Purcell's scallop theorem states that a swimmer deforming in a fluid at low Reynolds number cannot undergo a net displacement if its sequence of shapes is symmetric in time. Motivated by heterogeneous biological environments, here we consider a fluid with broken translational symmetry where the viscosity of the medium varies spatially. We show that, in a prescribed and smooth but otherwise arbitrary viscosity field, the swimmer's displacement is independent of its deformation rate and thus the scallop theorem continues to hold. Transport of the viscosity by the flow would therefore be key to enabling reciprocal locomotion in heterogeneous media.

This paper proposes an ordinary-differential-equation (ODE)-based nonequilibrium boundary layer (NEQBL) wall modeling in large-eddy simulation (LES) for accurate prediction of nonequilibrium separated turbulent boundary layers at a high Reynolds number. The proposed ODE-based wall model does not require computational grids with full connectivity. The key to the modeling is to incorporate the nonequilibrium effects into the pressure-gradient term, convective term, and turbulent eddy viscosity consistently. The model is inaccurate if any of these terms are modeled inconsistently from the others, and it is found important to include the nonequilibrium effects into the turbulent eddy viscosity, which has not been discussed in prior studies. The proposed modeling of the three nonequilibrium terms is first analyzed by a priori tests using the wall-resolved LES (WRLES) database of pressure-induced separated and reattached turbulent boundary layer at Reynolds number ${\text{Re}}_{\theta }\approx 2.0\times {10}^3$. Then, the wall-modeled LES using the proposed ODE-based NEQBL wall model is conducted under the same condition as the WRLES database. The proposed ODE-based NEQBL model yields accurate predictions of the resolved turbulence statistics for both equilibrium-attached and nonequilibrium-separated flows.

A temporally developing three-dimensional turbulent boundary layer is investigated using direct numerical simulation. The flow is initiated by subjecting a statistically stationary turbulent channel flow to a constant transverse pressure gradient while maintaining the streamwise pressure gradient unchanged. It is shown that this nonequilibrium three-dimensional boundary layer can be described as a turbulent-turbulent transition that is characterized by the development of a laminar boundary layer in an initial turbulent environment followed by a transition to turbulence. Both transient energy growth and crossflow instability may influence the transition, though the former is likely to have a stronger effect when the initial Reynolds number is lower and the transverse pressure gradient is stronger. The transient developments of both the mean flow and turbulence are understood by relating them to the process of transition. The rotation of streaks and the damping effect of the spanwise boundary layer work together to suppress the streamwise and wall-normal turbulence. This effect is stronger than the energy growth in the spanwise direction, causing the overall turbulent kinetic energy and the structure parameter to decrease, explaining the observations made of such flows.

We derive objective criteria to discern universality of the outer-layer mean velocity profile in wall-bounded flows, which yield a set of outer velocity and length scales. The new scaling generalizes the Rotta-Clauser scaling and includes the Zagarola-Smits scaling as a special case for internal flows, and it supports the friction velocity as the most plausible velocity scale in the asymptotic high-Reynolds-number regime. A composite logarithmic/parabolic formulation is proposed for the outer mean velocity profile, which yields simple and accurate approximations for boundary layers, pipes, and channels.

Air vehicles of all scales are susceptible to large-amplitude gusts that may lead to vehicle damage and instability. Therefore, effective physics-based control strategies and an understanding of the dominant unsteady flow physics underpinning gust encounters are desired to improve safety and reliability of flight in these conditions. To this end, this paper develops and experimentally demonstrates a proportional output-feedback lift regulation strategy based on the classical unsteady aerodynamic theories of Wagner and Küssner for wings encountering large-amplitude transverse gusts without a priori knowledge of gust strength or onset time. The tested vertical gust velocities ranged between 25% and 71% of the freestream speed. This strategy is found to successfully generalize to gusts of different strengths and directions, as well as wings at pre- and post-stall angles of attack. In addition, this paper applies dynamical systems analysis to Wagner's aerodynamic model to reveal the effect of the pitch-axis location, pitch input, and closed-loop feedback gains on the stability and robustness of the system along with the flow physics responsible. The real-time output feedback control strategy is experimentally tested in a water tow tank facility equipped with a transverse gust generator. Time-resolved force and flow-field measurements are used to discover the salient flow physics during these encounters and illustrate how closed-loop actuation mitigates their lift transients.

In this Letter, we systematically investigate the Leidenfrost temperature for hot solid substrates with various thermal diffusivities and surface roughnesses. Based on the experimental results, we build a phenomenological model that considers the thermal diffusivity of a solid substrate and derive a relationship between the surface roughness and the resulting vapor film thickness. The generality of this model is supported by experimental data for different liquids and solid substrates. Our model thus allows for a theoretical prediction of the Leidenfrost temperature and develops a comprehensive understanding of the Leidenfrost effect.

This survey investigates wall modeling in large-eddy simulations (LES) using data-driven machine-learning (ML) techniques. To this end, we implement three ML wall models in an open-source code and compare their performances with the equilibrium wall model in LES of half-channel flow at 11 friction Reynolds numbers between 180 and ${10}^{10}$. The three models have “seen” flows at only a few Reynolds numbers. We test if these ML wall models can be extrapolated to unseen Reynolds numbers. Among the three models, two are supervised ML models and one is a reinforcement learning ML model. The two supervised ML models are trained against direct numerical simulation (DNS) data, whereas the reinforcement learning ML model is trained in the context of a wall-modeled LES with no access to high-fidelity data. The two supervised ML models capture the law of the wall at both seen and unseen Reynolds numbers—although one model requires retraining and predicts a smaller von Kármán constant. The reinforcement learning model captures the law of the wall reasonably well but has errors at both low (${\text{Re}}_{\tau }<{10}^3$) and high Reynolds numbers (${\text{Re}}_{\tau }>{10}^6$). In addition to documenting the results, we try to “understand” why the ML models behave the way they behave. Analysis shows that the error of the supervised ML models is a result of the network design and the error in the reinforcement learning model arises due to the present choice of the “states” and the mismatch between the neutral line and the line separating the action map. In all, we see promises in data-driven ML wall models.

A generalized quasilinear (GQL) approximation [Marston et al., Phys. Rev. Lett. 116, 214501 (2016)] is applied to homogeneous shear turbulence following previous work on the quasilinear (QL) model [Hernández and Hwang, J. Fluid Mech. 904, A11 (2020)]. For the GQL approximation, the velocity fluctuations are decomposed into low- and high-wave-number groups, the former of which is solved by considering the full nonlinear equations whereas the latter is obtained from the linearized equations around the former. Unlike the QL model, which typically shows significant inhibition of the energy cascade in the direction along which the linearization is made, the GQL model shows an energy cascade that is more active than the QL model because more Fourier modes included in the low-wave-number group allow for an extra energy transfer mechanism from the low- to high-wave-number group via the so-called “scattering” mechanism. It is shown that this scattering mechanism is most active when a relatively small and suitable number of Fourier modes are included in the low-wave-number group instead of a large number of the Fourier modes being so, and this is explained in terms of the neutral Lyapunov vector forming the solution to the linear equations for the high-wave-number group. As a consequence, the turbulence statics from the GQL model with a relatively small number of the Fourier modes in the low-wave-number group are closer to those from DNS than those from the model with a large number of the Fourier modes in the low-wave-number group. Finally, the QL/GQL approximations made in the streamwise and spanwise directions are compared, with emphasis on the role of slow pressure and the related pressure strain transport.

We investigate nonlinear periodic and solitary two-dimensional rolling waves in a falling two-layer liquid film in the regime of nonzero Reynolds numbers. At any flow rate, a falling two-layer liquid film is known to be linearly unstable with respect to long-wave deformations of the liquid-air surface and liquid-liquid interface. Two different types of zero-amplitude neutrally stable waves propagate downstream without growing or shrinking: a zigzag surface mode and a thinning varicose interface mode. Using a boundary-layer reduction of the Navier-Stokes equation, we investigate the onset, possible bifurcations, and interactions of nonlinear periodic traveling waves. Periodic waves are obtained by continuation as stationary periodic solutions in the comoving reference frame starting from small-amplitude neutrally stable waves. We find a variety of solitary waves that appear when a periodic solution approaches a homoclinic loop. Similar to falling one-layer films, we find two families of homoclinics, each family containing countably many solutions that can be characterized by the number of the major humps or dips in their profiles. Solitary waves with humps can be identified with droplets and travel faster than neutrally stable waves, while solitary waves with dips resemble localised depression regions, or holes, and travel slower than neutrally stable waves. Wave interactions are studied using direct numerical simulations of the boundary-layer model. We reveal that in the early stages of temporal evolution coarsening is dominated by an inelastic collision and merging of waves that travel at different speeds. Eventually, coarsening becomes arrested when the waves have reached a nearly homoclinic solution with a single major hump. In the mixed regime, when both mode types are unstable, the temporal dynamics becomes highly irregular due to the competition between a faster-traveling zigzag mode and a slower-traveling varicose mode. A quintessentially two-layer dynamical regime is found, which corresponds to a ruptured second layer. In this regime, the first layer adjacent to the solid wall acts as a conveyor belt, transporting isolated rolling droplets made of the second fluid downstream.

This study concerns a turbulent jet at Mach number $M_j=0.9$, subject to a uniform external flow stream at $M_f=0.15$. The analysis combines experimental and numerical databases, spectral proper orthogonal decomposition (SPOD), and linear modeling. The experiments involve time-resolved, stereo PIV measurements at different cross-sections of the jet. A companion large-eddy simulation was performed with the same operating conditions using the “CharLES” solver by Cascade Technologies to obtain a complete and highly resolved three-dimensional database. We assess the mechanisms that underpin the reduction in fluctuation energy that is known to occur when a jet is surrounded by a flight stream. We show that this energy reduction is spread over a broad region of the frequency-wave-number space and involves, apart from the known stabilization of the modal Kelvin-Helmholtz (KH) instability, the attenuation of flow structures associated with the nonmodal Orr and lift-up mechanisms. Streaky structures, associated with helical azimuthal wave numbers and very slow timescales, are the most strongly affected by the flight stream, in terms of energy attenuation and spatial distortion. The energy reductions are accompanied by a weakening of the low-rank behavior of the jet dynamics. These trends are found to be consistent, to a great extent, with results of a local linear model based on the modified mean flow in the flight-stream case.

Thermal motions of molecules can generate nanowaves on the free surface of a liquid film. As nanofilms are susceptible to the contamination of surfactants, this work investigates the effects of surfactants on dynamics of nanowaves on a bounded film with a finite depth, using both molecular dynamics simulations and analytical theories. In molecular simulations, a bead-spring model is adopted to simulate surfactants, where beads are connected by the finite extensive nonlinear elastic potentials. Fourier transforms of the film surface profiles $h(x,t)$ extracted from molecular simulations are performed to obtain the static spectrum $|h_q{|}_{\mathrm{rms}}$ and temporal correlations of surface modes $\langle h_q\left(0\right)h_q^{*}\left(t\right)\rangle$. It is shown that the spectral amplitude is increased for the contaminated liquid surface compared to the clean surface because surfactants can decrease surface tension. A higher concentration of surfactants on the surface not only decreases the surface tension but also bring elastic energy to the free surface, as the scaling of spectral amplitude with wave numbers changes from $|h_q{|}_{\mathrm{rms}}\sim q^{-1}$ to $|h_q{|}_{\mathrm{rms}}\sim q^{-2}$ for modes with large wave numbers. Regarding the temporal correlations of surface modes, it is observed that the presence of surfactants leads to a slower decay, which, however, cannot be predicted by only considering the decreased surface tension. Based on the Boussinesq-Scriven model for surface viscosity, a linear stability analysis of Stokes flow for films with arbitrary depth is conducted and the obtained dispersion relation considering surface viscosity can justify the simulation results.

A spatiotemporal stability analysis is conducted on a flow representing both jets and wakes, subject to confinement by identical compliant walls. The walls are placed at equal distances from the fluid center line for a range of wall and flow parameters. By following the position of special saddle points (pinch points) of the dispersion relation in the complex wave-number plane, the absolute and convective instability stability properties of the flow are determined for various system parameters. The compliant walls are shown to modify the shear-induced instabilities, which exist in the rigid wall case, as well as introduce new additional instabilities originating from the presence of the wall itself. It is observed that under certain system parameters, these wall-induced modes become the dominant instability present in the system and can induce an absolute instability into flows which are only convectively unstable when confined by rigid walls, as well as extending the region of absolute instability to large confinement parameters. Results are presented for both a piecewise linear velocity profile and a smooth velocity profile, with the results of the two studies in qualitative agreement.

Fully developed turbulent flows through ribbed channels have been simulated using direct numerical simulation (DNS). Square ribs were arranged transversely to the flow on one of the channel walls, and based on their spanwise extent, resulted in two configurations—two-dimensional (2D) configuration resulting from full-span-width ribs and a three-dimensional (3D) configuration, where the ribs extend only up to half the span-width of the channel, leaving the other half smooth. The 3D configuration thus produced a unique problem of coflowing rough and smooth turbulent channel flows. A striking phenomenon has been observed of the secondary roll cells, exhibiting a strong updraft in the smooth half of the channel. The mean velocity profile from the smooth half surprisingly possesses a linear region of constant slope at the channel core. Comparisons were also drawn with DNS of a smooth channel at the same friction Reynolds number 400 and it was found that the roll cells on the smooth half not only affect the bulk flow negatively but also attenuate the turbulence significantly. In spite of having a higher bulk velocity, the rough half of the 3D configuration is more turbulent than the 2D configuration; this has been attributed to the momentum transfer from the smooth half to the rough half. Statistical turbulence quantities, and the production rates of turbulent kinetic energy and enstrophy have been used to arrive at the inferences. In essence, the roll cells buffer the variations between the rough and the smooth halves in the 3D configuration. The instantaneous streamwise velocity fluctuations in the 3D configuration displayed a wavelike form.

We report investigation of thermal waves in harmonically modulated turbulent thermal convection in a Rayleigh-Bénard cell. We probe the thermal waves in the working fluid—cryogenic helium gas—by temperature sensors placed in the cell and embedded in the plates. We observe propagation and interference of two coherent thermal waves and describe their behavior in terms of models that explain the weak attenuation and apparent superposition of thermal waves in the bulk, accounting for the temperature profile of convective turbulent flow via a spatially dependent effective thermal diffusivity.

We present a three-dimensional computational study of the impact of external magnetic fields on the dynamics of superparamagnetic ferrofluid droplets and rheology of dilute ferrofluid emulsions in planar extensional flows. Specifically, we show how the intensity and direction of uniform magnetic fields affect the planar extensional rheology of ferrofluid emulsions by changing the shape and magnetization of the constituent ferrofluid droplets in suspension. We find that the two traditional extensional viscosities associated with the normal stresses of the bulk emulsion in extension either remain constant or increase with the field intensity; the only exception occurs when the field direction is perpendicular to the extension plane, where increasing the field intensity keeps the planar extensional viscosity constant and modestly decreases the second extensional viscosity. We also find that the droplet tilts in the flow when the external field is not aligned with one of the flow main directions, which changes the recirculation pattern and flow topology inside the droplet. At the microscopic level, the droplet experiences a magnetic torque because of a small misalignment between its magnetization and the external field direction. At the macroscopic level, the bulk emulsion experiences a field-induced internal torque that leads to a nonsymmetric stress tensor with unexpected shear components in extension. To account for this unconventional stress-strain response, we introduce new extensional material functions such as shear and rotational viscosity coefficients that unveil novel rheological signatures of ferrofluid emulsions in planar extensional flows. This study offers new insights into applications based on the field-assisted manipulation of ferrofluid droplets and sheds light on the potential of ferrofluid emulsions as a model system for chiral fluids with internal rotational degrees of freedom that can be activated and controlled by coupling static magnetic fields with hydrodynamic flows.

We present experimental observations of the spatial distribution of large inertial particles suspended in a turbulent swirling flow at high Reynolds number. The plastic particles, which are tracked using several high-speed cameras, are heavier than the working fluid so that their dynamics results from a competition between gravitational effects and turbulent agitation. We observe two different regimes of suspension. At low rotation rate, particles are strongly confined close to the bottom and are not able to reach the upper region of the tank, whatever their size or density. At high rotation rate, particles are loosely confined: small particles become nearly homogeneously distributed while very large objects are preferentially found near the top, as if gravity was reversed. We discuss these observations in light of a minimal model of random walk accounting for particle inertia and show that large particles have a stronger probability to remain in the upper part of the flow because they are too large to reach descending flow regions. As a consequence, particles exhibit random horizontal motions near the top, until they reach the central region where the mean flow vanishes or until a turbulent fluctuation gets them down.

We study the orientation dynamics of two-dimensional concavo-convex solid bodies that are denser than the fluid through which they fall under gravity. We show that the orientation dynamics of the body, quantified in terms of the angle $\varphi$ relative to the horizontal, undergoes a transcritical bifurcation at a Reynolds number $R{e}_c^{\left(1\right)}$ and a subcritical pitchfork bifurcation at a Reynolds number $R{e}_c^{\left(2\right)}$. For $Re<R{e}_c^{\left(1\right)}$, the concave-downwards orientation of $\varphi =0$ is unstable and bodies overturn into the $\varphi =\pi$ orientation. For $R{e}_c^{\left(1\right)}<Re<R{e}_c^{\left(2\right)}$, the falling body has two stable equilibria at $\varphi =0\text{and}\varphi =\pi$ for steady descent. For $Re>R{e}_c^{\left(2\right)}$, the concave-downwards orientation of $\varphi =0$ is again unstable and bodies that start concave-downwards exhibit overstable oscillations about the unstable fixed point, eventually tumbling into the stable $\varphi =\pi$ orientation. The $R{e}_c^{\left(2\right)}\approx 15$ at which the subcritical pitchfork bifurcation occurs is distinct from the $Re$ for the onset of vortex shedding, which causes the $\varphi =\pi$ equilibrium to also become unstable, with bodies fluttering about $\varphi =\pi$. The complex orientation dynamics of irregularly shaped bodies evidenced here are relevant in a wide range of settings, from the tumbling of hydrometeors to the settling of mollusk shells.

The predictions obtained from resolvent analysis with and without an eddy viscosity model for turbulent channel flow at ${\text{Re}}_{\tau }=550$ are compared to direct numerical simulation data to identify the scales and wave speeds for which resolvent analysis provides good predictions. The low-rank behavior of the standard resolvent identifies energetic regions of the flow whereas the eddy resolvent is low rank when the resulting projection of the leading eddy resolvent mode onto the leading mode from spectral proper orthogonal decomposition is maximum. The highest projections are obtained for structures that are associated with the near-wall cycle and structures that are energetic at $z=\pm 0.5$. It is argued that these types of structures are likely to be correctly predicted for any friction Reynolds number due to the inner and outer scaling of the Cess eddy viscosity profile. The eddy resolvent also correctly identifies the most energetic wave speed for these two scales. For all other scales, neither analysis reliably predicts the most energetic wave speed or mode shapes. The standard resolvent tends to overestimate the most energetic wave speed while the eddy resolvent underestimates it. The resulting eddy resolvent modes are overly “attached” to the wall since the wall-normal gradient of the eddy viscosity overestimates the transport of energy towards the wall. These observations have direct implications for future work towards estimating turbulent channel flows using resolvent analysis and suggest that the Cess profile can be further optimized for individual scales to provide better low-order models of turbulent channel flows.

In the present paper, we theoretically study the shear force exerted on an infinite horizontal plate undergoing fast lateral oscillations in the presence of a rigid particle suspended in the viscous liquid above the plate. The study is largely motivated by the quartz crystal microbalance technique, which relies on analyzing the response (complex impedance) of a fast oscillating (in the MHz range) quartz crystal disk in a liquid medium due to small substances adsorbed at its surface. In fact, small substances suspended in the liquid medium in the vicinity of the oscillating crystal may also contribute to impedance, as they modify the local shear force that the suspending liquid exerts on the quartz crystal. For a dilute suspension the contributions of individual particles are additive, and therefore our analysis is restricted to the excess shear force due to a single spherical particle located at an arbitrary distance above the plate. Three distinct cases are considered: (i) a limiting case of high solid inertia, whereas the heavy particle can be considered as stationary; (ii) a freely suspended particle of arbitrary mass, undergoing fluid-mediated time-periodic rotation and translation; and (iii) an adsorbed particle moving with the plate as a whole without rotation. For small-amplitude plate oscillations, the unsteady Stokes flow equations apply. We construct the series solution of these equations using the method of reflections, whereas its terms are written explicitly. Due to the exponential decay of the flow away from the oscillating plate, the truncated series containing only a few low-order terms shows excellent agreement with the rigorous numerical results for a wide range of particle sizes and separation distances. The present results support the notion that the hydrodynamic contribution of the suspended small substances to the measured impedance is non-negligible or even dominant.

We derive from particle-level dynamics a constitutive model describing the rheology of two-dimensional dense soft suspensions below the jamming transition, in a regime where hydrodynamic interactions between particles are screened. Based on a statistical description of particle dynamics, we obtain through a set of physically plausible approximations a nonlinear tensorial evolution equation for the deviatoric part of the stress tensor, involving the strain rate and vorticity tensors. This tensorial evolution equation involves singular terms usually not taken into account in phenomenological constitutive models, which most often assume a regular expansion in terms of the stress tensor. All coefficients appearing in the equation have known expressions in terms of the microscopic parameters of the model. The predictions of this microscopically grounded constitutive model have several qualitative features that are specific to the rheology of soft suspensions measured in experiments or simulations. The model shows a typical behavior of polymeric viscoelastic materials, such as normal stress differences quadratic in the shear rate $\dot{\gamma }$, as well as typical behaviors of suspensions of stiff particles, such as a particle pressure linear in $\dot{\gamma }$ and a zero-shear viscosity diverging at the jamming transition. The model also predicts a sharper shear thinning than other viscoelastic models at small shear rates, in qualitative agreement with experimental observations. Furthermore the shear thinning follows a critical scaling close to the jamming transition.