Production, drainage, and stability of foam films, i.e., films in contact with their menisci, are fascinating problems that remain still unsolved. In this article, we propose to explore the regime of large velocities and large film sizes. This is not accessible in experiments classically conducted in the literature and allows us to study the regime of large extension and large extension rates. With our setup, we make soap films up to 2 m high by pulling a horizontal fishing line driven by belts out of a soapy solution at velocities ranging from 20 cm/s to 250 cm/s. We characterize the thickness profile of the central part of the film that behaves like a rubber band under tension. We show that its thickness profile is well described by a static model in which a homogeneous elastic film is stretched by its own weight. This leads to an exponential thickness profile with a characteristic length given by a competition between gravity and surface elasticity. The prefactor is fixed by the shape and area of the film, governed by the fishing line motion but also by a continuous extraction of foam film from the lateral menisci, thicker than the central part, and that progressively invades the film from its lateral boundaries. The model we propose captures the subtle interplay between gravity, film elasticity, and film extraction and leads to predictions in good agreement with our experimental data.

Stochastic linear modeling proposed in Tissot, Mémin, and Cavalieri [J. Fluid Mech. 912, A51 (2021)] is based on classical conservation laws subject to a stochastic transport. Once linearized around the mean flow and expressed in the Fourier domain, the model has proven its efficiency to predict the structure of the streaks of streamwise velocity in turbulent channel flows. It has been in particular demonstrated that the stochastic transport by unresolved incoherent turbulence allows us to better reproduce the streaks through lift-up mechanism. In the present paper, we focus on the study of streamwise-elongated structures, energetic in the buffer and logarithmic layers. In the buffer layer, elongated streamwise vortices, named rolls, are seen to result from coherent wave-wave nonlinear interactions, which have been neglected in the stochastic linear framework. We propose a way to account for the effect of these interactions in the stochastic model by introducing a stochastic forcing, which replaces the missing nonlinear terms. In addition, we propose an iterative strategy in order to ensure that the stochastic noise is decorrelated from the solution, as prescribed by the modeling hypotheses. We explore the prediction abilities of this more complete model in the buffer and logarithmic layers of channel flows at ${\mathrm{Re}}_{\tau }=180, {\mathrm{Re}}_{\tau }=550$, and ${\mathrm{Re}}_{\tau }=1000$. We show an improvement of predictions compared to resolvent analysis with eddy viscosity, especially in the logarithmic layer.

When the intensity of turbulence is increased (by increasing the Reynolds number, e.g., by reducing the viscosity of the fluid), the rate of the dissipation of kinetic energy decreases but does not tend asymptotically to zero: it levels off to a nonzero constant as smaller and smaller vortical flow structures are generated. This fundamental property, called the dissipation anomaly, is sometimes referred to as the zeroth law of turbulence. The question of what happens in the limit of vanishing viscosity (purely hypothetical in classical fluids) acquires a particular physical significance in the context of liquid helium, a quantum fluid which becomes effectively inviscid at low temperatures achievable in the laboratory. By performing numerical simulations and identifying the superfluid Reynolds number, here we show evidence for a superfluid analog to the classical dissipation anomaly. Our numerics indeed show that as the superfluid Reynolds number increases, smaller and smaller structures are generated on the quantized vortex lines on which the superfluid vorticity is confined, balancing the effect of weaker and weaker dissipation.

This paper reports a numerical study of the dispersion of bacteria modeled as active Brownian ellipsoids placed in a plane Poiseuille flow. The longitudinal (along the flow direction) and transverse (along the direction perpendicular to the plane of flow) macroscopic dispersion coefficients are determined from the analysis of a large number of trajectories and their scaling is studied as function of the Péclet number Pe. Three different regimes are observed. (i) At low shear rate, rotational diffusion associated to the swimming activity of the bacteria dominates and classical Taylor dispersion regime is observed. In this regime, the longitudinal dispersion coefficient scales like Péclet square. (ii) An intermediate active regime, where the shear induces a reorientation of the bacteria. This increases the longitudinal dispersion that scales as ${\text{Pe}}^{2+\kappa }$, with $\kappa$ ranging between 1.5 and 2 for aspect ratio between 10 and 1. In this regime, the dispersion coefficient in the direction perpendicular to the plane of the flow decreases like $\log (1/\text{Pe})$. (iii) A final new Taylor regime, where the diffusivity in the gap is set by the molecular diffusion coefficient. We also show that the active regime originates from the enhancement in the time taken by particles to diffuse across the channel gap. We further show that, decreasing the channel height delayed the transition to the active regime.

A modified iterative method is proposed to predict the mean profiles in compressible channel and pipe turbulence by solving a nonlinear system, which is constituted by the perfect gas assumption, the Sutherland's viscosity law, the variable-property scaling models for compressible wall turbulence, the incompressible velocity law of the wall and the relationship between the mean temperature and velocity. Systematic parametric studies display that the proposed iterative method is robust and does not depend on the initial guess of the undetermined parameters. The results also indicate that the present method works very well in both channel and pipe flows at various Reynolds and Mach numbers, and the relative errors of mean temperature profiles and velocity profiles, as compared with the available direct numerical simulation databases, in most cases are within 2% and 5%, respectively.

The flow-induced vibration of a whisker in the wake of a movable circular cylinder with time-varying streamwise gaps was experimentally investigated to understand how whiskers detect the variation of upstream target's swimming status. A time-resolved particle image velocimetry was used to characterize the vortex flow dynamics and vibrations of whisker across various initial gaps and gap growth rates. Results showed that despite the time-varying gaps, the evolution of vortex flow and whisker dynamics remained overall synchronized. Due to the nonlinear decaying rate of vortex strength along streamwise direction, the vibrations of whisker sensor were more sensitive to gap growth rates with smaller initial gaps. However, the sensitivity of whisker (i.e., the decaying rate of whisker vibration intensity over unit time) to gap growth rates gradually decreased when such growth rate became sufficiently high, regardless of initial gaps. Using a physical model based on the balance between whisker inertial force, system damping, restoring force, and flow loading with time-varying magnitudes, we well described the response of whisker sensor in the cylinder wake flow; the model revealed that the reduction of whisker's sensitivity under high gap growth rate was attributed to the sufficiently strong vortices initiated by the fast movement of upstream cylinder, which compensated the influence of vortex strength decay due to the growth of gap. In addition to cases with whisker vibrating in the wake centerline, our complementary measurements with the whisker in the cylinder edge highlighted the time-varying equilibrium vibration positions of whisker sensor due to the “wake-stiffness” effect.

Steady laminar flow over a blunt cone at $5^{\circ }$ angle of attack has been computed at Mach number 6 and unit Reynolds number ${\text{Re}}_{\infty }^{*}=2.079\times {10}^7{\mathrm{m}}^{-1}$. The flow conditions are selected to match the flight test conducted by China Aerodynamics Research and Development Center at an altitude of 16 km where windward-side boundary-layer transition was detected. In order to understand the underlying transition mechanisms, we perform local and global stability analyses, focusing on linear and nonlinear stability characteristics of Mack-mode instability which prevails in the windward side. The global instability spectrum contains two distinct types of modes: few isolated eigenmodes (branch D) lying in the vicinity of the windward ray, and an arc branch (branch S) of eigenmodes in the outboard region. D modes originate in branch S and are considerably more unstable than S modes, potentially causing an indented transition front. Nonlinear development of a single symmetric D mode that inherently contains broadband oblique components will inevitably trigger the fundamental resonance without additional perturbations, once the mode temperature amplitude exceeds 10% of the free-stream value; moreover, the combination resonance is subordinate to the fundamental resonance as the latter always occurs prior to the former. The antisymmetric D mode is less amplified than the symmetric counterpart, yet it is still able to rapidly broaden the azimuthal wave-number spectrum through triad interactions among oblique components. In either case, the global primary mode is found to act as a catalyst to promote rapid amplifications of certain oblique components that ultimately lead to streaky structures in the vicinity of the windward ray. The streaks in turn are significantly unstable to low-frequency waves that are likely responsible for the final breakdown.

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 through an additional parameter $\beta$. Using an appropriately defined dynamical Rayleigh number ${\text{Ra}}_{\mathrm{\Delta }}$, we recover many of the results from the standard Rayleigh-Bénard model. We hope that this paper will simplify the application of Rayleigh-Bénard theory in geophysical contexts, such as lakes.

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. Using confocal microscopy on a miniaturized setup, we observe that, in contrast with standard granular rheology, the flow profiles strongly depend on the particle size. Also, suspensions composed of small enough particles flow at infinitesimal inclinations. From the velocity measurements, an effective rheology is extracted in terms of a friction coefficient as a function of the dimensionless shear rate (the viscous number), and of the particle pressure normalized by the thermal pressure. 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. The model predicts the existence of a glassy friction angle lower than the granular athermal friction angle, a signature of the glass transition in the framework of a pressure-imposed rheology.

We study the properties of various Eulerian contributions to fluid particle acceleration by using well-resolved direct numerical simulations of isotropic turbulence, with the Taylor-scale Reynolds number $R_{\lambda }$ in the range $140–1300$. The variance of convective acceleration, when normalized by Kolmogorov scales, increases as $R_{\lambda }$, consistent with simple theoretical arguments, but differing from classical Kolmogorov's phenomenology, as well as Lagrangian extension of Eulerian multifractal models. The scaling of the local acceleration is also linear in $R_{\lambda }$ to the leading order, but more complex in detail. The strong cancellation between the local and convective acceleration—faithful to the random sweeping hypothesis—results in the variance of the Lagrangian acceleration increasing only as $R_{\lambda }^{0.25}$, as recently shown by Buaria and Sreenivasan [Phys. Rev. Lett. 128, 234502 (2022)]. The acceleration variance is dominated by the irrotational pressure gradient contribution, whose variance essentially follows the $R_{\lambda }^{0.25}$ scaling; the solenoidal viscous contributions are comparatively small and follow $R_{\lambda }^{0.13}$, which is the only acceleration component consistent with multifractal prediction.

This experimental study explored the effects of various axisymmetric temporal excitation waveforms on gaseous transverse jet synchronization and dynamical characteristics, vorticity evolution, and molecular mixing. The study focused on the naturally absolutely unstable transverse jet, with a jet-to-crossflow momentum flux ratio $J=6$, employing simultaneous acetone planar laser-induced fluorescence imaging and stereo particle image velocimetry, enabling new perspectives on the nature of jet control and characteristic signatures associated with optimization. Jet excitation with sinusoidal, square-wave, and double-pulse forcing waveforms was examined, the latter two created with differing numbers of underlying Fourier timescales, and the number of Fourier modes was shown to affect the degree of lock-in of the jet's upstream shear layer to the applied excitation, consistent with an analogous Van der Pol oscillator model. Proper orthogonal decomposition (POD) analysis of the jet's evolving velocity field enabled comparisons of the most energetic mode structures for different excitation conditions and, more significantly, comparisons of various phase portraits associated with three-dimensional plots of the three most energetic POD mode coefficients. Phase portraits revealed significantly different topologies for different excitation conditions, ranging from fairly simple periodic (circular) shapes for sinusoidal excitation to more complex single and multiple loop trajectories for double-pulse forcing with varying degrees of temporal spacing between slow and fast pulses. Subsequent quantification of molecular mixing via acetone PLIF showed that the simpler phase portrait topologies tended to have improved molecular mixing as compared with more complex shapes, but all cases with excitation improved mixing over the unforced transverse jet.

We develop a reduced model for the slow unsteady dynamics of an isotropic chemically active particle near the threshold for spontaneous motion. Building on the steady theory developed in part I of this series, we match a weakly nonlinear expansion valid on the particle scale with a leading-order approximation in a larger-scale unsteady remote region, where the particle acts as a moving point source of diffusing concentration. The resulting amplitude equation for the velocity of the particle includes a term representing the interaction of the particle with its own concentration wake in the remote region, which can be expressed as a time integral over the history of the particle motion, allowing efficient simulation and theoretical analysis of fully three-dimensional unsteady problems. To illustrate how to use the model, we study the effects of a weak force acting on the particle, including the stability of the steady states and how the velocity vector realigns toward the stable one, neither of which previous axisymmetric and steady models were able to capture. This unsteady formulation could also be applied to most of the other perturbation scenarios studied in part I as well as the dynamics of interacting active particles.

In this series, we study the weakly nonlinear dynamics of chemically active particles near the threshold for spontaneous motion. In this part, we focus on steady solutions and develop an “adjoint method” for deriving the nonlinear amplitude equation governing the particle's velocity, first assuming the canonical model in the literature of an isotropic chemically active particle and then considering general perturbations about that model. As in previous works, the amplitude equation is obtained from a solvability condition on the inhomogeneous problem at second order of a particle-scale weakly nonlinear expansion, the formulation of that problem involving asymptotic matching with a leading-order solution in a remote region where advection and diffusion are balanced. We develop a generalized solvability condition based on a Fredholm alternative argument, which entails identifying the adjoint linear operator at the threshold and calculating its kernel. This circumvents the apparent need in earlier theories to solve the second-order inhomogeneous problem, resulting in considerable simplification and adding insight by making it possible to treat a wide range of perturbation scenarios on a common basis. To illustrate our approach, we derive and solve amplitude equations for a number of perturbation scenarios (external force and torque fields, nonuniform surface properties, first-order surface kinetics and bulk absorption), demonstrating that sufficiently near the threshold weak perturbations can appreciably modify and enrich the landscape of steady solutions.

Geophysical flows are often turbulent and subject to rotation. This rotation modifies the structure of turbulence and is thereby expected to sensibly affect its Lagrangian properties. Here, we investigate the relative dispersion and geometry of pairs, triads, and tetrads in homogeneous rotating turbulence by using direct numerical simulations at different rotation rates. Pair dispersion is shown to be faster in the vertical direction (along the rotation axis) than in the horizontal one. At long times, in Taylor's regime, this is due to the slower decorrelation of the vertical velocity component as compared to the horizontal one. At short times, in the ballistic regime, this result can be interpreted by considering pairs of different orientations at the release time and is a signature of the anisotropy of Eulerian second-order structure functions. Rotation also enhances the distortion of triads and tetrads also present in homogeneous and isotropic turbulence. In particular, at long times, the flattening of tetrads increases with the rotation rate. The maximal dimension of triads and tetrads is shown to be preferentially aligned with the rotation axis, in agreement with our observations for pairs.

The effect of freestream turbulence on the spreading of the near wake of a circular cylinder $(<11$ cylinder diameters from the rear face of the cylinder) is investigated through particle image velocimetry data. Different “flavors” of freestream turbulence, in which the turbulence intensity and integral length scale are independently varied, are subjected to the cylinder. The time-averaged spreading of the near wake is decoupled into the growth through entrainment of background fluid and the envelope of the spatial extent of the instantaneous wake due to wake “meandering,” induced by the presence of large-scale vortical coherent structures, i.e., the von Kármán vortex street. Unlike for the far-field of a turbulent wake, examined by Kankanwadi and Buxton [J. Fluid Mech. 905, A35 (2020)], it is shown that freestream turbulence enhances the entrainment rate into the wake in comparison to a nonturbulent background. Furthermore, both the turbulence intensity and the integral length scale of the background turbulence are important in this regard, further contrasting to the far wake where only the turbulence intensity is important. Additionally, wake meandering is enhanced by the presence of background turbulence, and here the integral length scale is the dominant parameter. Combining these findings yields the oft-reported result that background turbulence enhances the time-averaged near-wake growth rate. The influence of wake meandering is isolated by conducting similar experiments in which a splitter plate is mounted to the rear face of the cylinder, thereby eliminating the von Kármán vortex street. These results show that when large-scale vortices are not present within the turbulent wake then freestream turbulence actually suppresses the entrainment rate, relative to a nonturbulent background, in results that mirror Kankanwadi and Buxton [J. Fluid Mech. 905, A35 (2020)]. We therefore postulate that freestream turbulence has the effect to enhance large-scale entrainment via engulfment, but suppress entrainment via small-scale nibbling. Finally, we observe that the presence of freestream turbulence occasionally leads to a transient elimination of vortex shedding, an effect that is bound to have consequences on the instantaneous entrainment rate as outlined above.

The behavior of neutrally buoyant, non-Brownian suspensions subject to square-wave flow oscillations in Hele-Shaw cells is investigated. The velocity field across the cell gap is determined by tracking particles in a plane parallel to the main flow. Initially, the velocity field of the particles is parallel to the main flow and its profile across the gap is blunted due to a higher volume fraction of particles in the gap center; this has been confirmed by direct estimations of the particle fraction and likely results from shear-induced migration. Velocity fluctuations, both along and transverse to the flow direction, agree reasonably well with previous studies. At longer times, 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 characteristic onset time of this instability is observed for Reynolds numbers varying over four decades below $\mathrm{Re}=0.4$. The inverse of the onset time increases linearly with the amplitude of the oscillatory flow. The dependence of the onset time on the particle volume fraction and the gap thickness is consistent with the characteristic time for particle migration across the gap due to shear-induced diffusion.

We study the freezing of water drops on a copper substrate for temperatures ranging from $-9$ to $-79{}^{\circ }\mathrm{C}$. We propose a thermal and geometrical analytical model for the freezing front dynamics. It assumes a propagation of the front at the center described by the three-phase (liquid, ice, substrate) Stefan model in one dimension. The growth is characterized by an effective diffusion coefficient that increases as the substrate temperature decreases. We also consider a spherical front that meets the edges of the drop perpendicularly. Our model captures well our experimental data between $-9$ and $-40{}^{\circ }\mathrm{C}$ and highlights the importance of the heat diffusion in the liquid for the freezing process. Beyond these temperatures, the adhesion of the drops to the copper decreases and the substrate temperature must be considered equal to $-41{}^{\circ }\mathrm{C}$ to rationalize the experimental findings.

Linear stability of solid body rotating flows with axisymmetric density variations is addressed analytically. Considering inviscid disturbances, a nontrivial dispersion relation is obtained and it is shown that the instability is of Rayleigh-Taylor type in cylindrical frame. The viscous correction is derived, in the limit of large Reynolds numbers and large azimuthal wave numbers, allowing the determination of the most unstable mode. Theoretical predictions are checked by comparing them to (spectrally accurate) computed eigenvalues and direct numerical simulations.

We study the statistics of free surface turbulence at large Reynolds numbers produced by direct numerical simulations in a fluid layer at different thicknesses with fixed characteristic forcing scale. We observe the production of a transient inverse cascade, with a duration which depends on the thickness of the layer, followed by a transition to three-dimensional turbulence initially produced close to the bottom, no-slip boundary. By switching off the forcing, we study the decaying turbulent regime and we find that it cannot be described by an exponential law. Our results show that boundary conditions play a fundamental role in the nature of turbulence produced in thin layers and give limits on the conditions to produce a two-dimensional phenomenology.

We investigate the interaction between laboratory scale internal seiches and double-diffusive instabilities in the diffusive-convection regime using two-dimensional, high-resolution numerical simulations. A natural separation exists between the scale of the seiche and the scale of the mature instability. We report on how instabilities are modulated by, and how they modulate, the internal seiches. We find that seiche evolution leads to an earlier onset of instabilities compared to either an initially still fluid with a flat (i.e., seiche-free) interface, or an initially flat interface with an imposed stable shear current. We find that double-diffusion increases the buoyancy frequency and thereby decreases the period of the seiche. We interpret both mechanisms using existing internal wave theories. Additionally, we find that the combined viscous dissipation due to double-diffusive structures and shear stress induced by the seiche is greater than the viscous dissipation produced by either phenomenon in isolation. We discuss implications for more realistic configurations in which the internal seiche degenerates into a nonlinear internal wave train, how the observed mutual modulation may or may not manifest at the field scale, and how the full equation of state for sea water causes double-diffusive structures to grow asymmetrically in contrast to results using a linear equation of state.