The motion of conducting fluids in Earth’s convective core and in the solar convective region generate magnetic fields, but how strong must convection be to sustain a dynamo, and how do boundary conditions affect its onset? We examine this with a new method, treating different boundaries on equal footing, and show that changing the boundaries from conductors to vacuum greatly increases the energetic cost of sustaining magnetic fields against Ohmic losses. The threshold for magnetic field generation is shown to become independent of turbulence strength for strong enough convection. Our results impact the study of planetary and stellar dynamos and can guide experimental and numerical studies.

Experiments show that vertical liquid jet impact on a solid plate creates a hydraulic jump which takes on a stable polygonal shape with sharp corners. The corner shape exhibits a striking universality that is characterized by the radius of curvature and corner angle at the tip, which remains nearly constant over a wide range of flow conditions. Knowledge of the corner angle allows one to determine the global jump shape, as defined by a dimensionless geometry number related to the isoperimetric inequality, thus giving a complete description of the jump shape.

The acceleration of a fluid particle, given by the Navier-Stokes equations, is a key quantity in the study of turbulence, both from Lagrangian and Eulerian viewpoints. It is well known that, due to small-scale intermittency, acceleration statistics deviate from Kolmogorov’s mean-field hypotheses. Using theoretical analysis and a massive direct numerical simulation database, we investigate the intermittency of Lagrangian acceleration in terms of its underlying Eulerian decompositions. We find that their intermittency is even at odds with standard multifractal models, because of strong underlying correlations, which can be otherwise explained by simple theoretical arguments.

Many of the microscopic plankton that live in aquatic environments perform vertical migrations up and down through the water column each day to reach sunlight, acquire nutrients and avoid predators. However, these daily migrations can be thwarted by flow, which is ubiquitous in these environments, because it redirects their motility in other directions. This study explores how the shape of swimmers affects their ability to vertically migrate through hydrodynamic shear. Our results suggest that the highly elongated body morphologies observed in many species of swimming phytoplankton and zooplankton is an adaptation to help them navigate through flow.

We utilize Purcell’s swimmer as a model swimmer to probe the impacts of shear-thinning rheology, an ubiquitous non-Newtonian behavior of biological fluids, on swimming at low Reynolds numbers. We show how the propulsion characteristics of Purcell’s swimmer in a shear-thinning fluid differ from that in a Newtonian fluid in terms of both magnitude and direction of propulsion velocity. We also demonstrate how unequal arm rotational rates can couple with the shear-thinning effect to induce net vertical motion of the swimmer otherwise impossible in a Newtonian fluid.

The suspension of Brownian rods in flow has a major effect in many engineering applications. We numerically examine Brownian rod suspensions through a rectangular channel with and without the effect of circular obstacles, taking into consideration the isotropic translational diffusion tensor using the finite element method. We develop a kinetic macro-model that reduces the computational effort of the Brownian rod suspensions and it gives a good approximation with errors less than 5%.

It is well-known and intuitive that addition of a dilute volume concentration of spheres increases the viscosity of a Newtonian liquid. We find that a viscoelastic liquid undergoing uniaxial extensional flow at small $De$ (extension rate times the polymer relaxation time) experiences a larger increase in viscosity than the Newtonian case due to wakes of extra polymer stretch produced downstream of the spheres. However, when $De\gtrsim 0.6$, the highly stretched polymer in the bulk fluid collapses near the particle surface and the suspension deforms more easily than the particle-free viscoelastic fluid.

Turbulent Rayleigh-Bénard convection is often modeled with a constant surface temperature. However, the surface temperature of many geophysical systems, such as lakes, is coupled to the atmospheric forcing. In this paper, we account for this dynamic surface temperature and show that many of the classical results from the Rayleigh-Bénard literature are recovered.

We propose a thermal and geometrical analytical model for the freezing front dynamics of a spherical drop. The growth is characterized by an effective diffusion coefficient that increases as the substrate temperature decreases and a spherical front that meets the edges of the drop perpendicularly. We compare our model with experimental data for substrate temperature ranging from -9 to -80 °C. We highlight the importance of heat diffusion in the liquid and the adhesion of drops to the substrate that decreases at low temperature.

Isotropic chemically active particles can spontaneously self-propel owing to a symmetry-breaking instability when diffusion of the chemical is sufficiently weak relative to advection. This series revisits the weakly nonlinear theory describing the dynamics of such spontaneous swimmers near the instability threshold. Part II presents an extension to the general framework from part I to include unsteadiness in the form of an integral over the history of the particle motion, representing the interaction of the particle with its own chemical wake. This allows efficient simulation and theoretical analysis of fully three-dimensional unsteady problems in a range of physical scenarios.

The stability of variable density rotating flows is studied analytically and numerically. We show that the dynamics which arises is of the cylindrical Rayleigh-Taylor type when density gradients are opposed to centrifugal acceleration. Asymptotic viscous correction determines the most unstable mode and is in very good agreement with direct numerical simulations.

This experimental study examines the effects of various axisymmetric temporal excitation waveforms on gaseous transverse jet synchronization and dynamical characteristics, vorticity evolution, and molecular mixing. Stereo PIV-derived vorticity fields and proper orthogonal decomposition analysis of the jet’s evolving velocity field enable comparisons of the evolving jet dynamics and documentation of rather significant differences in phase portraits and corresponding mixing characteristics for various excitation conditions.

What is the natural transition scenario for the windward boundary layer over a hypersonic inclined cone? Based on comprehensive linear and nonlinear global stability analyses, this work shows that the K-type breakdown triggered by the Mack-mode instability is responsible for the windward boundary-layer transition.

Stochastic modeling under location uncertainty considers conservation laws of quantities subject to a stochastic transport. This framework allows us to extend the linearized models of the type of resolvent analysis into a form which models the influence of turbulence onto coherent structures in a physically consistent manner, i.e. through a transport. We show the ability of this model to predict coherent structures in the logarithmic layer of a turbulent channel flow at the friction Reynolds number $R{e}_{\tau }=1000$, where standard models are less accurate.

In this work, we measure and model the thickness profile of soap films in the regime of large extensions and large extension rates. For this purpose, we developed an experiment to generate soap films up to two meters high at velocities of the order of a meter per second. We show that the thickness profile in the central part of the film is exponential and described by a static model where the soap film is modeled by an elastic object stretched under gravity.

The rotation of slender objects in Stokes flows is often neglected in favor of translation, though it can play a dominant role in velocity boundary conditions. Here, we pose and explore a simple but rich ansatz that captures this rapid rotation, and highlights its broad validity and utility. Further, we derive a simple, local relation between torque and angular velocity, termed resistive torque theory, which is accurate up to algebraic corrections.

Minimal models are used frequently when building up intuition for microswimmers and their behaviors. In this paper, we highlight how the commonplace omission of rapid variation in the parameters used in these models can lead to qualitatively incorrect predictions, even in the simplest and most common models of swimmers near boundaries. Further, we show how appropriate, effective parameterizations can be found through an often-straightforward multiscale analysis.

Isotropic chemically active particles can spontaneously self-propel owing to a symmetry-breaking instability when diffusion of the chemical is sufficiently weak relative to advection. This series revisits the weakly nonlinear theory describing the dynamics of such spontaneous swimmers near the instability threshold. Part I identifies the adjoint linearized equations, a key element towards a versatile theory that can be used to model general motion in three dimensions including perturbation effects and interactions. The general theoretical framework is demonstrated by deriving and analyzing steady amplitude equations in a range of physical scenarios.

Recent experiments in cell biology have probed the impact of artificially induced intracellular flows, known as focused-light-induced cytoplasmic streaming (FLUCS), in cell division. Here, we present a fully analytical, theoretical model of FLUCS experiments, describing the instantaneous fluid flow and resulting transport of tracers at all length scales under two-dimensional confinement. In agreement with recent experimental measurements, we show that the average velocity of tracers is a hydrodynamic source dipole in the far field. Our quantitative findings will enable the design of new controlled experiments to establish the physiological role of physical transport processes inside cells.

The behavior of neutrally buoyant, non-Brownian suspensions subject to square-wave flow oscillations in Hele-Shaw cells is investigated experimentally. The velocity field across the cell gap is determined by tracking particles in a plane parallel to the main flow. The suspension develops an instability characterized by the growth of a transverse velocity component that is periodic along the main flow direction and in time. No influence of inertia on the development of the instability was observed. The characteristic onset time varies as the inverse of the oscillation amplitude with particle volume fraction dependence similar to that of the shear-induced diffusivity across the cell aperture.

We experimentally revisit the flow down an inclined plane of dense granular suspensions, with particles of sizes in the micron range, for which thermal fluctuations cannot be ignored. In contrast with standard granular rheology, the flow strongly depends on the particles size. A phenomenological model based on the sum of a thermal contribution describing the glass transition and an athermal contribution capturing the jamming transition is developed, which reproduces well the experimental observations.

This work investigates the role played by a forest of pillars on the steady flow of a granular layer down an inclined plane. We realized experiments for different inter-pillar distances to observe how the forest density slows down the granular flow. These observations are rationalized by an average approach that considers a granular rheology for the flow and includes the additional force exerted by the pillars on the granular layer.

Bacteria have long been assumed to behave as a passive colloid. In this paper, we show that the alignment of bacteria in the flow modifies their dispersion dynamics. We determine here the resulting relation between the macroscopic longitudinal dispersion coefficient and the Péclet number.

The inverse cascade of energy is a peculiar feature of two-dimensional turbulence. Numerical and experimental studies have shown that it is possible to produce an inverse cascade also in a three-dimensional flow in a thin layer configuration. Here we study how the friction produced by the confining box induces three-dimensional fluctuations which disrupt the inverse cascade and eventually stop the transfer of energy to large scales.

The dispersion and deformation of Lagrangian pairs, triads, and tetrads are investigated in homogeneous rotating turbulence using direct numerical simulations. At short times, the ballistic regime shows signs of the anisotropy induced by rotation. At long times, dispersion is faster along the rotation axis, leading to triads and tetrads being preferentially stretched along that direction.

The influence of freestream turbulence (FT) on near-field development of turbulent wakes is assessed with regards to both the entrainment rate of background fluid into the wake and the extent of wake meandering. It is shown that FT increases the entrainment rate into the near wake, and thereby the rate at which the wake spreads. The influence of FT on wake meandering is more complex, but it is shown that the integral length scale is the dominant property affecting meandering. In a novel control experiment, large-scale coherent motion in the wake is suppressed, and the far-wake results are recovered: that is, turbulent entrainment is reduced via the suppression of small-scale nibbling.

A robust modular iterative method is proposed to predict the mean profiles in compressible channel and pipe turbulence by solving a nonlinear system using the perfect gas assumption, Sutherland’s viscosity law, the variable-property scaling models for compressible wall turbulence, the incompressible velocity law of the wall, and the temperature-velocity relation.

In this work we show evidence for a superfluid analog to the classical dissipation anomaly: When the friction tends to zero, the dissipation does not vanish, but levels off to a constant non-zero value. This characteristic stems from the generation of smaller and smaller structures on the quantized vortex lines as the friction is lowered. This property of quantum turbulence is universal, not depending on the dynamics of the large scales.

A theory of the position dependence of the statistical average of the energy dissipation rate per unit mass (<$ϵ$>) in the inertial sublayer of turbulent channel flow is proposed on the basis of the spirit of the Linear Response Theory (LRT) of turbulence. The theory with data consisting of a series of direct numerical simulations up to Re${}_{\tau }\approx$ 8000 suggests ${\kappa }_{ϵ}\approx$ 0.44 for the von Kármán constant of <$ϵ$>.

This work investigates a quantized system of thin vortex rings with a flow in the core. Examples show that the set of permissible circulation values has a fractal structure. Circulation values in the domain of a round tube with a radius R${}_0$ in the shape of a torus of radius R${}_1\gg R_0$ are given by the accompanying expression where quantities ${\zeta }_k^{(l)}$ stand for zeros of the Bessel function J${}_l$(ρ). A general expression for the partition function of a turbulent flow is also suggested.

The flow-induced vibration of a whisker in the wake of a movable circular cylinder with time-varying streamwise gaps is experimentally investigated to understand how whiskers detect variations in the swimming status of an upstream target. The results show that whisker sensitivity to gap growth rates gradually decreases when such growth rates become sufficiently high, regardless of initial gaps. From the integrated experimental measurements and theoretical model, the reduction of whisker sensitivity under high gap growth rates can be attributed to sufficiently strong vortices initiated by fast movement of the upstream cylinder, which compensate vortex strength decay due to the gap growth.

In idealized settings energy and momentum are transferred from immediately larger flow features to immediately smaller flow features, but this is not true in general. In this investigation we show evidence of mutual interaction between flow features at disparate size scales. We do this by simulating a domain-scale internal seiche in a two-component fluid that undergoes a double-diffusive instability in the diffusive-convection regime.