We have experimentally investigated an unsteady separating flow over a NACA-0012 aerofoil. Both the surface pressure measurements and the whole flow field measurements using the time-resolved particle image velocimetry (TR-PIV) technique were carried out at different angles of attack for a chord-based Reynolds number, ${\text{Re}}_c=5\times {10}^4$. The instantaneous flow fields were measured at the stall angle of attack ($\alpha ={10}^{\circ }$) and at different post-stall angles of attack ($\alpha ={11}^{\circ },{12}^{\circ },{13}^{\circ }$) using the TR-PIV system. Although the mean flow data, as expected, show that the flow is fully/massively separated for $\alpha >{10}^{\circ }$ over the suction surface of the aerofoil, the time sequence of the instantaneous flow fields reveals that the massive separation is intermittent in nature. A small separated region grows with time, eventually leading to the massive flow separation and then the massively separated region decays with time leading to a small separated region. In this process, the vortex shedding from the separated shear layer is also observed. We find that an interplay exists between the temporal growth of the separated shear layer and the vortex shedding during the intermittent massive separation. The mechanism for the intermittent massive flow separation has been explained using the time sequence of the instantaneous flow fields. This has further been supported using the proper orthogonal decomposition analysis. Furthermore, the spatiotemporal stability analysis of the local velocity profile shows that when the small separated region goes to a fully separated state, the velocity profiles become absolutely unstable from a convectively unstable state, and vice versa. In addition, these results are found to be consistent with the absolute instability criteria proposed in Alam and Sandham [J. Fluid Mech. 410, 1 (2000)] and Avanci et al. [Phys. Fluids 31, 014103 (2019)].

This work is a unified study of stable and unstable steady states of 2D active nematic channel flow using the framework of Exact Coherent Structures (ECSs). ECSs are stationary, periodic, quasiperiodic, or traveling wave solutions of the governing equations that, together with their invariant manifolds, organize the dynamics of nonlinear continuum systems. We extend our earlier work on ECSs in the preturbulent regime by performing a comprehensive study of stable and unstable ECSs for a wide range of activity values spanning the preturbulent and turbulent regimes. In the weakly turbulent regime, we compute more than 200 unstable ECSs that coexist at a single set of parameters, and uncover the role of symmetries in organizing the phase space geometry. We provide conclusive numerical evidence that in the preturbulent regime, generic trajectories shadow a series of unstable ECSs before settling onto an attractor. Finally, our studies hint at shadowing of quasiperiodic-type ECSs in the turbulent regime.

Free-surface cusps appear as a generic feature in viscous flow with a free surface. However, a mathematical description has so far only been possible by constructing exact solutions to the Stokes equation in very specific and idealized geometries, using complex mapping techniques. Here we use the boundary integral formulation of the Stokes equation to show that cusps are local singular solutions to Stokes' equation. We recover Jeong and Moffatt's [J. Fluid Mech. 241, 1 (1992)] local cusp solution in the limit of diverging cusp curvature, demonstrating its universality across all viscous flows.

The similarity of turbulent structures between compressible and incompressible wall turbulence has been well recognized through mostly visualization of instantaneous fields. However, some questions remain unclear, such as will Morkovin's hypothesis and semilocal scaling, with which many mean flow profiles collapse, also be applicable to instantaneous features of turbulence structures and why. The present work dissects features of vortical structures in compressible channel flows comprehensively to address these questions by employing the direct numerical simulations database of turbulent channel flows covering broad Mach and Reynolds numbers. Most features investigated show satisfactory agreement quantitatively with the incompressible counterparts in semilocal units, which indicates the validity of Morkovin's hypothesis based on the semilocal scaling. This observation extends Morkovin's hypothesis from standard mean flow statistics to instantaneous vortex features and suggests that the dominant mechanism governing vortex evolution remains the same as incompressible flows. Specifically, the streamwise vortex inclination angle approaches ${45}^{\circ }$ as the wall-normal distance grows, which is supported by a theoretical estimation extended from incompressible flows by claiming the compressibility does not alter the vortex orientation. Regarding the size and strength of vortices, the average radius of vortices grows with the wall-normal distance, while the average strength becomes weaker. The vortex population increases with Reynolds number evidently, while it decreases marginally with Mach numbers. It is impressive that the population percentage of different types of vortices is similar to all the cases in the near-wall region. Last, a heuristic model is developed as a potential candidate for describing the topology of instantaneous vortices. In cooperation with the topological model, these statistical results could be crucial input references to reconstruct flow fields using vortex methods.

Recent theoretical and experimental work has demonstrated the generation of nonlinear harmonics when internal waves propagate in nonuniform stratification. This effect is most pronounced if the harmonic frequency is near resonance with a freely propagating mode. It may play a significant role in the evolution of low-mode internal tides in the ocean, possibly leading to the formation of strongly nonlinear waves. Here, global ocean stratification profiles measured by ARGO floats are used to quantify the potential for nonlinear harmonic generation for semidiurnal mode-1 internal tides. The results show that the first harmonic, with double the wave number of the parent mode, is often expected to attain an amplitude exceeding a fifth of the parent mode in equatorial regions. Potentially strong harmonic responses were calculated most frequently for the Pacific and Indian Oceans. A strong harmonic is not expected in the Atlantic, despite near-resonance conditions, because weaker and more shallow pycnoclines do not provide a sufficient harmonic forcing. Hence near resonance is found to be a necessary, but not sufficient, condition for harmonic generation in measured ocean stratifications. A second criterion, based on pycnocline depth and density change, is proposed as an additional condition for harmonic generation.

In the study of rotating channel flow, the key dimensionless parameters typically include the Reynolds number, rotation number, Prandtl number, and buoyancy number. Our research focused on comparing the flow characteristics between the enlarged model, analyzed under the rotating similarity theory, and the original channel flow. Significantly different flow behaviors were observed between these two cases. Through theoretical derivation and dimensional analysis, we identified a new significant parameter––the centrifugal work number. This parameter characterizes the ratio of centrifugal work to gas enthalpy in the rotating channel and plays a crucial role in measuring the compressibility of fluids within the rotating channel. Additionally, we utilized large-eddy simulation to validate the impact of the centrifugal work ratio on the flow state of the rotating channel, thus enhancing the similarity theory of rotating channel compressible flow.

We study the interaction between knotted flame and vortex tubes using the direct numerical simulation. A 3D configuration of the flame-vortex interaction is proposed. The premixed flame is initially located within a vortex tube with the same trefoil knotted centerline, and it propagates outward and interacts with the knotted vortex tube. This configuration is able to investigate the flame extinction, flame-flame interaction, and suppression of the vortex reconnection. Compared to the nonreacting knotted vortex tube, the flame-vortex interaction modifies the helicity dynamics and the morphology of vortex and flame tubes. The combustion generally decreases the helicity due to enhanced viscosity effects, but also slightly increases the helicity during a short time when the local extinction occurs. The nonmonotonic variation of the helicity results from the unsymmetrical flame propagation along the vortex axis after the local flame extinction. Moreover, some parts of the flame and vortex tubes are flattened through the early evolution. The flattening is primarily due to the baroclinic effects arising from the misalignment between the local density gradient and the nonlocal pressure gradient that strongly depends on the flame-vortex configuration.

It has recently been shown that a significant slowdown of many stars can be attributed to the emergence of a strong magnetic field within the radiative region, where heat is transferred through radiation in a stably stratified layer. Here we describe how this transition can be understood as a subcritical bifurcation to small-scale turbulence in linearly stable flows. The turbulence is sustained by a nonlinear mean-field dynamo and can be observed down to relatively small differential rotation, arbitrarily far from the linear onset of any hydrodynamic instability. In this regime, turbulent fluctuations provide diffusivity-free transfer of angular momentum that increases the transport generated by the magnetic field triggering the turbulence. Finally, we present a simple nonlinear model that captures this scenario and can be used as a general description of the transition to turbulence in astrophysical flows, as long as it involves a competition between a large-scale dynamo and a small-scale magnetic instability.

In their 2016 paper, Wei and Klewicki [Phys. Rev. Fluids 1, 082401 (2016)] developed an integral relation, $U_e{V}_e/u_{\tau }^2=H_{12}$, which connects key parameters in zero-pressure-gradient (ZPG) boundary layer flows: mean velocity components $U_e$ and $V_e$ at the boundary layer edge, and friction velocity $u_{\tau }$ to shape factor $H_{12}$. While this relation holds exactly for ZPG laminar boundary layers featuring self-similar streamwise velocity profiles, it is an approximation for ZPG turbulent boundary layers (TBLs), with its accuracy improving as the Reynolds number increases. In this paper, we present a correction to the original integral relation, providing an exact integral relation that is applicable to ZPG boundary layer flows at arbitrary Reynolds numbers. The correction comprises two terms: one addressing deviations from self-similarity in mean streamwise velocity, and the other considering the impact of Reynolds normal stresses. Experimental and numerical data are shown to support the relative insignificance of the newly identified correction terms, except for Reynolds numbers in the transitional regime.

Direct numerical simulation is employed to investigate the characteristics of wall shear stress (WSS) and wall heat flux (WHF) beneath a spatially developing supersonic turbulent boundary layer with a cold-wall thermal condition subjected to a concavely curved compression ramp with a deflection angle of ${24}^{\circ }$. The Mach number is 2.25 and the friction Reynolds number is 769. Numerical data are exploited to characterize the effect of the concave surface curvature on the statistical and structural properties of the fluctuating WSS and WHF, including the probability density function, space-time correlations, and frequency spectra. Across the curved region, the occurrence probability of extreme negative events is strongly affected by the curvature, as manifested by a noticeable dissimilarity in the large negative tails of the probability density functions. The correlation results show that the streamwise extent of the WSS fluctuations becomes smaller, in contrast to that of the WHF fluctuations, and a considerable decrease in the convection velocity is observed downstream from the curvature. It is found that the curvature qualitatively modifies the WHF frequency spectra, leading to a shift to lower frequencies, while the spectral alternation is less pronounced for the WSS. Importantly, the mean WHF and WSS are also decomposed into different physically informed components, with the finding that the mean WSS generation is fundamentally changed by the curvature but the generation mechanism of the mean WHF is constant throughout the concave surface. Finally, an analysis of velocity and temperature structures is performed with the aid of bidimensional empirical mode decomposition to quantitatively demonstrate the contributions of specific spanwise length scales. We highlight that the outer large-scale organized structures, which are significantly energized by the concave surface, make an increasingly important contribution to the mean WSS and WHF generation.

The net impact of aircraft contrails on global climate change is a matter of controversy today. Among the many parameters potentially influencing this issue, the role played by the aircraft wake has received only little attention so far. Yet the interaction between the engine exhaust jets causing these contrails and the aircraft wake can lead to modifications in the altitude of the contrails on the order of hundreds of meters. This change in altitude heavily influences the net impact of contrails to global climate change, since it affects the ambient temperature and thereby the ice content and the radiative properties of these contrails. The wake entrainment supporting these effects basically depends on the relative positioning of the jet with respect to the tip vortices and on the buoyant forces associated with atmospheric stratification. Here we focus on these two parameters by running a large number of two-dimensional simulations of the flow from the aftermath of the jet turbulent diffusion, vortex roll-up, and initial ice formation up to the vortex destabilization stage, for a range of values of the vortex based normalization of the Brunt-Väisälä frequency and the jet to wing span ratio. The very near wake dynamics are not simulated and instead replaced by an analytical description for the vortex, the jet, and the ice plume. Ice water content is determined from the offset to ice saturation, given prescribed ambient conditions. The jet lateral spacing is considered in the range from fuselage to wing tip. The potential radiative impact of the early wake is calculated using the total extinction induced by the ice plume. The results are indicative of the impact of older contrail cirrus clouds, the largest proportion in the whole contrail radiative impact. The parametric mapping (stratification, jet spacing) highlights the important role played by the jet position on the opacity of early contrails, for regular stratification levels. In particular, a jet located closer to the wing tip results in contrails located at lower altitudes and reduced optical thickness, suggesting that jet positioning could be an interesting mean of contrail mitigation.

The displacement of a viscous liquid by a gas within a Hele-Shaw cell is a classical problem. The gas–liquid interface is hydrodynamically unstable, forming striking fingerlike patterns that have attracted research interest for decades. Generally, both the gas and liquid phases are taken to be incompressible, with the capillary number being the key parameter that determines the severity of the instability. Here, we consider a radially outward displacement driven by the steady compression of a gas reservoir. The associated gas-injection rate is then unsteady due to the compressibility of the gas. We identify a second nondimensional parameter, the compressibility number, that plays a strong role in the development of the fingering pattern. We use an axisymmetric model to study the impact of compressibility number on the unsteady evolution of injection rate and gas pressure. We use linear stability analysis to show that increasing the compressibility number delays the onset of finger development relative to the corresponding incompressible case. Finally, we present and compare a series of experiments and fully nonlinear simulations over a broad range of capillary and compressibility numbers. These results show that increasing the compressibility number systematically decreases the severity of the fingering pattern at high capillary number. Our results provide an unprecedented comparison of experiments with simulations for viscous fingering, a comprehensive understanding of the role of compressibility in unstable gas–liquid displacement flows, and insight into a new mechanism for controlling the development of fingering patterns.

The “squirmer model” is a classical hydrodynamic model for the motion of interfacially driven microswimmers, such as self-phoretic colloids or volvocine green algae. To date, most studies using the squirmer model have considered spherical particles with axisymmetric distribution of surface slip. Here, we develop a general approach to the pairing and scattering dynamics of two spheroidal squirmers. We assume that the direction of motion of the squirmers is restricted to a plane, which is approximately realized in many experimental systems. In the framework of an analytically tractable kinetic model, we predict that, for identical squirmers, an immotile “head-to-head” configuration is stable only when the particles have oblate shape and a nonaxisymmetric distribution of surface slip. We also obtain conditions for stability of a motile “head-to-tail” configuration: for instance, the two particles must have unequal self-propulsion velocities. Our analytical predictions are compared against detailed numerical calculations obtained using the boundary element method.

The symmetry-breaking instability of the steady axisymmetric thermocapillary flow in a nonvolatile sessile droplet on a hot or cold substrate under zero gravity conditions is investigated by linear stability analysis. The dependence of the critical Marangoni number on the contact angle and the Prandtl number is computed, and the structures of the most dangerous perturbation modes are analyzed. For a small contact angle and a high-Prandtl-number droplet with $\text{Pr}=16.36$ (corresponding to 1 cSt silicone oil) on a hot wall, we find classical Marangoni instabilities near the center of the droplet. In contrast, no instability is observed for small-contact-angle droplets on a cold wall. For large contact angles with $\alpha >{90}^{\circ }$ either on a hot or a cold wall, the first instability of the basic axisymmetric toroidal vortex is inertial for low Prandtl numbers and of hydrothermal-wave type for high Prandtl numbers.

Microparticles migrate in response to gradients in solute concentration through diffusiophoresis and diffusioosmosis. Merging streams of fluid with distinct solute concentrations is a common strategy for producing a steady concentration gradient with continuous flow in microfluidic devices; the solute concentration gradient and consequent diffusiophoresis are primarily normal to the background flow. This is particularly useful in separation and filtration processes, as it results in regions of particle accrual and depletion in continuous flows. Such systems have been examined in several classic papers on diffusiophoresis, with a focus on the particle dynamics far from boundaries. We show, through experiments, simulations, and theory, that diffusioosmotic flow along certain boundaries can result in significant changes in particle dynamics and particle focusing in near-wall regions. The nonzero velocity at charged surfaces draws solute and particles along the boundary until the flow ultimately recirculates. These convection rolls, which result in the spanwise migration of polystyrene particles close to boundaries, are apparent near a glass surface but vanish when the surface is coated with gold. The three-dimensional nature of the dynamics could have implications for the design of microfluidic devices: Channel materials can be selected to enhance or suppress near-wall flows. Additionally, we demonstrate the importance of considering solute concentration-dependent models for diffusiophoretic and diffusioosmotic mobility in capturing the dynamics of particles, particularly in regions of low solute concentration.

We carry out direct numerical simulations of horizontally or vertically vibrated Rayleigh–Bénard (RB) convection over a wide range of Rayleigh number $\left(Ra\right)$ and dimensionless vibration frequency $\left(\omega \right)$ at fixed Prandtl number $Pr=4.38$ and dimensionless vibration amplitude $a=1.52\times {10}^{-3}$. It is shown that the global heat transport (measured by the Nusselt number $Nu$) is close to the value of standard RB convection in buoyancy-dominant regime at small $\omega$, whereas it is significantly enhanced by horizontal vibration or suppressed by vertical vibration in the vibration-dominant regime at large $\omega$. The division between the two regimes yields a critical vibration frequency ${\omega }^{*}$, which indicates the onset of vibration-induced $Nu$ enhancement or $Nu$ reduction. The values of ${\omega }^{*}$ are obtained based on the fitting between the numerical data and our proposed crossover functions. The dependence of ${\omega }^{*}$ on $Ra$ is then studied. It is found that the fitted critical frequency exhibits two close scaling relations: ${\omega }^{*}\sim R{a}^{-0.164}$ in horizontally vibrated RB convection and ${\omega }^{*}\sim R{a}^{-0.172}$ in vertically vibrated cases. Moreover, based on the competition of the kinetic energy production between buoyancy-dominant and vibration-dominant regimes, a physical model is proposed to predict the scaling behavior between ${\omega }^{*}$ and $Ra$, i.e., ${\omega }^{*}\sim R{a}^{-1/6}$, which agrees well with the measured scaling exponents of our numerical data.

This paper is associated with a poster winner of a 2022 American Physical Society's Division of Fluid Dynamics (DFD) Milton van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original poster is available online at the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2022.GFM.P0039

The global stability of the flow in a spatially developing ${180}^{\circ }$-bend pipe with curvature $\delta =R/R_c=1/3$ is investigated by performing direct numerical simulations to understand the underlying transitional mechanism. A unique application of the adaptive mesh refinement technique is used during the stability analysis for minimizing the interpolation and quadrature errors. Independent meshes are created for the direct and adjoint solutions, as well as for the base flow extracted via selective frequency damping. The spectrum of the linearized Navier-Stokes operator reveals a pair of complex conjugate eigenvalues, with frequency $f\approx 0.233$. Therefore, the transition is attributed to a Hopf bifurcation that takes place at ${\text{Re}}_{b,\text{cr}}=2528$. A structural sensitivity analysis is performed by extracting the wavemaker. We identify the primary source of instability located on the outer wall, $\theta \approx {15}^{\circ }$ downstream of the bend inlet. This region corresponds to the separation bubble on the outer wall. We thus conclude that the instability is caused by the strong shear resulting from the backflow, similar to the ${90}^{\circ }$-bend pipe flow. We believe that understanding the stability mechanism and characterizing the base flow in bent pipes is crucial for studying various biological flows, like blood vessels. Hence, this paper aims to close the knowledge gap between a ${90}^{\circ }$-bend and toroidal pipes by investigating the transition nature in a ${180}^{\circ }$-bend pipe flow.

We investigate theoretically the influence of a temperature-dependent viscosity on the pressure drop versus flow rate relationship in pipe flows for cases where the Reynolds number is small, as expected for printing and other flows of highly viscous fluids. By applying different temperature boundary conditions at the wall, the viscosity field is altered under the same flow conditions and thus we can compare how this external heating affects the pressure drop along the length of the pipe. We use analytical and similarity-solution methods to solve for the temperature distribution under constant temperature and constant heat flux boundary conditions, as well as assumed linear and other imposed polynomial temperature versus distance (along the flow) boundary conditions at the wall. Also, for the momentum and energy equations we use the lubrication and boundary-layer approximations, respectively, which we expect to be typically appropriate for flows where the pipe radius is much less than the pipe length. The reciprocal theorem is used to derive an expression for the pressure drop across the channel for a viscosity field that depends on temperature and spatially varies across and along the flow. Assuming the fractional change in viscosity with temperature is small, we arrive at an analytical expression for the pressure drop for a given flow rate. The results are reported as a function of the effective Peclet number for each boundary condition and the numerical results are compared with analytical predictions in the low- and high-Peclet-number limits.

Frictional fluid dynamics describes the displacement patterns that arise when a confined mixture of liquid and grains are displaced by an immiscible fluid under pressures that are too small to cause drainage into single pores. The flow, which is governed by solid friction and capillary forces, thus bulldozes the grains into compaction fronts which give rise to propagating fingers that eventually interact to create a range of patterns, including labyrinthine ones. We derive an analytic description that successfully reproduces the experimental results for the shape of a single finger as well as the compaction front profile. The theory thus depends on only one fitting parameter.