The dynamics of decaying, strictly axisymmetric, incompressible turbulence is investigated using direct numerical simulations. It is found that the angular momentum is a robust invariant of the system. It is further shown that long-lived coherent structures are generated by the flow. These structures can be associated with stationary solutions of the Euler equations. The structures obey relations in agreement with predictions from selective decay principles, compatible with the decay laws of the system. Two different types of decay scenarios are highlighted. The first case results in a quasi-two-dimensional flow with a dynamical behavior in the poloidal plane similar to freely decaying two-dimensional turbulence. In a second regime, the long-time dynamics is dominated by a single three-dimensional mode.

Two-dimensional natural doubly diffusive convection in a vertical slot driven by an imposed temperature difference in the horizontal is studied using numerical continuation and direct numerical simulation. Two cases are considered and compared. In the first a concentration difference that balances thermal buoyancy is imposed in the horizontal and stationary localized structures are found to be organized in a standard snakes-and-ladders bifurcation diagram. Disconnected branches of traveling pulses ${\mathrm{TP}}_n$ consisting of $n,n=1,2,\cdots$, corotating cells are identified and shown to accumulate on a tertiary branch of traveling waves. With Robin or mixed concentration boundary conditions on one wall all localized states travel and the hitherto stationary localized states may connect up with the traveling pulses. The stability of the ${\mathrm{TP}}_n$ states is determined and unstable ${\mathrm{TP}}_n$ shown to evolve into spatio-temporal chaos. The calculations are done with no-slip boundary conditions in the horizontal and periodic boundary conditions in the vertical.

The flow of liquid films on rotating discrete objects having complicated cross sections is encountered in coating processes for a broad variety of products. To advance fundamental understanding of this problem, we study viscous free-surface flows on rotating elliptical cylinders by solving the governing equations in a rotating reference frame using the Galerkin finite-element method. Results of our simulations agree well with Hunt's maximum-load condition [Hunt, Numer. Methods Partial Differ. Eqs. 24, 1094 (2008)], which was obtained in the absence of surface tension and inertia. The simulations are also used to track the transient behavior of the free surface. For $O\left(1\right)$ cylinder aspect ratios, cylinder rotation results in a droplike liquid bulge hanging on the upward-moving side of the cylinder. This bulge shrinks in size due to surface tension provided that the liquid load is smaller than a critical value, leaving a relatively smooth coating on the cylinder. A decrease in cylinder aspect ratio leads to larger gradients in film thickness, but enhances the rate of bulge shrinkage and thus shortens the time required to obtain a smooth coating. Moreover, with a suitably chosen time-dependent rotation rate, more liquid can be supported by the cylinder relative to the constant-rotation-rate case. For cylinders with even smaller aspect ratios, film rupture and liquid shedding may occur over the cylinder tips, so simultaneous drying and rotation along with the introduction of Marangoni stresses will likely be especially important for obtaining a smooth coating.

We investigate the dispersion of finite lengths of concentrated suspended particles, or suspension plugs, in a microcapillary as they are sheared in an oscillating pressure-driven flow. In the experiments, plugs of neutrally buoyant, noncolloidal particles (90-$\mu \mathrm{m}$ mean diameter) suspended in viscous fluid at low and high concentrations are observed for various values of applied strain of this cyclic shearing flow. No significant increase in the overall plug length is seen near the centerline after numerous cycles. However, significant streamwise particle migration was observed near the walls of the capillary, becoming more pronounced with increasing strain amplitude. Related numerical simulations for a suspension plug sheared in a planar channel show similar results and elucidate the dynamics for this strongly inhomogeneous flow and the anomalous particle fluxes that develop.

This research involves an experimental study of steady streaming of a fluid excited in an oscillating cylindrical container with an elastically deformable boundary. The influence of the vibration parameters and fluid properties on the structure and intensity of flows in the container is studied. The dependence of the structure and intensity of the flows on the governing parameters, the Froude number, and the dimensionless frequency, which determines the ratio between the cavity size and the Stokes boundary layer, is investigated. It is shown that steady streaming is generated within a region of high dimensionless frequencies, which does not depend on frequency and is fully determined by the dimensionless amplitude. It is discovered that steady flows change qualitatively in a region of intermediate and low frequencies where the thickness of the dynamic boundary layers is comparable to the cavity size. In a region of low frequencies, the direction of steady flow is opposite to that in a region of high frequencies and the flow intensity decreases with frequency. The discovered dependencies have a similar nature and shed light on flows in oscillating containers, including droplets with a saturated interface.

The analytical study of long-wave scattering in a canal with a rapidly varying cross-section is presented. It is assumed that waves propagate on a stationary current with a given flow rate. Due to the fixed flow rate, the current speed is different in the different sections of the canal, upstream and downstream. The scattering coefficients (the transmission and reflection coefficients) are calculated for all possible orientations of incident wave with respect to the background current (downstream and upstream propagation) and for all possible regimes of current (subcritical, transcritical, and supercritical). It is shown that in some cases negative energy waves can appear in the process of waves scattering. The conditions are found when the over-reflection and over-transmission phenomena occur. In particular, it is shown that a spontaneous wave generation can arise in a transcritical accelerating flow, when the background current enhances due to the canal narrowing. This resembles a spontaneous wave generation on the horizon of an evaporating black hole due to the Hawking effect.

This Rapid Communication investigates boundary layer flows with a pressure gradient using a similarity/integral analysis of the continuity equation and momentum equation in the streamwise direction. The analysis yields useful analytical relations for $V_e$, the mean wall-normal velocity at the edge of the boundary layer, and for the skin friction coefficient $C_f$ in terms of the boundary layer parameters and in particular ${\beta }_{\text{RC}}$, the Rotta-Clauser pressure gradient parameter. The analytical results are compared with experimental and numerical data and are found to be valid. One of the main findings is that for large positive ${\beta }_{\text{RC}}$ (an important effect of an adverse pressure gradient), the friction coefficient is closely related to ${\beta }_{\text{RC}}$ as $C_f\propto 1/{\beta }_{\text{RC}}$, because $\delta /{\delta }_1,{\delta }_1/{\delta }_2=H$, and $d\delta /dx$ become approximately constant. Here, $\delta$ is the boundary layer thickness, ${\delta }_1$ is the displacement thickness, ${\delta }_2$ is the momentum thickness, and $H$ is the shape factor. Another finding is that the mean wall-normal velocity at the edge of the boundary layer is related to other flow variables as $U_e{V}_e/u_{\tau }^2=H+(1+\delta /{\delta }_1+H){\beta }_{\text{RC}}$, where $U_e$ is the streamwise velocity at the edge of the boundary layer. At zero pressure gradient, this relation reduces to $U_{\infty }{V}_{\infty }/u_{\tau }^2=H$, as recently derived by Wei and Klewicki [Phys. Rev. Fluids 1, 082401 (2016)].

We study the acoustic field of a circular cylinder immersed in a rarefied gas and subject to harmonic small-amplitude normal-to-wall displacement and heat-flux excitations. The problem is analyzed in the entire range of gas rarefaction rates and excitation frequencies, considering both single cylinder and coaxial cylinders setups. Numerical calculations are carried out via the direct simulation Monte Carlo method, applying a noniterative algorithm to impose the boundary heat-flux condition. Analytical predictions are obtained in the limits of ballistic- and continuum-flow conditions. Comparing with a reference inviscid continuum solution, the results illustrate the specific impacts of gas rarefaction and boundary curvature on the acoustic source efficiency. Inspecting the far-field properties of the generated disturbance, the continuum-limit solution exhibits an exponential decay of the signal with the distance from the source, reflecting thermoviscous effects, and accompanied by an inverse square-root decay, characteristic of the inviscid problem. Stronger attenuation is observed in the ballistic limit, where boundary curvature results in “geometric reduction” of the molecular layer affected by the source, and the signal vanishes at a distance of few acoustic wavelengths from the cylinder. The combined effects of mechanical and thermal excitations are studied to seek for optimal conditions to monitor the vibroacoustic signal. The impact of boundary curvature becomes significant in the ballistic-flow regime, where the optimal heat-flux amplitude required for sound reduction decreases with the distance from the source and is essentially a function of the acoustic-wavelength-scaled distance only.

This paper deals with buoyant convection generated by a horizontal gradient of temperature in an infinite fluid layer, which is known as Hadley circulation, and studies the effects induced by applying a rotation around the vertical axis. First, the basic flow profile with rotation is derived and the influence of the rotation is depicted: The original longitudinal velocity profile is decreased in intensity when rotation is applied and its structure is progressively changed, whereas a transverse velocity component is created, which increases with the rotation intensity, overcomes the longitudinal velocity, and eventually decreases. Different asymptotic behaviors for these profiles have also been highlighted. The stability of these flows is then studied. The effects of the Prandtl number, the Taylor number, and the thermal boundary conditions are highlighted for the three types of instability occurring in such a situation (shear, oscillatory, and Rayleigh instabilities). It is observed that they are all stabilized by the rotation and that the increase of the critical thresholds is accompanied by a spinning of the wave vector corresponding to a progressive change of the orientation of the marginal perturbation rolls. Energy budgets are finally used to analyze the instability mechanisms.

Flow resistance of liquids flowing through microchannels can be reduced by replacing flat, no-slip boundaries with boundaries adjacent to longitudinal grooves containing an inert gas, resulting in apparent slip. With applications of such textured microchannels in areas such as microfluidic systems and direct liquid cooling of microelectronics, there is a need for predictive mathematical models that can be used for design and optimization. In this work, we describe a model that incorporates the physical effects of gas viscosity (interfacial shear), meniscus protrusion (into the grooves), and channel aspect ratio and show how to generate accurate solutions for the laminar flow field using Chebyshev collocation and domain decomposition numerical methods. While the coupling of these effects are often omitted from other models, we show that it plays a significant role in the behavior of such flows. We find that, for example, the presence of gas viscosity may cause meniscus protrusion to have a more negative impact on the flow rate than previously appreciated. Indeed, we show that there are channel geometries for which meniscus protrusion increases the flow rate in the absence of gas viscosity and decreases it in the presence of gas viscosity. In this work, we choose a particular definition of channel height: the distance from the base of one groove to the base of the opposite groove. Practically, such channels are used in constrained geometries and therefore are of prescribed heights consistent with this definition. This choice allows us to easily make meaningful comparisons between textured channels and no-slip channels occupying the same space.

Metrics used to assess the quality of large-eddy simulations commonly rely on a statistical assessment of the solution. While these metrics are valuable, a dynamic measure is desirable to further characterize the ability of a numerical simulation for capturing dynamic processes inherent in turbulent flows. To address this issue, a dynamic metric based on the Lyapunov exponent is proposed which assesses the growth rate of the solution separation. This metric is applied to two turbulent flow configurations: forced homogeneous isotropic turbulence and a turbulent jet diffusion flame. First, it is shown that, despite the direct numerical simulation (DNS) and large-eddy simulation (LES) being high-dimensional dynamical systems with $O\left({10}^7\right)$ degrees of freedom, the separation growth rate qualitatively behaves like a lower-dimensional dynamical system, in which the dimension of the Lyapunov system is substantially smaller than the discretized dynamical system. Second, a grid refinement analysis of each configuration demonstrates that as the LES filter width approaches the smallest scales of the system the Lyapunov exponent asymptotically approaches a plateau. Third, a small perturbation is superimposed onto the initial conditions of each configuration, and the Lyapunov exponent is used to estimate the time required for divergence, thereby providing a direct assessment of the predictability time of simulations. By comparing inert and reacting flows, it is shown that combustion increases the predictability of the turbulent simulation as a result of the dilatation and increased viscosity by heat release. The predictability time is found to scale with the integral time scale in both the reacting and inert jet flows. Fourth, an analysis of the local Lyapunov exponent is performed to demonstrate that this metric can also determine flow-dependent properties, such as regions that are sensitive to small perturbations or conditions of large turbulence within the flow field. Finally, it is demonstrated that the global Lyapunov exponent can be utilized as a metric to determine if the computational domain is large enough to adequately encompass the dynamic nature of the flow.

The mean-square pressure fluctuations ${\langle pp\rangle }^{+}$ in the inner and outer regions are correlated for various Reynolds numbers using published direct numerical simulation data. It is found that the overlap matching region has logarithmic behavior. The outer region overlap law is ${\langle pp\rangle }^{+}(y/h)=(1/\epsilon )ln(y/h)+D_o$. In the inner region, the correlation has two terms and is of the form $\mathcal{P}\left(y^{+}\right)\equiv {\langle pp\rangle }^{+}(y^{+},{\text{Re}}_{\tau })-{\langle pp\rangle }^{+}(0,{\text{Re}}_{\tau })$. The inner matching law is $\mathcal{P}\left(y^{+}\right)=(1/\epsilon )ln\left(y^{+}\right)+D_i$. In the inner region, $\mathcal{P}\left(y^{+}\right)$ is the same for channel flow and boundary layers; however, in the outer region, the ${\langle pp\rangle }^{+}(y/h)$ for channel flow and boundary layers are quite different. A compatibility equation, obtained by equating the matching laws, is a relation for the wall pressure in terms of the matching constants ${\langle pp\rangle }^{+}\left(0\right)=(1/\epsilon )ln\left({\text{Re}}_{\tau }\right)+D_o-D_i$. Alternately, an expression becoming logarithmically infinite may be expressed as two finite terms with a mixed scaling ${\langle pp\rangle }^{\#}\left(0\right)\equiv \frac{\langle pp\rangle }{{\rho }^2{u}_{\tau }^3{U}_o}={\langle pp\rangle }^{+}\left(0\right)\frac{u_{\tau }}{U_o}=\alpha +\beta \frac{u_{\tau }}{U_o}\left({\text{Re}}_{\tau }\right)$. Channel flow has an extensive overlap region, while boundary layers have a very limited overlap region. The wall-pressure spectra $E_{{\langle pp\rangle }^{+}}\left(k_{x}h\right)$, as a function of the streamwise wave number $k_{x}h$, does not have a ${\left(k_{x}h\right)}^{-1}$ overlap region. Nevertheless, trends show that this behavior might occur at higher Reynolds numbers.

We analyze the temporal dynamics associated with axisymmetric coherent structures in a turbulent jet. It has long been established that turbulent jets comprise large-scale coherent structures, now more commonly referred to as “wave packets” [Jordan and Colonius, Annu. Rev. Fluid Mech. 45, 173 (2013)]. These structures exhibit a marked spatiotemporal organization, despite turbulence, and we aim to characterize their temporal dynamics by means of nonlinear statistical tools. The analysis is based on data presented Breakey et al., in Proceedings of the 19th AIAA/CEAS Aeroacoustics Conference, AIAA Paper 2013–2083 (AIAA, Reston, VA, 2013), where time series of the wave-packet signatures are extracted at different streamwise locations. The experiment runs at $\text{Ma}=0.6$ and $\text{Re}=5.7\times {10}^5$. A thorough analysis is performed. Statistical tools are used to estimate the embedding and correlation dimensions that characterize the dynamical system. Input-output transfer functions are designed as control-oriented models; and for this special case, consistent with other recent studies, we find that linear models can reproduce much of the convective input-ouput behavior. Finally, we show how surrogate models can partially reproduce the nonlinear dynamics.

We combine experiments, large-scale simulations, and continuum models to study the emergence of coherent structures in a suspension of magnetically driven microrollers sedimented near a floor. Collective hydrodynamic effects are predominant in this system, leading to strong density-velocity coupling. We characterize a uniform suspension and show that density waves propagate freely in all directions in a dispersive fashion. When sharp density gradients are introduced in the suspension, we observe the formation of a shock. Unlike Burgers' shocklike structures observed in other active and driven confined hydrodynamic systems, the shock front in our system has a well-defined finite width and moves rapidly compared to the mean suspension velocity. We introduce a continuum model demonstrating that the finite width of the front is due to far-field nonlocal hydrodynamic interactions and governed by a geometric parameter, the average particle height above the floor.

Instability waves traveling within subsonic turbulent jets have a modal linear growth until approximatively the end of the potential core. At these stations it is believed that nonlinear and/or nonmodal effects become important and a mismatch appears between experimental measurements and linear models. In this paper the response of the linearized operator to nonlinearities treated here as an external forcing is found to be consistent with a simplified model of the Orr mechanism, supporting the idea that a nonmodal growth of disturbances occurs in the downstream region of the jet in response to the modeled nonlinear forcing.

A liquid film wetting the interior of a long circular cylinder redistributes under the action of surface tension to form annular collars or occlusive plugs. These equilibrium structures are invariant under axial translation within a perfectly smooth uniform tube and therefore can be displaced axially by very weak external forcing. We consider how this degeneracy is disrupted when the tube wall is rough, and determine threshold conditions under which collars or plugs resist displacement under forcing. Wall roughness is modeled as a nonaxisymmetric Gaussian random field of prescribed correlation length and small variance, mimicking some of the geometric irregularities inherent in applications such as lung airways. The thin film coating this surface is modeled using lubrication theory. When the roughness is weak, we show how the locations of equilibrium collars and plugs can be identified in terms of the azimuthally averaged tube radius; we derive conditions specifying equilibrium collar locations under an externally imposed shear flow, and plug locations under an imposed pressure gradient. We use these results to determine the probability of external forcing being sufficient to displace a collar or plug from a rough-walled tube, when the tube roughness is defined only in statistical terms.

The filtered density function (FDF) closure is extended to a “self-contained” format to include the subgrid-scale (SGS) statistics of all of the hydro-thermo-chemical variables in turbulent flows. These are the thermodynamic pressure, the specific internal energy, the velocity vector, and the composition field. In this format, the model is comprehensive and facilitates large-eddy simulation (LES) of flows at both low and high compressibility levels. A transport equation is developed for the joint pressure-energy-velocity-composition filtered mass density function (PEVC-FMDF). In this equation, the effect of convection appears in closed form. The coupling of the hydrodynamics and thermochemistry is modeled via a set of stochastic differential equation for each of the transport variables. This yields a self-contained SGS closure. For demonstration, LES is conducted of a turbulent shear flow with transport of a passive scalar. The consistency of the PEVC-FMDF formulation is established, and its overall predictive capability is appraised via comparison with direct numerical simulation (DNS) data.

This study investigates the effect of a magnetohydrodynamic (MHD) shear flow on the growth and detachment of single sub-millimeter-sized hydrogen gas bubbles. These bubbles were electrolytically generated at a horizontal Pt microelectrode ($100\mu \mathrm{m}$ in diameter) in an acidic environment (1 M ${\mathrm{H}}_2{\mathrm{SO}}_4)$. The inherent electric field was superimposed by a homogeneous electrode-parallel magnetic field of up to 700 mT to generate Lorentz forces in the electrolyte, which drive the MHD flow. The growth and motion of the hydrogen bubble was analyzed by microscopic high-speed imaging and measurements of the electric current, while particle tracking velocimetry $\left(\mu \mathrm{PTV}\right)$ and particle image velocimetry $\left(\mu \mathrm{PIV}\right)$ were applied to measure the surrounding electrolyte flow. In addition, numerical flow simulations were performed based on the experimental conditions. The results show a significant reduction of the bubble growth time and detachment diameter with increasing magnetic induction, which is known to improve the efficiency of water electrolysis. In order to gain further insight into the bubble detachment mechanism, an analysis of the forces acting on the bubble was performed. The strong MHD-induced drag force causes the bubble to slowly slide away from the center of the microelectrode before its detachment. This motion increases the active electrode area and enhances the bubble growth rate. The results further indicate that at large current densities the coalescence of tiny bubbles formed at the foot of the main bubble might play an important role for the bubble detachment. Moreover, the occurrence of Marangoni stresses at the gas-liquid interface is discussed.

Motivated by the need for understanding the boiling processes in three-phase microscopic systems, the present work aims to uncover the physics of forced dewetting of a liquid film initially attached to a metal wire frame, which is heated with a rate up to $O\left({10}^8\right)\mathrm{K}{\mathrm{s}}^{-1}$ by discharging a capacitor impulsively. Depending on the corresponding heat flux $\le O\left({10}^{11}\right)\mathrm{J}{\mathrm{m}}^{-2}$, there are several key dewetting regimes—no detachment, nonuniform detachment, and uniform detachment of a film—differentiated by boiling transitions in the film Plateau borders. Transitions between these regimes prove to occur, for various wire diameters and frame sizes, around the same values of the capacitor energy per unit wire volume. Also, an intrinsic transverse instability manifesting itself in the formation of fingers along the detached liquid film rim is discovered and analyzed in detail.

In this work, we present observable consequences of a parity-violating odd-viscosity term in incompressible 2+1D hydrodynamics. For boundary conditions depending on the velocity field (flow) alone we show that (i) the fluid flow quantified by the velocity field is independent of odd viscosity, (ii) the force acting on a closed contour is independent of odd viscosity, and (iii) the odd-viscosity part of torque on a closed contour is proportional to the rate of change of area enclosed by the contour with the proportionality constant being twice the odd viscosity. The last statement allows us to define a measurement protocol of odd viscostance in analogy to Hall resistance measurements. We also consider no-stress boundary conditions that explicitly depend on odd viscosity. A classic hydrodynamics problem with no-stress boundary conditions is that of a bubble in a planar Stokes flow. We solve this problem exactly for shear and hyperbolic flows and show that the steady-state shape of the bubble in the shear flow depends explicitly on the value of odd viscosity.