We report an experimental study on the statistical properties of the thermal plumes in turbulent thermal convection. A method has been proposed to extract the basic characteristics of thermal plumes from temporal temperature measurement inside the convection cell. It has been found that both plume amplitude $A$ and cap width $w$, in a time domain, are approximately in the log-normal distribution. In particular, the normalized most probable front width is found to be a characteristic scale of thermal plumes, which is much larger than the thermal boundary layer thickness. Over a wide range of the Rayleigh number, the statistical characterizations of the thermal fluctuations of plumes, and the turbulent background, the plume front width and plume spacing have been discussed and compared with the theoretical predictions and morphological observations. For the most part good agreements have been found with the direct observations.

We study the fundamental physics of cascades and spectra in two-dimensional (2D) Cahn-Hilliard-Navier-Stokes (CHNS) turbulence, and compare and contrast this system with 2D magnetohydrodynamic (MHD) turbulence. The important similarities include basic equations, ideal quadratic invariants, cascades, and the role of linear elastic waves. Surface tension induces elasticity, and the balance between surface tension energy and turbulent kinetic energy determines a length scale (Hinze scale) of the system. The Hinze scale may be thought of as the scale of emergent critical balance between fluid straining and elastic restoring forces. The scales between the Hinze scale and dissipation scale constitute the elastic range of the 2D CHNS system. By direct numerical simulation, we find that in the elastic range, the mean square concentration spectrum $H_k^{\psi }$ of the 2D CHNS system exhibits the same power law $\left(-7/3\right)$ as the mean square magnetic potential spectrum $H_k^A$ in the inverse cascade regime of 2D MHD. This power law is consistent with an inverse cascade of $H^{\psi }$, which is observed. The kinetic energy spectrum of the 2D CHNS system is $E_k^K\sim k^{-3}$ if forced at large scale, suggestive of the direct enstrophy cascade power law of 2D Navier-Stokes turbulence. The difference from the energy spectra of 2D MHD turbulence implies that the back reaction of the concentration field to fluid motion is limited. We suggest this is because the surface tension back reaction is significant only in the interfacial regions. The interfacial regions fill only a small portion of the 2D CHNS system, and their interface packing fraction is much smaller than that for 2D MHD.

Swimming cells and microorganisms are a critical component of many biological processes. In order to better interpret experimental studies of low Reynolds number swimming, we combine experimental and numerical methods to perform an analysis of the flow field around the swimming nematode Caenorhabditis elegans. We first use image processing and particle tracking velocimetry to extract the body shape, kinematics, and flow fields around the nematode. We then construct a three-dimensional model using the experimental swimming kinematics and employ a boundary element method to simulate flow fields, obtaining very good quantitative agreement with experiment. We use this numerical model to show that calculation of flow shear rates using purely planar data results in significant underestimates of the true three-dimensional value. Applying symmetry arguments, validated against numerics, we demonstrate that the out-of-plane contribution can be accounted for via incompressibility and therefore simply calculated from particle tracking velocimetry. Our results show how fundamental fluid mechanics considerations may be used to improve the accuracy of measurements in biofluiddynamics.

It has been observed that the amount of effective slip for transverse flow over a bubble mattress is maximum for bubbles that protrude somewhat in the channel flow. In this paper we provide an explanation for this characteristic feature by analyzing the spatial distribution of viscous dissipation for bubbles of varying protrusion angles. Bubbles protruding in the channel act as obstacles and reduce the effective channel height, thereby increasing the viscous dissipation in the bulk flow. At small scales, however, our numerical analysis reveals that increasing the bubble protrusion angle reduces the dissipation near the contact points of the no-slip channel wall and the no-shear bubble surface. We obtain an analytical expression to quantify this effect based on classical corner flow solutions. The two antagonistic effects, decreased dissipation near the bubble corners and increased dissipation on larger scale, explain why the effective slip length is maximum for a bubble mattress that is slightly bumpy.

A series of direct numerical simulations in large computational domains has been performed in order to probe the spatial feature robustness of the Taylor rolls in turbulent Taylor-Couette flow. The latter is the flow between two coaxial independently rotating cylinders of radius $r_i$ and $r_o$, respectively. Large axial aspect ratios $\mathrm{\Gamma }=7–8$ [with $\mathrm{\Gamma }=L/(r_o-r_i)$, and $L$ the axial length of the domain] and a simulation with $\mathrm{\Gamma }=14$ were used in order to allow the system to select the most unstable wave number and to possibly develop multiple states. The radius ratio was taken as $\eta =r_i/r_o=0.909$, the inner cylinder Reynolds number was fixed to ${\text{Re}}_i=3.4\times {10}^4$, and the outer cylinder was kept stationary, resulting in a frictional Reynolds number of ${\text{Re}}_{\tau }\approx 500$, except for the $\mathrm{\Gamma }=14$ simulation where ${\text{Re}}_i=1.5\times {10}^4$ and ${\text{Re}}_{\tau }\approx 240$. The large-scale rolls were found to remain axially pinned for all simulations. Depending on the initial conditions, stable solutions with different number of rolls $n_r$ and roll wavelength ${\lambda }_z$ were found for $\mathrm{\Gamma }=7$. The effect of ${\lambda }_z$ and $n_r$ on the statistics was quantified. The torque and mean flow statistics were found to be independent of both ${\lambda }_z$ and $n_r$, while the velocity fluctuations and energy spectra showed some box-size dependence. Finally, the axial velocity spectra were found to have a very sharp dropoff for wavelengths larger than ${\lambda }_z$, while for the small wavelengths they collapse.

We derive a simple model, valid within the Boussinesq approximation, for the dynamics of small buoyant particles in stratified turbulence, in the presence of a mean linear density profile. By means of extensive direct numerical simulations, we investigate the statistical distribution of particles as a function of the two dimensionless parameters of the problem. We find that vertical confinement of particles is mainly ruled by the degree of stratification, with a weak dependence on the particle properties. In contrast, small-scale fractal clustering is found to depend on the particles relaxation time and is only slightly dependent on the flow stratification. The implications of our findings for the formation of thin phytoplankton layers are discussed.

We investigate the flow resistance caused by the propagation of a liquid plug in a liquid-lined tube and propose a simple semiempirical formula for the flow resistance as a function of the plug length, the capillary number, and the precursor film thickness. These formulas are based on computational investigations of three key contributors to the plug resistance: the front meniscus, the plug core, and the rear meniscus. We show that the nondimensional flow resistance in the front meniscus varies as a function of the capillary number and the precursor film thickness. For a fixed capillary number, the flow resistance increases with decreasing precursor film thickness. The flow in the core region is modeled as Poiseuille flow and the flow resistance is a linear function of the plug length. For the rear meniscus, the flow resistance increases monotonically with decreasing capillary number. We investigate the maximum mechanical stress behavior at the wall, such as the wall pressure gradient, the wall shear stress, and the wall shear stress gradient, and propose empirical formulas for the maximum stresses in each region. These wall mechanical stresses vary as a function of the capillary number: For semi-infinite fingers of air propagating through pulmonary airways, the epithelial cell damage correlates with the pressure gradient. However, for shorter plugs the front meniscus may provide substantial mechanical stresses that could modulate this behavior and provide a major cause of cell injury when liquid plugs propagate in pulmonary airways. Finally, we propose that the reduced-dimension models developed herein may be of importance for the creation of large-scale models of interfacial flows in pulmonary networks, where full computational fluid dynamics calculations are untenable.

A series of direct numerical simulations of spanwise-rotating turbulent plane Couette flows at a Reynolds number of 1300 with rotation numbers $\text{Ro}$ between 0 and 0.9 is carried out to investigate the effects of anticyclonic rotation on turbulent statistics and flow structures. Several typical turbulent statistics are presented, including the mean shear rate at the centerline, the wall-friction Reynolds number, and volume-averaged kinetic energies with respect to the secondary flow field, turbulent field, and total fluctuation field. Our results show that the rotation changes these quantities in different manners. Volume-averaged balance equations for kinetic energy are analyzed and it turns out that the interaction term acts as a kinetic energy bridge that transfers energy from the secondary flow to the turbulent fluctuations. Several typical flow regimes are identified based on the correlation functions across the whole channel and flow visualizations. The two-dimensional roll cells are observed at weak rotation $\text{Ro}=0.01$, where alternant clustering of vortices appears. Three-dimensional roll cells emerge around $\text{Ro}\approx 0.02$, where the clustering of vortices shows the meandering and bifurcating behavior. For moderate rotation $0.07\lesssim \text{Ro}\lesssim 0.36$, well-organized structures are observed, where the herringbonelike vortices are clustered between streaks from the top view of three-dimensional flow visualization and form annuluses. More importantly, the vortices are rather confined to one side of the walls when $\text{Ro}\le 0.02$ and are inclined from the bottom to upper walls when $\text{Ro}\ge 0.07$.

We study the stability of density stratified flow between corotating vertical cylinders with rotation rates ${\mathrm{\Omega }}_o<{\mathrm{\Omega }}_i$ and radius ratio $r_i/r_o=0.877$, where subscripts $o$ and $i$ refer to the outer and inner cylinders. Just as in stellar and planetary accretion disks, the flow has rotation, anticyclonic shear, and a stabilizing density gradient parallel to the rotation axis. The primary instability of the laminar state leads not to axisymmetric Taylor vortex flow but to a nonaxisymmetric stratorotational instability (SRI). The present work extends the range of Reynolds numbers and buoyancy frequencies $[N=\sqrt{(-g/\rho )(\partial \rho /\partial z)}]$ examined in previous experiments. We present the first experimental results for the axial wavelength $\lambda$ of the instability as a function of the internal Froude number, $\text{Fr}={\mathrm{\Omega }}_i/N$; $\lambda$ increases by nearly an order of magnitude over the range of $\text{Fr}$ examined. For small outer cylinder Reynolds number, the SRI occurs for inner inner Reynolds number larger than for the axisymmetric Taylor vortex flow (i.e., the SRI is more stable). For somewhat larger outer Reynolds numbers the SRI occurs for smaller inner Reynolds numbers than Taylor vortex flow and even below the Rayleigh stability line for an inviscid fluid. Shalybkov and Rüdiger [Astron. Astrophys. 438, 411 (2005)] proposed that the laminar state of a stably stratified rotating shear flow should be stable for ${\mathrm{\Omega }}_o/{\mathrm{\Omega }}_i>r_i/r_o$, but we find that this stability criterion is violated for $N$ sufficiently large. At large Reynolds number the primary instability is not the SRI but a previously unreported nonperiodic state that mixes the fluid.

The Rayleigh-Taylor instability (RTI) is investigated using the direct simulation Monte Carlo (DSMC) method of molecular gas dynamics. Here, fully resolved two-dimensional DSMC RTI simulations are performed to quantify the growth of flat and single-mode perturbed interfaces between two atmospheric-pressure monatomic gases as a function of the Atwood number and the gravitational acceleration. The DSMC simulations reproduce many qualitative features of the growth of the mixing layer and are in reasonable quantitative agreement with theoretical and empirical models in the linear, nonlinear, and self-similar regimes. In some of the simulations at late times, the instability enters the self-similar regime, in agreement with experimental observations. For the conditions simulated, diffusion can influence the initial instability growth significantly.

Linear control applied to fluid systems near an equilibrium point has important applications for many flows of industrial or fundamental interest. In this article we give an exposition of tools and approaches for the design of control strategies for globally stable or unstable flows. For unstable oscillator flows a feedback configuration and a model-based approach is proposed, while for stable noise-amplifier flows a feedforward setup and an approach based on system identification is advocated. Model reduction and robustness issues are addressed for the oscillator case; statistical learning techniques are emphasized for the amplifier case. Effective suppression of global and convective instabilities could be demonstrated for either case, even though the system-identification approach results in a superior robustness to off-design conditions.

We investigate shear-induced clustering and its impact on fluid rheology in polymer-colloid mixtures at moderate colloid volume fraction. By employing a thermoresponsive system that forms associative polymer-colloid networks, we present experiments of rheology and flow-induced microstructure on colloid-polymer mixtures in which the relative magnitudes of the time scales associated with relaxation of viscoelasticity and suspension microstructure are widely and controllably varied. In doing so, we explore several limits of relative magnitude of the relevant dimensionless shear rates, the Weissenberg number Wi and the Péclet number Pe. In all of these limits, we find that the fluid exhibits two distinct regimes of shear thinning at relatively low and high shear rates, in which the rheology collapses by scaling with Wi and Pe, respectively. Using three-dimensionally-resolved flow small-angle neutron scattering measurements, we observe clustering of the suspension above a critical shear rate corresponding to $\mathrm{Pe}\sim 0.1$ over a wide range of fluid conditions, having anisotropy with projected orientation along both the vorticity and compressional axes of shear. The degree of anisotropy is shown to scale with Pe. From this we formulate an empirical model for the shear stress and viscosity, in which the viscoelastic network stress is augmented by an asymptotic shear thickening contribution due to hydrodynamic clustering. Overall, our results elucidate the significant role of hydrodynamic interactions in contributing to shear-induced clustering of Brownian suspensions in viscoelastic liquids.

Plateau borders (PBs) are liquid microchannels located at the contact between three bubbles in liquid foams. They are stable, deformable, and can be thought of as quasi-one-dimensional model systems to study surface waves in fluid dynamics. We show that the burst of a bubble trapped in a PB produces local constrictions which travel along the liquid channel at constant velocity, without significant change in shape. These patterns are reminiscent of the depression solitary waves encountered in nonlinear systems. By coupling flow inertia to capillary stresses, we derive a simple model that admits solitonic solutions, which we characterized numerically and analytically in the limit of small deformation. These solutions capture most of the features observed experimentally.

Minimum-dissipation models are a simple alternative to the Smagorinsky-type approaches to parametrize the subfilter turbulent fluxes in large-eddy simulation. A recently derived model of this type for subfilter stress tensor is the anisotropic minimum-dissipation (AMD) model [Rozema et al., Phys. Fluids 27, 085107 (2015)], which has many desirable properties. It is more cost effective than the dynamic Smagorinsky model, it appropriately switches off in laminar and transitional flows, and it is consistent with the exact subfilter stress tensor on both isotropic and anisotropic grids. In this study, an extension of this approach to modeling the subfilter scalar flux is proposed. The performance of the AMD model is tested in the simulation of a high-Reynolds-number rough-wall boundary-layer flow with a constant and uniform surface scalar flux. The simulation results obtained from the AMD model show good agreement with well-established empirical correlations and theoretical predictions of the resolved flow statistics. In particular, the AMD model is capable of accurately predicting the expected surface-layer similarity profiles and power spectra for both velocity and scalar concentration.

We study the intrinsic dynamics of cusps, or indentations, moving along a liquid sheet border, and characterize their ensemble statistics. Gordillo and collaborators [J. Fluid Mech. 754, R1 (2014)] have shown that the symmetrical stationary cusp is the only structure accommodating for both mass and momentum conservation at a steadily receding liquid sheet rim. Cusps are also known to typically move along a sheet border, to present an asymmetry, and to be distributed in size around a mean. We show here why a heterogeneous assembly of cusps traveling along the sheet rim occurs spontaneously, why big and small cusps coexist at the same time, and, more precisely, we establish a specific link between the microscopic dynamics directing their motion, and the ensemble averaged distribution of their sizes.

The central aim of the paper is to carry out a theoretical and numerical study of active wall transpiration control of streaks generated within an incompressible boundary layer by free-stream turbulence. The disturbance flow model is based on the linearized unsteady boundary-region (LUBR) equations, studied by Leib, Wundrow, and Goldstein [J. Fluid Mech. 380, 169 (1999)], which are the rigorous asymptotic limit of the Navier-Stokes equations for low-frequency and long-streamwise wavelength. The mathematical formulation of the problem directly incorporates the random forcing into the equations in a consistent way. Due to linearity, this forcing is factored out and appears as a multiplicative factor. It is shown that the cost function (integral of kinetic energy in the domain) is properly defined as the expectation of a random quadratic function only after integration in wave number space. This operation naturally introduces the free-stream turbulence spectral tensor into the cost function. The controller gains for each wave number are independent of the spectral tensor and, in that sense, universal. Asymptotic matching of the LUBR equations with the free-stream conditions results in an additional forcing term in the state-space system whose presence necessitates the reformulation of the control problem and the rederivation of its solution. It is proved that the solution can be obtained analytically using an extension of the sweep method used in control theory to obtain the standard Riccati equation. The control signal consists of two components, a feedback part and a feed-forward part (that depends explicitly on the forcing term). Explicit recursive equations that provide these two components are derived. It is shown that the feed-forward part makes a negligible contribution to the control signal. We also derive an explicit expression that a priori (i.e., before solving the control problem) leads to the minimum of the objective cost function (i.e., the fundamental performance limit), based only on the system matrices and the initial and free-stream boundary conditions. The adjoint equations admit a self-similar solution for large spanwise wave numbers with a scaling which is different from that of the LUBR equations. The controlled flow field also has a self-similar solution if the weighting matrices of the objective function are chosen appropriately. The code developed to implement this algorithm is efficient and has modest memory requirements. Computations show the significant reduction of energy for each wave number. The control of the full spectrum streaks, for conditions corresponding to a realistic experimental case, shows that the root-mean-square of the streamwise velocity is strongly suppressed in the whole domain and for all the frequency ranges examined.

We present a molecular-level investigation of nitrogen dissociation at high temperature. The computational technique, called direct molecular simulation (DMS), solely relies on an ab initio potential energy surface and both ${\mathrm{N}}_2+{\mathrm{N}}_2$ and $\mathrm{N}+{\mathrm{N}}_2$ processes are simulated as they concurrently take place in an evolving nonequilibrium gas system. Quasiclassical trajectory calculations (QCT) reveal that dissociation rate coefficients calculated at thermal equilibrium, i.e., assuming Boltzmann energy distributions, are approximately equal (within less than 15%) for both ${\mathrm{N}}_2+{\mathrm{N}}_2$ and $\mathrm{N}+{\mathrm{N}}_2$ collisions for the range of temperatures considered. The DMS (nonequilibrium) results indicate, however, that the presence of atomic nitrogen significantly affects the dissociation rate of molecular nitrogen, but indirectly. In fact, the presence of atomic nitrogen causes an important reduction of the vibrational relaxation time of ${\mathrm{N}}_2$, by almost one order of magnitude. This, in turn, speeds up the replenishment of high-$v$ states that are otherwise significantly depleted if only ${\mathrm{N}}_2+{\mathrm{N}}_2$ collisions are considered. Because of the strong favoring of dissociation from high-$v$ states, this results in dissociation rates that are 2–3 times higher when significant atomic nitrogen is present compared to systems composed of mainly diatomic nitrogen, such as during the initial onset of dissociation. Specifically, we find that exchange events occur frequently during $\mathrm{N}+{\mathrm{N}}_2$ collisions and that such exchange collisions constitute an effective mechanism of scrambling the internal energy states, resulting in multiquantum jumps in vibrational energy levels that effectively promote energy transfers. The resulting vibrational relaxation time constant we calculate for $\mathrm{N}+{\mathrm{N}}_2$ collisions is significantly lower than the widely used Millikan-White model. Significant discrepancies are found between predictions of the Park two-temperature model (using the Millikan-White vibrational relaxation model) and the DMS results for dissociating nitrogen systems involving both atomic and molecular nitrogen. Such direct comparisons also illustrate how the DMS method is able to reveal all relevant nonequilibrium physics without the need to compute large numbers of state-transition probabilities. In this manner, DMS presents an accurate and tractable approach to construct models for direct-simulation Monte Carlo and computational fluid dynamics simulations from first principles.

We study the rheology of a sheared two-dimensional (2D) suspension of non-Brownian disks in the presence of walls. Although it is of course possible today with modern computers and powerful algorithms to perform direct numerical simulations that fully account for multiparticle 3D interactions in the presence of walls, the analysis of the simple case of a 2D suspension provides valuable insights and helps in the understanding of 3D results. Due to the direct visualization of the whole 2D flow (the shear plane), we are able to give a clear interpretation of the full hydrodynamics of semidilute confined suspensions. For instance, we examine the role of disk-wall and disk-disk interactions to determine the dissipation of confined sheared suspensions whose effective viscosity depends on the area fraction $\varphi$ of the disks as ${\eta }_{\text{eff}}={\eta }_0[1+\left[\eta \right]\varphi +\beta {\varphi }^2+O\left({\varphi }^3\right)]$. We provide numerical estimates of $\left[\eta \right]$ and $\beta$ for a wide range of confinements. As a benchmark for our simulations, we compare the numerical results obtained for $\left[\eta \right]$ and $\beta$ for very weak confinements with analytical values ${\left[\eta \right]}_{\infty }$ and ${\beta }_{\infty }$ obtained for an infinite fluid. If the value ${\left[\eta \right]}_{\infty }=2$ is well known in the literature, much less is published on the value of $\beta$. Here we analytically calculate with very high precision ${\beta }_{\infty }=3.6$. We also reexamine the 3D case in the light of our 2D results.

We report the results of an experimental study of the fully developed flow of a viscoelastic, shear-thinning aqueous polymer solution through two large-scale parallel shear flows: a pipe and channel-flow facility. We show that, at low flow rates, the velocity profile in both geometries is steady and is in good agreement with expected analytical solutions. However, in both geometries at higher flow rates the flow becomes weakly time dependent and the mean velocity profile is radically altered, exhibiting an overshoot near the duct center, a reduced shear rate at the wall, and an inflection point (i.e., a nonmonotonic gradient). Although inertia is not completely negligible at instability onset, we speculate that the origin of these unstable flows lies in the combination of elasticity and strong shear thinning.

The concept of electromagnetic energy enhancement and nanofocusing phenomena near the tip of a metaconical conducting tip by means of a surface plasmon-polaritons mechanism is discussed theoretically. In particular, we consider conical metallic structures with small apex angles and derive the corresponding dispersion relation under optimal (maximal field enhancement) operating conditions. It is demonstrated analytically that the aforementioned conditions can induce large dielectrophoretic forces near the conical tip, which can be harnessed for sorting and controlling nanoparticles in a manner similar to optical tweezers. Similarly, by considering Joule heating effects in the metal and heat conduction in the surrounding solute, it is shown that a considerable (dc) flow convection and mixing can be generated in the aqueous phase near the tip by such ac incited optical means (including common low-input lasers operating in the visible and near-infrared spectrum ranges). Analytic near-field expressions are also obtained for the opto-electro-thermo-induced flow and vorticity distributions in the electrolyte exhibiting a singular behavior near the rounded tip. Using a coax conical metastructure composed of two noble metals, surface-plasmon field enhancement is a technique for the optimal manipulation of dielectric and polarizable nanoparticles as well as for inducing indirect mixing in the liquid around the tip by generating microvortices.