Numerical simulations are carried out to discover the flow structure that plays an important role in the laminar-turbulent transition process of a boundary layer on a flat plate. The boundary layer is destabilized by ejecting a short-duration jet from a hole in the surface. When the jet velocity is set to 20% of the uniform-flow velocity, a laminar-turbulent transition takes place, whereas in the 18% case, the disturbances created by the jet decay downstream. It is found that in both cases, hairpin vortices are generated; however, these first-generation hairpins do not directly cause the transition. Only in the 20% case does a new hairpin vortex of a different shape with wider distance between the legs appear. The new hairpin grows with time and evokes the generation of vortical structures one after another around it, turning the flow turbulent. It is found that the difference between the two cases is whether or not one of the first-generation hairpin vortices gets connected with the nearby longitudinal vortices. Only when the connection is successful is the new hairpin vortex with wider distance between the legs created. For each of several cases tested with changing jet-ejecting conditions, no difference is found in the importance of the role of the hairpin structure. Therefore, we conclude that the hairpin vortex with widespread legs is a key structure in the transition to turbulence.

The wake behind a sphere, rotating about an axis aligned with the streamwise direction, has been experimentally investigated in a low-velocity water tunnel using laser-induced fluorescence visualizations and particle image velocimetry measurements. The measurements focused on the evolution of the flow regimes that appear depending on two control parameters: the Reynolds number Re and the dimensionless rotation or swirl rate $\mathrm{\Omega }$, which is the ratio of the maximum azimuthal velocity of the body to the free-stream velocity. In the present investigation, we cover the range of Re smaller than 400 and $\mathrm{\Omega }$ from 0 and 4. Different wakes regimes such as an axisymmetric flow, a low helical state, and a high helical mode are represented in the (Re, $\mathrm{\Omega }$) parameter plane.

We propose an estimation of the effective viscosity of a random mixture of Newtonian fluids that ignores capillary effects. The local viscosity of the mixture is assumed to be a random function of the position. Using perturbation expansions up to the second order, the resulting formula can be recast under the form of a simple power averaging mixing low. Numerical tests are used to assess the validity of the formula and the range of its applicability.

Spreading and decay rates of several synthetic jets are experimentally measured up to 70–100 diameters ($d$) away from the orifice. It is found that, consistent with previous studies, after $10d–15d$ from the nozzle a synthetic jet displays a self-similar velocity profile together with enhanced spreading and decay behaviors than a continuous jet. However, this enhancement does not persist throughout the downstream region, as the spreading and decay rates around $30d–50d$ away from the orifice decrease to asymptotic values that are comparable to continuous jets. This intermediate region with enhanced spreading and decay rates is dubbed the transitional region, while the region beyond $30d–50d$, where the spreading and decay rates approach the continuous jet values, is referred to as the actual far field of a synthetic jet. Physically, the enhanced spreading and decay rates of the transitional region are caused by an enhanced mode of mixing related to the forced instability of the pulsed large vortices, which eventually break down into smaller eddies in the fully turbulent far field.

We study suspensions of deformable (viscoelastic) spheres in a Newtonian solvent in plane Couette geometry, by means of direct numerical simulations. We find that in the limit of vanishing inertia, the effective viscosity $\mu$ of the suspension increases as the volume fraction occupied by the spheres $\mathrm{\Phi }$ increases and decreases as the elastic modulus of the spheres $G$ decreases; the function $\mu (\mathrm{\Phi },G)$ collapses to a universal function $\mu \left({\mathrm{\Phi }}_{\mathrm{e}}\right)$ with a reduced effective volume fraction ${\mathrm{\Phi }}_{\mathrm{e}}(\mathrm{\Phi },G)$. Remarkably, the function $\mu \left({\mathrm{\Phi }}_{\mathrm{e}}\right)$ is the well-known Eilers fit that describes the rheology of suspension of rigid spheres at all $\mathrm{\Phi }$. Our results suggest different ways to interpret the macrorheology of blood.

Secondary flow structures in a ${180}^{\circ }$ curved pipe model of an artery are studied using particle image velocimetry. Both steady and pulsatile inflow conditions are investigated. In planar curved pipes with steady flow, multiple (two, four, six) vortices are detected. For pulsatile flow, various pairs of vortices, i.e., Dean, deformed-Dean, Lyne-type, and split-Dean, are present in the cross section of the pipe at ${90}^{\circ }$ into the bend. The effects of nonplanar curvature (torsion) and vessel dilatation on these vortical structures are studied. Torsion distorts the symmetric secondary flows (which exist in planar curvatures) and can result in formation of more complex vortical structures. For example, the split-Dean and Lyne-type vortices with same rotation direction originating from opposite sides of the cross section tend to merge together in pulsatile flow. The vortical structures in elastic vessels with dilatation (0.61%–3.23%) are also investigated and the results are compared with rigid model results. It was found that the secondary flow structures in rigid and elastic models are similar, and hence the local compliance of the vessel does not affect the morphology of secondary flow structures.

We perform a combined experimental and numerical investigation into the static deformation of perforated elastic strips under uniform aerodynamic loading at high-Reynolds-number conditions. The static shape of the porous strips, clamped either horizontally or vertically, is quantified as they are deformed by wind loading, induced by a horizontal flow. The experimental profiles are compared to numerical simulations using a reduced model that takes into account the normal drag force on the deformed surface. For both configurations (vertical and horizontal clamping), we compute the drag coefficient of the strip, by fitting the experimental data to the model, and find that it decreases as a function of porosity. Surprisingly, we find that, for every value of porosity, the drag coefficients for the horizontal configuration are larger than those of the vertical configuration. For all data in both configurations, with the exception of the continuous strip clamped vertically, a linear relation is found between the porosity and drag. Making use of this linearity, we can rescale the drag coefficient in a way that it becomes constant as a function of the Cauchy number, which relates the force due to fluid loading on the elastic strip to its bending rigidity, independently of the material properties and porosity of the strip and the flow speed. Our findings on flexible strips are contrasted to previous work on rigid perforated plates. These results highlight some open questions regarding the usage of reduced models to describe the deformation of flexible structures subjected to aerodynamic loading.

In this work we study the dynamical behavior of two interacting vortex pairs, each one of them consisting of two point vortices with opposite circulation in the two-dimensional plane. The vortices are considered as effective particles and their interaction can be described in classical mechanics terms. We first construct a Poincaré section, for a typical value of the energy, in order to acquire a picture of the structure of the phase space of the system. We divide the phase space in different regions which correspond to qualitatively distinct motions and we demonstrate its different temporal evolution in the “real” vortex space. Our main emphasis is on the leapfrogging periodic orbit, around which we identify a region that we term the “leapfrogging envelope” which involves mostly regular motions, such as higher order periodic and quasiperiodic solutions. We also identify the chaotic region of the phase plane surrounding the leapfrogging envelope as well as the so-called walkabout and braiding motions. Varying the energy as our control parameter, we construct a bifurcation tree of the main leapfrogging solution and its instabilities, as well as the instabilities of its daughter branches. We identify the symmetry-breaking instability of the leapfrogging solution (in line with earlier works), and also obtain the corresponding asymmetric branches of periodic solutions. We then characterize their own instabilities (including period doubling ones) and bifurcations in an effort to provide a more systematic perspective towards the types of motions available to this dynamical system.

A persistent problem in wall-bounded large-eddy simulations (LES) with Dirichlet no-slip boundary conditions is that the near-wall streamwise velocity fluctuations are overpredicted, while those in the wall-normal and spanwise directions are underpredicted. The problem may become particularly pronounced when the near-wall region is underresolved. The prediction of the fluctuations is known to improve for wall-modeled LES, where the no-slip boundary condition at the wall is typically replaced by Neumann and no-transpiration conditions for the wall-parallel and wall-normal velocities, respectively. However, the turbulence intensity peaks are sensitive to the grid resolution and the prediction may degrade when the grid is refined. In the present study, a physical explanation of this phenomena is offered in terms of the behavior of the near-wall streaks. We also show that further improvements are achieved by introducing a Robin (slip) boundary condition with transpiration instead of the Neumann condition. By using a slip condition, the inner energy production peak is damped, and the blocking effect of the wall is relaxed such that the splatting of eddies at the wall is mitigated. As a consequence, the slip boundary condition provides an accurate and consistent prediction of the turbulence intensities regardless of the near-wall resolution.

We experimentally and theoretically describe the dynamics of evolution and eventual rupture of Landau-Levich-Bretherton films of partially wetting liquids in microchannels in terms of nonplanar interface curvatures and disjoining pressure. While both the early-stage dynamics of film evolution and near-collapse dynamics of rupture are understood, we match these regimes and find theoretically that the dimensionless rupture time, $T_r$, scales with ${\kappa }^{-10/7}$. Here, $\kappa$ is the dimensionless curvature given by the ratio of the Laplace-pressure discontinuity that initiates film thinning to the initial strength of the disjoining pressure that drives the rupture. We experimentally verify the rupture times and highlight the crucial consequences of early film rupture in digital microfluidic contexts: pressure drop in segmented flow and isolation of droplets from the walls.

Simultaneous particle image velocimetry (PIV) and wall-shear-stress sensor measurements were performed to study structures associated with shear-stress events in a flat plate turbulent boundary layer at a Reynolds number ${\text{Re}}_{\tau }\approx 4000$. The PIV field of view covers $8\delta$ (where $\delta$ is the boundary layer thickness) along the streamwise direction and captures the entire boundary layer in the wall-normal direction. Simultaneously, wall-shear-stress measurements that capture the large-scale fluctuations were taken using a spanwise array of hot-film skin-friction sensors (spanning $2\delta )$. Based on this combination of measurements, the organization of the conditional wall-normal and streamwise velocity fluctuations $(u$ and $v)$ and of the Reynolds shear stress $\left(-uv\right)$ can be extracted. Conditional averages of the velocity field are computed by dividing the histogram of the large-scale wall-shear-stress fluctuations into four quartiles, each containing 25% of the occurrences. The conditional events corresponding to the extreme quartiles of the histogram (positive and negative) predominantly contribute to a change of velocity profile associated with the large structures and in the modulation of the small scales. A detailed examination of the Reynolds shear-stress contribution related to each of the four quartiles shows that the flow above a low wall-shear-stress event carries a larger amount of Reynolds shear stress than the other quartiles. The contribution of the small and large scales to this observation is discussed based on a scale decomposition of the velocity field.

A hypersonic flowfield model that treats electronic levels of the dominant afterbody radiator N as individual species is presented. This model allows electron-ion recombination rate and two-temperature modeling improvements, the latter which are shown to decrease afterbody radiative heating by up to 30%. This decrease is primarily due to the addition of the electron-impact excitation energy-exchange term to the energy equation governing the vibrational-electronic electron temperature. This model also allows the validity of the often applied quasi-steady-state (QSS) approximation to be assessed. The QSS approximation is shown to fail throughout most of the afterbody region for lower electronic states, although this impacts the radiative intensity reaching the surface by less than 15%. By computing the electronic-state populations of N within the flowfield solver, instead of through the QSS approximation in the radiation solver, the coupling of nonlocal radiative transition rates to the species continuity equations becomes feasible. Implementation of this higher-fidelity level of coupling between the flowfield and radiation solvers is shown to increase the afterbody radiation by up to 50% relative to the conventional model.

A spectral analysis of strictly axisymmetric turbulence is performed. Both freely decaying and statistically steady flows are considered. In helical flows we identify a dual cascade, where energy is transferred towards the large scales and helicity to the smallest ones. It is shown that even in the absence of net helicity, a dual cascade persists, transferring energy backward and positively and negatively polarized helicity fluctuations forward.

Direct numerical simulations of turbulent boundary layers over longitudinal surface roughness are performed to investigate the impact of the surface roughness on the mean flow characteristics related to counter-rotating large-scale secondary flows. By systematically changing the two parameters of the pitch (P) and width (S) for roughness elements in the ranges of $0.57\le P/\delta \le 2.39$ and $0.15\le S/\delta \le 1.12$, where δ is the boundary layer thickness, we find that the size of the secondary flow in each case is mostly determined by the value of P − S, i.e., the valley width, over the ridge-type roughness. However, the strength of the secondary flows on the cross-stream plane relative to the flow is increased when the value of P increases or when the value of S decreases. In addition to the secondary flows, additional tertiary and quaternary flows are observed both above the roughness crest and in the valley as the values of P and S increase further. Based on an analysis using the turbulent kinetic energy transport equation, it is shown that the secondary flow over the ridge-type roughness is both driven and sustained by the anisotropy of turbulence, consistent with previous observations of a turbulent boundary layer over strip-type roughness [Anderson et al., J. Fluid Mech. 768, 316 (2015)]. Careful inspection of the turbulent kinetic energy budget reveals that the opposite rotational sense of the secondary flow between the ridge- and strip-type roughness elements is primarily attributed to the local imbalance of energy budget created by the strong turbulent transport term over the ridge-type roughness. The active transport of the kinetic energy over the ridge-type roughness is closely associated with the upward deflection of spanwise motions in the valley, mostly due to the roughness edge.

Local isotropy of passive scalars in fully developed turbulent channel flow is studied by way of direct numerical simulations. We observe a persistent small-scale anisotropy that (i) persists after the flow has undergone substantial mixing and (ii) is independent of the original large-scale anisotropic initial conditions of the scalar field. This latter observation is in sharp contrast with the persistent local anisotropy observed in homogeneous, isotropic turbulence with imposed mean scalar gradients, for which the small-scale anisotropy is directly correlated to the imposed large-scale anisotropy by way of ramp-cliff structures. The anisotropy observed in the present work is linked to the production of $〈{\varepsilon }_{\theta }〉$ due to the mean velocity gradient. A major implication of the work is that local isotropy of passive scalar fields may never hold in flows in which mean velocity gradients exist, even after mean scalar gradients have been eliminated by the turbulence.

The concept of added mass arises from potential flow analysis and is associated with the acceleration of a body in an inviscid irrotational fluid. When shed vorticity is modeled as vortex singularities embedded in this irrotational flow, the associated force can be superimposed onto the added-mass force due to the linearity of the governing Laplace equation. This decomposition of force into added-mass and circulatory components remains common in modern aerodynamic models, but its applicability to viscous separated flows remains unclear. The present work addresses this knowledge gap by presenting a generalized derivation of the added-mass and circulatory force decomposition which is valid for a body of arbitrary shape in an unbounded, incompressible fluid domain, in both two and three dimensions, undergoing arbitrary motions amid continuous distributions of vorticity. From the general expression, the classical added-mass force is rederived for well-known canonical cases and is seen to be additive to the circulatory force for any flow. The formulation is shown to be equivalent to existing theoretical work under the specific conditions and assumptions of previous studies. It is also validated using a numerical simulation of a pitching plate in a steady freestream flow, conducted by Wang and Eldredge [Theor. Comput. Fluid Dyn. 27, 577 (2013)]. In response to persistent confusion in the literature, a discussion of the most appropriate physical interpretation of added mass is included, informed by inspection of the derived equations. The added-mass force is seen to account for the dynamic effect of near-body vorticity and is not (as is commonly claimed) associated with the acceleration of near-body fluid which “must” somehow move with the body. Various other consequences of the derivation are discussed, including a concept which has been labeled the conservation of image-vorticity impulse.

This Rapid Communication derives the Zagarola-Smits scaling directly from the governing equations for zero-pressure-gradient turbulent boundary layers (ZPG TBLs). It has long been observed that the scaling of the mean streamwise velocity in turbulent boundary layer flows differs in the near surface region and in the outer layer. In the inner region of small-velocity-defect boundary layers, it is generally accepted that the proper velocity scale is the friction velocity, $u_{\tau }$, and the proper length scale is the viscous length scale, $\nu /u_{\tau }$. In the outer region, the most generally used length scale is the boundary layer thickness, $\delta$. However, there is no consensus on velocity scales in the outer layer. Zagarola and Smits [ASME Paper No. FEDSM98-4950 (1998)] proposed a velocity scale, $U_{{}_{\mathrm{ZS}}}=({\delta }_1/\delta )U_{\infty }$, where ${\delta }_1$ is the displacement thickness and $U_{\infty }$ is the freestream velocity. However, there are some concerns about Zagarola-Smits scaling due to the lack of a theoretical base. In this paper, the Zagarola-Smits scaling is derived directly from a combination of integral, similarity, and order-of-magnitude analysis of the mean continuity equation. The analysis also reveals that $V_{\infty }$, the mean wall-normal velocity at the edge of the boundary layer, is a proper scale for the mean wall-normal velocity $V$. Extending the analysis to the streamwise mean momentum equation, we find that the Reynolds shear stress in ZPG TBLs scales as $U_{\infty }{V}_{\infty }$ in the outer region. This paper also provides a detailed analysis of the mass and mean momentum balance in the outer region of ZPG TBLs.

We give the first correction to the suspension viscosity due to fluid elasticity for a dilute suspension of spheres in a viscoelastic medium. Our perturbation theory is valid to $O\left(\varphi {\mathrm{Wi}}^2\right)$ in the particle volume fraction $\varphi$ and the Weissenberg number $\mathrm{Wi}=\dot{\gamma }\lambda$, where $\dot{\gamma }$ is the typical magnitude of the suspension velocity gradient, and $\lambda$ is the relaxation time of the viscoelastic fluid. For shear flow we find that the suspension shear-thickens due to elastic stretching in strain “hot spots” near the particle, despite the fact that the stress inside the particles decreases relative to the Newtonian case. We thus argue that it is crucial to correctly model the extensional rheology of the suspending medium to predict the shear rheology of the suspension. For uniaxial extensional flow we correct existing results at $O\left(\varphi \mathrm{Wi}\right)$, and find dramatic strain-rate thickening at $O\left(\varphi {\mathrm{Wi}}^2\right)$. We validate our theory with fully resolved numerical simulations.

Magnetohydrodynamic Rayleigh-Bénard convection was studied experimentally and numerically using a liquid metal inside a box with a square horizontal cross section and an aspect ratio of 5. Applying a sufficiently strong horizontal magnetic field converts the convective motion into a flow pattern of quasi-two-dimensional (quasi-2D) rolls arranged parallel to the magnetic field. The aim of this paper is to provide a detailed description of the flow field, which is often considered as quasi-2D. In this paper, we focus on the transition from a quasi-two-dimensional state toward a three-dimensional flow occurring with decreasing magnetic-field strength. We present systematic flow measurements that were performed by means of ultrasound Doppler velocimetry. The measured data provide insight into the dynamics of the primary convection rolls, the secondary flow induced by Ekman pumping, and they reveal the existence of small vortices that develop around the convection rolls. New flow regimes have been identified by the velocity measurements, which show a pronounced manifestation of three-dimensional flow structures as the ratio $\mathrm{Ra}/Q$ increases. The interaction between the primary swirling motion of the convection rolls and the secondary flow becomes increasingly strong. Significant bulging of the convection rolls causes a breakdown of the original recirculation loop driven by Ekman pumping into several smaller cells. The flow measurements are completed by direct numerical simulations. The numerical simulations have proven to be able to qualitatively reproduce the newly discovered flow regimes in the experiment.