, however, can be thwarted by flow which is ubiquitous in the ocean and acts to reorient the motility of swimming plankton in different directions. The torques exerted on an organism by hydrodynamic shear are a strong function of its shape—while spherical organisms only experience the overturning effect of vorticity, more elongated organisms experience additional torques that tend to align them in the direction of principal strain. Recent simulations of directed migration through turbulence indicate that organisms with larger aspect ratios are capable of faster vertical migration, however, the underlying physical processes are not well understood. Here, we use simple models of flow to study how elongation affects the capacity of a swimmer to vertically migrate through shear. We explore how the orientation of a migrating swimmer in simple shear depends both on its aspect ratio and nondimensional stability, highlighting where a unique stable upward equilibrium is globally attracting, and where particles can undergo periodic orbits. In addition, we identify that stable up and down equilbria can coexist when there is a nonzero vertical component of vorticity. We go on to investigate how elongation affects the transport and spatial distribution of a migrating swimmer in an inhomogeneous Kolmogorov shear flow. Our results show that a swimmer's shape can profoundly affect its mean-field behavior in flow and tendency to aggregate in regions of high shear. These findings reveal how flow can select for the elongated morphologies commonly found in marine plankton and may also provide insights to rationally design microrobots to navigate ambient flows.

Simple models are used throughout the physical sciences as a means of developing intuition, capturing phenomenology, and qualitatively reproducing observations. In studies of microswimming, simple force-dipole models are commonplace, arising generically as the leading-order, far-field descriptions of a range of complex biological and artificial swimmers. Though many of these swimmers are associated with intricate, time varying flow fields and changing shapes, we often turn to models with constant, averaged parameters for intuition, basic understanding, and back-of-the-envelope prediction. In this brief study, via an elementary multitimescale analysis, we examine whether the standard use of a priori-averaged parameters in minimal microswimmer models is justified, asking if their behavioural predictions qualitatively align with those of models that incorporate rapid temporal variation through simple extensions. In doing so, we find that widespread, seemingly innocuous choices of parameters can give rise to qualitatively incorrect conclusions from simple models, with the potential to alter our intuition for swimming on the microscale. Further, we highlight and exemplify how a straightforward asymptotic analysis of the non-autonomous models can result in effective, systematic parametrizations of minimal models of microswimming.

We investigate the steady-state extensional rheology of a dilute suspension of spherical particles in a dilute polymer solution modeled by the FENE-P constitutive relation. The ensemble-averaged suspension stress uses a recent construct of Koch et al. [Phys. Rev. Fluids 1, 013301 (2016)], based on perturbation for small polymer concentration and the generalized reciprocal theorem, to determine the polymers' influence on the particle stresslet and the particles' influence on the polymer stress. The extensional viscosity is defined as half of the constant of proportionality between the deviatoric stress and the imposed rate of strain tensor in uniaxial extensional flow. For a particle-free polymeric fluid, the extensional viscosity (nondimensionalized by the solvent viscosity) is $1+{\mu }^{\text{poly}}$, where ${\mu }^{\text{poly}}$ is the polymer contribution to the extensional viscosity. When a small volume fraction, $\varphi$, of spheres is added to a polymeric fluid, we find that the stress is altered by the Einstein viscosity of $2.5\varphi$ and two additional stress contributions: the polymer influence on the stresslet and the particle-induced polymer stress (PIPS). At lower Deborah numbers (defined as the product of extension rate and polymer relaxation time), $\mathrm{De}\lesssim 0.5$, the net interaction stress is positive, while it becomes negative at large De. Relative to undisturbed flow, the presence of spheres in uniaxial extensional flow creates regions of both larger and smaller local stretching. Below the coil-stretch transition, the polymers far from the particles are in a coiled state, while they are stretched more than their undisturbed state by large stretching regions around the particle. Due to their finite relaxation time, they also form a wake of stretched polymers downstream of the particle. This leads to a positive contribution to the suspension stress from both the stresslet (surface) and the PIPS (stretched wake). Beyond the coil-stretch transition, polymers far from the particle are highly stretched, but they collapse closer to the coiled state as they arrive at the low stretching regions near the particle surface. Therefore, a negative PIPS results from the regions of collapsed polymers. At sufficiently high Deborah numbers, $\mathrm{De}\gtrsim 1.5$, this region is very thin, and it becomes thinner and more intense upon further increasing De. For large maximum polymer extensibility, $L$, the particle-polymer contribution to the suspension rheology is independent of $L$ below the coil-stretch transition, whereas it scales as $L^2$ above the coil-stretch transition. When $\mathrm{De}\gtrsim 0.6$, the changes in extensional viscosity from the stresslet and the PIPS are $\varphi {\mu }^{\text{poly}}$ and approximately $-1.85\varphi {\mu }^{\text{poly}}$, respectively. At large De, the polymer extensional viscosity, ${\mu }^{\text{poly}}$, is orders of magnitude larger than that of Newtonian solvent. Hence, adding particles reduces the extensional viscosity of the suspension as $(2.5-0.85{\mu }^{\text{poly}})\varphi <0$.

This paper presents a theory of the position dependence of the statistical average $\langle \varepsilon \rangle$ of the energy dissipation rate ε per unit mass in the inertial sublayer of turbulent channel flow. The theory gives $\langle \varepsilon \rangle y/u_{\tau }^3\sim 1/{\kappa }_{\varepsilon }+C_p\left(y/h\right)+C_v\left(l_{\tau }/y\right)$ for small but finite ratios $y/h$ and $l_{\tau }/y$, at large but finite friction Reynolds number ${\mathrm{Re}}_{\tau }=h/l_{\tau }$, where $y$ is the distance from the wall, $h$ is the channel half-width, $u_{\tau }$ and $l_{\tau }$ are the friction velocity and length respectively, and ${\kappa }_{\varepsilon }$, $C_p$, and $C_v$ are nondimensional constants. The theory agrees well with the data of a series of direct numerical simulations of turbulent channel flow with ${\mathrm{Re}}_{\tau }$ up to approximately 8000. The data suggest ${\kappa }_{\varepsilon }\approx 0.44$, which is distinctively different from the widely accepted value ($\approx 0.40$ or so) for the von Kármán constant for the mean velocity in the log-law region of wall-bounded flows.

A new kinetic macromodel based on moments of the probability distribution function is proposed to investigate the flow of rodlike Brownian particle suspensions. The rods concentration-orientation coupling is taken into account. A numerical study is presented for rods through the planar channel, with and without introducing a circular obstacle which develops a nonhomogeneous flow. To verify this macromodel, the results are compared with the solution of the associated Fokker-Planck equation taking into consideration an anisotropic translational diffusion tensor. This tensor depends on the local orientation of the rod. Low (smaller than ${10}^3$) Brownian translational Peclet number causes rod migrations across the flow streamlines.