The large-scale turbulent statistics of mechanically driven superfluid ${}^4\mathrm{He}$ was shown experimentally to follow the classical counterpart. In this paper, we use direct numerical simulations to study the whole range of scales in a range of temperatures $T\in [1.3,2.1]$ K. The numerics employ self-consistent and nonlinearly coupled normal and superfluid components. The main results are that (i) the velocity fluctuations of normal and super components are well correlated in the inertial range of scales, but decorrelate at small scales. (ii) The energy transfer by mutual friction between components is particulary efficient in the temperature range between 1.8 and 2 K, leading to enhancement of small-scale intermittency for these temperatures. (iii) At low $T$ and close to $T_{\lambda }$, the scaling properties of the energy spectra and structure functions of the two components are approaching those of classical hydrodynamic turbulence.

This study considers the onset of stress-free Boussinesq thermal convection in rotating spherical shells with an aspect ratio $\eta =r_i/r_o=0.9$ ($r_i$ and $r_o$ being the inner and outer radius), Prandtl numbers $Pr\in [{10}^{-4},{10}^{-1}]$, and Taylor numbers $\mathrm{Ta}\in [{10}^4,{10}^{12}]$. We are particularly interested in the form of the convective cell pattern that develops, and in its time scales, since this may have observational consequences. For a fixed $\mathrm{Ta}<{10}^9$ and by decreasing $Pr$ from 0.1 to ${10}^{-4}$, a transition between spiraling columnar (SC) and equatorially attached (EA) modes, and a transition between EA and equatorially antisymmetric or symmetric polar (AP/SP) weakly multicellular modes, are found. The latter modes are preferred at very low $Pr$. Surprisingly, for $\mathrm{Ta}>3\times {10}^9$, the unicellular polar modes become also preferred at moderate $Pr\sim {10}^{-2}$ because two new transition curves between EA and AP/SP and between AP/SP and SC modes are born at a triple-point bifurcation. The dependence on $Pr$ and $\mathrm{Ta}$ of the transitions is studied to estimate the types of modes, and their critical parameters, preferred at different stellar regimes.

We investigate the flows and deformations resulting from the deposition of a water soluble surfactant at a bare oil-water interface. Once the surfactant is deposited, we show that the oil-water interface is deformed with a water bump rising upward into the oil. For a given oil, the maximal deformation—located at the surfactant deposition point—decreases with the oil-layer thickness. We also observe a critical oil-layer thickness below which the deformation becomes as large as the oil layer, leading to the rupture of this layer and an oil-water dewetting. Experimentally, it is found that this critical thickness depends on the oil density and viscosity. We then provide an analytical modelization that explains quantitatively all these experimental features. In particular, our analysis allows us to derive an analytical relationship between the vertical profile of the oil-water interface and the in-plane surface tension profile. Therefore, we propose that the monitoring of the interface vertical shape can be used as a new spatially resolved tensiometry technique.

A shock-preserving finite volume solver with the generalized Lax-Friedrichs splitting flux for morphing continuum theory (MCT) is presented and verified. The numerical MCT solver is showcased in a supersonic turbulent flow with Mach 2.93 over an $8^{\circ }$ compression ramp. The simulation results validated MCT with experiments as an alternative for modeling compressible turbulence. The required size of the smallest mesh cell for the MCT simulation is shown to be almost an order larger than that in a similar direct numerical simulation study. The comparison shows MCT is a much more computationally friendly theory than the classical Navier-Stokes equations. The dynamics of energy cascade at the length scale of individual eddies is illuminated through the subscale rotation introduced by MCT. In this regard, MCT provides a statistical averaging procedure for capturing energy transfer in compressible turbulence, not found in classical fluid theories. Analysis of the MCT results show the existence of a statistical coupling of the internal and translational kinetic energy fluctuations with the corresponding eddy rotational energy fluctuations, indicating a multiscale transfer of energy. In conclusion, MCT gives a new characterization of the energy cascade within compressible turbulence without the use of excessive computational resources.

This work explores a model waterspout: a flow of water and sunflower oil driven by the rotating lid in a sealed vertical cylindrical container. The experiments reveal the hysteretic growth and decay of a water column. The numerical simulations uncover vortex breakdown (VB) in the water and oil flows. As the rotation speeds up, (1) a VB water cell emerges near the bottom center, (2) it expands and occupies almost the entire water volume except a thin layer adjusted to the interface, (3) a VB oil cell emerges and disappears above the interface-axis intersection, (4) the interface rises near the axis, descends at the periphery, and shifts from the sidewall to the bottom, (5) the water touches the lid near the axis and forms a column, extending from the bottom up to the lid. As the rotation decelerates, the process reverses, but the flow states differ from those for the direct process at same rotation speeds. It is argued that the hysteresis is a capillary phenomenon and occurs because the interface-wall contact angle differs in the direct and reverse processes.

The bacterial flagellum thickness is smaller than the radius of gyration of long polymer chain molecules. The flow velocity gradient over the length of polymer chains can be nonuniform and continuum models of polymeric liquids break in this limit. In this work, we use Brownian dynamics simulations to study a rotating helical flagellum in a polymer solution and overcome this limitation. As the polymer size increases, the viscosity experienced by the flagellum asymptotically reduces to the solvent viscosity. The contribution of polymer molecules to the local viscosity in a solution of long polymer chains decreases with the inverse of polymer size to the power 1/2. The difference in viscosity experienced by the bacterial cell body and flagella can predict the nonmonotonic swimming speed of bacteria in polymer solutions.

The structure of a standing plane shock wave in a polyatomic gas is investigated on the basis of kinetic theory, with special interest in gases with large bulk viscosities, such as ${\mathrm{CO}}_2$ gas. The ellipsoidal statistical model for a polyatomic gas is employed. First, the shock structure is computed numerically for various upstream Mach numbers and for various (large) values of the ratio of the bulk viscosity to the shear viscosity, and different types of profiles, such as the double-layer structure consisting of a thin upstream layer with a steep change and a much thicker downstream layer with a mild change, are obtained. Then, an asymptotic analysis for large values of the ratio is carried out, and an analytical solution that describes the different types of profiles obtained by the numerical analysis, such as the double-layer structure, correctly is obtained.

We present a study of Taylor dispersion in premixed combustion and use it to clarify fundamental issues related to flame propagation in a flow field. In particular, simple analytical formulas are derived for variable density laminar flames with arbitrary Lewis number $\text{Le}$ providing clear answers to important questions arising in turbulent combustion, when these questions are posed for the case of one-scale laminar parallel flows. Exploiting, in the context of a laminar Poiseuille flow model, a thick flame distinguished asymptotic limit for which the flow amplitude is large with the Reynolds number $\text{Re}$ fixed, three main contributions are made. First, a link is established between Taylor dispersion [G. Taylor, Proc. R. Soc. London Ser. A 219, 186 (1953)] and Damköhler's second hypothesis [G. Damköhler, Ber. Bunsen. Phys. Chem. 46, 601 (1940)] by describing analytically the enhancement of the effective propagation speed $U_T$ due to small flow scales. More precisely, it is shown that Damköhler's hypothesis is only partially correct for one-scale parallel laminar flows. Specifically, while the increase in $U_T$ due to the flow is shown to be directly associated with the increase in the effective diffusivity as suggested by Damköhler, our results imply that $U_T\sim \text{Re}$ (for $\text{Re}\gg 1)$ rather than $U_T\sim \sqrt{\text{Re}}$, as implied by Damköhler's hypothesis. Second, it is demonstrated analytically and confirmed numerically that, when $U_T$ is plotted versus the flow amplitude for fixed values of $\text{Re}$, the curve levels off to a constant value depending on $\text{Re}$. We may refer to this effect as the laminar bending effect as it mimics a similar bending effect known in turbulent combustion. Third, somewhat surprising implications associated with the dependence of $U_T$ and of the effective Lewis number ${\text{Le}}_{\text{eff}}$ on the flow are reported. For example, ${\text{Le}}_{\text{eff}}$ is found to vary from $\text{Le}$ to ${\text{Le}}^{-1}$ as $\text{Re}$ varies from small to large values. Also, $U_T$ is found to be a monotonically increasing function of $\text{Re}$ if $\text{Le}<\sqrt{2}$ and a nonmonotonic function if $\text{Le}>\sqrt{2}$.

The problem of accretion of small particles by a sphere embedded in a mean flow is studied in the case where the particles undergo inelastic collisions with the solid object. The collision efficiency, which gives the flux of particles experiencing at least one bounce on the sphere, is found to depend upon the sphere Reynolds number only through the value of the critical Stokes number below which no collision occurs. In the absence of molecular diffusion, it is demonstrated that multiple bounces do not provide enough energy dissipation for the particles to stick to the surface within a finite time. This excludes the possibility of any kind of inelastic collapse, so that determining an accretion efficiency requires modeling more precisely particle-surface microphysical interactions. A straightforward choice is to assume that the particles stick when their kinetic energy at impact is below a threshold. In this view, numerical simulations are performed to describe the statistics of impact velocities at various values of the Reynolds number. Successive bounces are shown to enhance accretion. These results are put together to provide a general qualitative picture on how the accretion efficiency depends upon the nondimensional parameters of the problem.

It is well known that the spanwise rotation in turbulent channel flow alters the mean velocity distribution to a linear law. In the present work, we have studied the higher-order moments of the streamwise fluctuations in a turbulent channel flow with spanwise rotation. Our results show that in a significant part of the channel the $2p$-order moments, raised by the power $1/p$ with $p=1,2,...,6$, also follow linear behavior according to ${\langle {\left(u^{\prime +}\right)}^{2p}\rangle }^{1/p}=a_p(y/h)+b_p$. Here, $u^{\prime +}$ is the streamwise velocity fluctuation normalized by the global friction velocity, $h$ is the channel half width, and $b_p$ and $a_p$ are the intercept and the slope, respectively, which vary with Reynolds and rotation numbers. The linear regions can be extended by introducing a self-similar scaling, that is, $2p$-order moments as a function of $2q$-order moments. The slopes in the self-similar scaling $a_p/a_1$ do not reveal sub-Gaussian behavior as in nonrotating wall-bounded flows, but rather Gaussian or super-Gaussian behaviors.

The article considers the strain-rate tensor distribution in various isotropically distributed incompressible flows. By means of a fortunate choice of variables, a strong degeneracy in the probability distribution of strain-rate tensor characteristics is found in numerical simulations of isotropic turbulence. This allows us to reduce the probability density function (PDF) of the strain-rate tensor to a function of one variable. Also it appears that for those particular parameters that reflect the ratio of different eigenvalues of the strain tensor $(s$ and $\beta$ parameters), the shapes of their probability distributions are universal and do not depend on the specific shape of distribution. Furthermore, it is also shown analytically that for all time-reversible statistical isotropic flows the probability distribution of $s$ is uniform, which generalizes previous numerical calculations.

In this paper, we consider a recent theoretical prediction [Bragg et al., Phys. Fluids 28, 013305 (2016)] that for inertial particles in two-dimensional (2D) turbulence, the nature of the irreversibility of the particle-pair dispersion inverts when the particle inertia exceeds a certain value. In particular, when the particle Stokes number, $\mathrm{St}$, is below a certain value, the forward-in-time (FIT) dispersion should be faster than the backward-in-time (BIT) dispersion, but for $\mathrm{St}$ above this value, this should invert so that BIT becomes faster than FIT dispersion. This nontrivial behavior arises because of the competition between two physically distinct irreversibility mechanisms that operate in different regimes of $\mathrm{St}$. In three-dimensional (3D) turbulence, both mechanisms act to produce faster BIT than FIT dispersion, but in 2D turbulence, the two mechanisms have opposite effects because of the flux of energy from the small to the large scales. We supplement the qualitative argument given by Bragg et al. [Phys. Fluids 28, 013305 (2016)] by deriving quantitative predictions of this effect in the short time limit. We confirm the theoretical predictions using results of inertial particle dispersion in a direct numerical simulation of 2D turbulence. A more general finding of this analysis is that in turbulent flows with an inverse energy flux, inertial particles may yet exhibit a net downscale flux of kinetic energy because of their nonlocal-in-time dynamics.

The kinetic energy spectrum of high-Reynolds turbulent swirling flows is experimentally studied. This spectrum, obtained from direct measurements in space, exhibits nearly two decades of Kolmogorov $k^{-5/3}$ decay in the inertial range of scales. Beyond this regime, in the dissipative range of scales, a crossover to a stretched exponential decay on scale $k^{2/3}$ is observed, in full agreement with a recent theoretical prediction based on nonperturbative renormalization group theory.

The coalescence of a droplet and a liquid/air interface of lower surface tension was numerically studied by using the lattice Boltzmann phase-field method. The experimental phenomenon of droplet ejection observed by Blanchette et al. [Phys. Fluids 21, 072107 (2009)] at sufficiently large surface tension differences was successfully reproduced for the first time. Furthermore, the emergence, disappearance, and re-emergence of “partial coalescence” with increasing surface tension difference was observed and explained. The re-emergence of partial coalescence under large surface tension differences is caused by the remarkable lifting motion of the Marangoni flow, which significantly retards the vertical collapse. Two different modes of partial coalescence were identified by the simulation, namely peak injection occurs at lower Ohnesorge numbers and bottom pinch-off at higher Ohnesorge numbers. By comparing the characteristic timescales of the upward Marangoni flow with that of the downward flow driven by capillary pressure, a criterion for the transition from partial to total coalescence was derived based on scaling analysis and numerically validated.

In this paper we study the boundary-layer separation produced in a high-speed subsonic boundary layer by a small wall roughness. Specifically, we present a direct numerical simulation (DNS) of a two-dimensional boundary-layer flow over a flat plate encountering a three-dimensional Gaussian-shaped hump. This work was motivated by the lack of DNS data of boundary-layer flows past roughness elements in a similar regime which is typical of civil aviation. The Mach and Reynolds numbers are chosen to be relevant for aeronautical applications when considering small imperfections at the leading edge of wings. We analyze different heights of the hump: The smaller heights result in a weakly nonlinear regime, while the larger result in a fully nonlinear regime with an increasing laminar separation bubble arising downstream of the roughness element and the formation of a pair of streamwise counterrotating vortices which appear to support themselves.

Nectar-drinking bats and honeybees have tongues covered with hairlike structures, enhancing their ability to take up viscous nectar by dipping. Using a combination of model experiments and theory, we explore the physical mechanisms that govern viscous entrainment in a hairy texture. Hairy surfaces are fabricated using laser cut molds and casting samples with polydimethylsiloxane (PDMS) elastomer. We model the liquid trapped within the texture using a Darcy-Brinkmann-like approach and derive the drainage flow solution. The amount of fluid that is entrained is dependent on the viscosity of the fluid, the density of the hairs, and the withdrawal speed. Both experiments and theory reveal an optimal hair density to maximize fluid uptake.

Flows involving solid particulates have been widely studied in recent years, but their dynamics are still a complex issue to model because they strongly depend on the interaction with the boundary conditions. We report on laboratory investigations regarding homogeneous and steady flows of identical particles over a loose bed in a rectangular channel. Accurate measurements were carried out through imaging techniques to estimate profiles of the mean velocity, solid concentration, and granular temperature for a large set of flow rates and widths. Vertical and transversal structures observed in the flow change as interparticle interactions become more collisional, and they depend on the bottom over which the flow develops. The lateral confinement has a remarkable effect on the flow, especially for narrow channels compared with the grain size, and a hydraulic analogy is able to show how the walls influence the mechanisms of friction and energy dissipation.

The role of medium viscosity on a non-deformable rolling body has long been understood while its deformable counterpart still awaits clarification. In this article, we present a scaling analysis with experimental evidences to demonstrate that in creeping flow, medium viscosity significantly alters how the descent speed of a drop responds to an increase in drop size. While descending down an incline in a viscous medium, a rolling drop may travel with either increasing or decreasing velocities as its size increases. The boundary between these two motion behaviors can be maneuvered by altering the viscosity of the surrounding medium.

In many applications, finite-sized particles are immersed in a turbulent boundary layer (TBL) and it is of interest to study wall effects on the instantaneous shedding of turbulence structures and associated mean velocity and Reynolds stress distributions. Here, 3D flow field dynamics in the wake of a prototypical, small sphere ($D^{+}=50$, $692<{\mathrm{Re}}_D<959$) placed in the TBL's outer, logarithmic, and buffer layer, were measured using time-resolved tomo-PIV. Increasing wall proximity increasingly tilted the mean recirculating wake away from the wall implying a negative lift force. Mean velocity deficit recovery scaled with the mean wake length with minor effects of wall proximity. Farthest from the wall, streamwise Reynolds normal stresses encircled the mean wake as an axisymmetric tubular “shell,” while transverse and wall-normal stresses extended off its tip as axisymmetric tapered cones. Wall proximity removed axisymmetry and attenuated values near the wall. Reynolds shear stresses were distributed as antisymmetric lobes extending off the mean wake displaying increasing values with reducing sphere-wall gap. Instantaneous snapshots revealed a wake densely populated by “archlike” vortices with shedding frequencies lower than for a sphere in uniform flow except in the buffer layer. Tilting of the wake away from the wall resulted from self-induced motion of shed hairpinlike vortices whose symmetry plane was increasingly wall-normal oriented with reduced sphere-wall gap.