In this work, a nonequilibrium wall model is proposed for the prediction of turbulent flows experiencing adverse pressure gradients, including separated flow regimes. The mean-flow nonequilibrium is identified by comparing two characteristic velocities: the friction velocity ($u_{\tau }$) and the viscous-pressure-gradient velocity ($u_p$). In regions where the pressure-gradient velocity is comparable to the friction velocity ($u_p\sim u_{\tau }$), the near-wall turbulent closure is modified to include the effect of the pressure-gradient and convective terms. The performance of this wall model is evaluated in two canonical flows experiencing smooth body separation: the NASA/Boeing speed bump and the Bachalo-Johnson bump. Improvements in the predictive capabilities of the proposed model for the conventional equilibrium wall model are theorized and then demonstrated through numerical experiments. In particular, the proposed wall model is able to capture the onset of boundary layer separation observed in experiments or direct numerical simulations at resolutions where the equilibrium wall model fails to separate.

A universal theory of linear instabilities in swirling flows, occurring in both natural settings and industrial applications, is formulated. The theory encompasses a wide range of open and confined flows, including spiral isothermal flows and baroclinic flows driven by radial temperature gradients and natural gravity in rotating fluids. By employing short-wavelength local analysis, the theory generalizes previous findings from numerical simulations and linear stability analyses of specific swirling flows, such as spiral Couette flow, spiral Poiseuille flow, and baroclinic Couette flow. A general criterion, extending and unifying existing criteria for instability to both centrifugal and shear-driven perturbations in swirling flows is derived, taking into account viscosity and thermal diffusion, and guiding experimental and numerical investigations in the otherwise inaccessible parameter regimes.

Orbital sloshing is a technique to gently mix a container's liquid content and it is commonly used in fermentation and cell cultivation processes. Besides the rich wave dynamics observed at the interface, Bouvard et al. [Phys. Rev. Fluids 2, 084801 (2017)] unveiled the structure of the Lagrangian mean flow hiding in the fluid bulk. The latter flow shows a global toroidal (azimuthal) rotation codirected with the wave and nontrivial poloidal vortices near the contact line. Rotating sloshing waves are known to induce a net motion of fluid particles and hence a wave-averaged difference between the Eulerian flow—viscous streaming—and the Lagrangian flow, that is commonly referred to as Stokes drift. Nevertheless, discerning these two components in an experiment is challenging as they scale similarly with the forcing amplitude and frequency. Their relative contributions remain therefore unquantified, particularly for highly viscous fluids, for which prior analysis, based on inviscid arguments, fails. In this work, we construct a truncated asymptotic approximation of the problem, where the solution at each order is computed numerically to describe as accurately as possible the contact line region, otherwise analytically untractable. The results of this weakly nonlinear analysis in terms of first-order wave and second-order mean flow are then thoroughly compared with the experiments by Bouvard et al. [Phys. Rev. Fluids 2, 084801 (2017)], showing a remarkable agreement for off-resonance frequencies. When viscosity matters, our findings suggest that it is incorrect to attribute the poloidal patterns solely to the Eulerian streaming flow and that viscous corrections to the Stokes drift are equally important in the resulting mean Lagrangian flow.

Erosion and deposition are prevalent and integral phenomena in natural and industrial settings such as agriculture, dam construction, and fluid filtration, among others. As such, we develop a mathematical continuum model that exhibits the behavior of these processes in an idealized two-dimensional porous medium and that allows for predictions of values and limitations of parameters such as porosity, shear stress, particle concentration, and porous medium deformation. By exploiting established governing equations such as Darcy's law, advection-diffusion-reaction, and Navier-Cauchy equations, and then simplifying calculations via nondimensionalization and asymptotic analysis based on the small aspect ratio of the medium, we successfully model from a macroscale perspective how the erosion and deposition processes alter the internal morphology of an elastic porous medium. The essence of our results, beyond displaying how the medium evolves subject to the complex interplay among multiple parameters, covers how the total volume of the medium changes as we vary quantities of coefficients that measure the tendency of particles to erode or become deposited based on the physical properties of those particles and of the fluid and medium in which they travel.

We numerically investigate the effects of mixed convection on the nonlinear dynamics and heat transfer of the flow through a two-dimensional wavy channel with varying degrees of symmetry at Reynolds numbers ranging from 100 to 2200. Our findings reveal that the introduction of mixed convection significantly alters the routes to chaos of the system compared to its isothermal counterpart. We demonstrate that (i) a symmetric channel can host both the Ruelle-Takens-Newhouse and degenerate period-doubling routes to chaos, (ii) an asymmetric channel can host only the latter route, and (iii) a semiwavy channel can host no routes to chaos under the present conditions. Crucially, the Pomeau-Manneville intermittency route to chaos, previously observed in the isothermal system, is absent under mixed convection. Furthermore, our analysis of the heat transfer characteristics reveals quadratic and cubic relationships for the Nusselt number and the thermal performance factor, respectively, as functions of the Reynolds number. This study provides valuable insights for understanding and manipulating chaotic flow in wavy channels under mixed convection, with potential applications for enhancing the performance of thermal management devices.

The Faraday instability has been extensively studied in bounded containers but only recently has research on this phenomenon in flexible domains been conducted. Here, we study floating liquid droplets with Faraday waves excited on their surface, which undergo a slow time evolution toward a stable noncircular shape. We develop a theoretical model for the evolution of the boundary of the droplet, thus allowing us to simulate its full transient motion toward steady state. By changing the forcing frequency and amplitude of our system, we observe a variety of stable droplet shapes. We experimentally measure the geometrical properties of these droplets and conditions under which different shapes are stable, which match our theoretical predictions well. Interesting transient behavior such as hysteresis is also discussed, where the final droplet shape depends on its previous shape. Finally, we touch upon droplets that do not reach a steady state shape, instead oscillating periodically in time or rotating at a constant angular velocity.

Viscoelastic shear flows support additional chaotic states beyond simple Newtonian turbulence. In vanishing Reynolds number flows, the nonlinearity in the polymer evolution equation alone can sustain inertialess “elastic” turbulence (ET) while “elasto-inertial” turbulence (EIT) appears to rely on an interplay between elasticity and finite-$Re$ effects. Despite their distinct phenomenology and industrial significance, transition routes and possible connections between these states are unknown. We identify here a common Ruelle-Takens transition scenario for both of these chaotic regimes in two-dimensional direct numerical simulations of FENE-P fluids in a straight channel. The primary bifurcation is caused by a recently discovered “polymer diffusive instability” associated with small but nonvanishing polymer stress diffusion which generates a finite-amplitude, small-scale traveling wave localized at the wall. This is found to be unstable to a large-scale secondary instability which grows to modify the whole flow before itself breaking down in a third bifurcation to either ET or EIT. The secondary large-scale instability waves resemble “center” and “wall” modes, respectively—instabilities which have been conjectured to play a role in viscoelastic chaotic dynamics but were previously only thought to exist far from relevant areas of the parameter space.

We theoretically and experimentally study the propagation of a bubble in a Hele-Shaw cell under a uniform background flow at low Reynolds number. We consider situations where both the capillary number $\mathrm{Ca}$ and the ratio $\epsilon$ of the cell height to the bubble diameter are small. The bubble is then flattened into a pancake-like shape, with an approximately circular profile when viewed from above, and thin liquid films lie between the bubble and the cell walls. Bubble motion and deformation are determined by an interplay between the Hele-Shaw viscous pressure, the pressure drop due to the thin films, and the capillary pressure due to the in-plane curvature of the apparent bubble boundary. Numerical and asymptotic results indicate that, with all other parameters held constant, the in-plane aspect ratio of the bubble varies nonmonotonically with its size, with smaller bubbles being flattened in the flow direction and larger bubbles being elongated. These theoretical predictions are validated experimentally, as well as the expected loss of fore-aft symmetry of the bubble shape due to differences between the advancing and retreating menisci. Measurements of the bubble velocity are also shown to agree well with theoretical predictions. We extend our results to describe a bubble moving in an inclined cell due to buoyancy. Experimental results for the bubble velocity, as well as results found in the literature, are shown to collapse under a scaling motivated by the theory. As in the case of a horizontal Hele-Shaw cell, we find that, with increasing bubble size, the bubble shape can switch from being flattened to elongated in the direction of motion.

Experimental investigations of the exit dynamics of a horizontal cylindrical object were performed in water and silicone oil (50 cS). The fully immersed cylinder was initially at rest in a still fluid tank before being pushed (or pulled according to the measurement procedure) upwards at a constant velocity. The cylinder geometry was chosen to approach two-dimensional conditions in the transverse direction. First, we demonstrate that these conditions are better satisfied for a large aspect ratio cylinder equipped with vertical end plates. Second, the influence of the initial depth on the liquid entrained and the wake generated by the cylinder is discussed. It is shown that the wake destabilizes in the form of symmetry breaking in the case of water, while it remains symmetrical in the case of oil even for long travel in the bath. The deformation of the interface is found to be independent of the starting depth when the starting depth is larger than six times the cylinder diameter. In the present case, this criterion reflects also the finite acceleration of the cylinder to reach the determined constant exit velocity. Measurements in a range of exit speeds between 0.1 and 1 m/s indicate that the thickness of the liquid above the cylinder when the cylinder starts crossing the interface increases with the speed according to a logarithmic law of the Froude number. During the subsequent drainage, the evolution of the coated liquid thickness is found to first decrease exponentially with time just after the crossing of the interface. At later times, a change of regime occurs and the drainage follows the inverse of the square root of time irrespective of the crossing speed. Finally, the force necessary to maintain a constant exit speed during the motion of the cylinder inside and outside the bath is analyzed. This global measurement of the entrained liquid confirms the square root scaling of the thinning with time during the drainage process.

The current research was conducted to investigate bedload transport in sparsely vegetated channels through theoretical derivation. Most research on bedload transport in vegetated channels has relied on theories developed for bare beds. The classical Engelund formula is highly effective in predicting bedload transport rate on bare beds, but is based on four oversimplified assumptions. Meng et al. [Int. J. Sediment Res. 31, 251 (2016)] modified those oversimplified assumptions and proposed an improved version of the Engelund formula for bare beds. In this work, the improved Engelund formula was successfully extended to sparsely vegetated channels through the redefinition of key parameters. For instance, we adjusted the number of moving sediment particles per unit bed area and the effective Shields number (dimensionless bed shear stress acting on sediment movement in vegetated channels) to account for the impact of emergent rigid vegetation. Parameter calibration was accomplished using published data from a variety of reliable sources, ensuring the accuracy and applicability of the extended model. The prediction results correlated well with measured data across a broad range of bedload transport rates, particularly in scenarios of medium and high bedload transport rates.

The perturbation evolution of both free and forced falling jets has been studied in the presence of insoluble surfactants. The effects of gravity, surface tension, and Marangoni stress on the nonparallel basic flow are investigated. On the basis of the steady basic flow, the maximum growth rate and corresponding leading frequency of the perturbation of the free jet are calculated. For globally stable or critical jets, their responses to the external forcing with different frequencies are further investigated. The mechanisms of the nonparallel effect of the falling jet due to gravitational stretching and the inhomogeneous distribution of the surfactants in the linear stability stage are highlighted. The results show that both surfactant and gravity act to stabilize the jets and that gravity also causes the optimal forcing frequency of the stable basic jets to be greater than their intrinsic frequency. However, the optimal forcing frequency of the critical jets is always equal to their intrinsic frequency, which is similar to the resonance behavior.

The oscillatory boundary layer over an array of wall-mounted flexible filaments is studied using a penalty-immersed boundary method to explore the dynamic interaction between the boundary layer and filaments in two-dimensional (2D) flows. It is found that as the bending rigidity increases, the motion of the filament exhibits two patterns, undulation and sway. The undulating pattern exhibits a shorter wavelength of filament displacement and a reduced average filament height. In the swaying pattern, resonance occurs when the flow frequency is close to the natural frequency of the submerged filament, resulting in a peak value in the mechanical energy of the filament. When shifting the profile of the root mean square of the disturbance velocity downwards by the average height of the filament, the curves collapse for different filament parameters and the smooth wall, indicating that the presence of filaments can be modeled as an offset on the bottom boundary. A complex-valued slip length is introduced at the incoming flow frequency to quantify the velocity-velocity gradient relation near the filament tip, which takes into account both the magnitude and the phase lag of the slip velocity. Although this slip length varies dramatically inside the filament layer, it reaches a plateau at the upper edge of the filaments, with a smaller absolute value than those of the smooth wall. This finding provides insight into modeling the effective boundary condition of the filament-attached wall. Furthermore, the three-dimensional (3D) effects of the finite-span filaments are discussed. The 3D vortex has a U shape for very small aspect ratios, which transits to a ring-shape with the increasing aspect ratio. The spanwise range of the 3D effects is approximately one filament length on each side, and these effects can be neglected for the aspect ratios greater than 2, 4, and 8 in swaying, periodic undulating, and aperiodic undulating patterns, respectively.

In many thermal convection studies, enclosure inclination against gravity (measured as $\mathrm{\Phi }$) changes both flow features and heat transport. We numerically investigated thermal convection in a quasi-two-dimensional circular enclosure in the range ${10}^7\le \text{Ra}\le {10}^{10}, 0.1\le \text{Pr}\le 15$, and $0\le \mathrm{\Phi }\le \pi /2$, where $\text{Ra}$ is the Rayleigh number and $\text{Pr}$ is the Prandtl number. The dimensionless heat transport follows a nonmonotonic trend due to the change in plume nature near the walls, elimination of secondary rolls, core bulk instabilities, and flow stratification. Our scaling analysis shows dimensionless heat transport is proportional to ${\left(\text{Ra}\text{cos}\mathrm{\Phi }\right)}^{1/3}$ at small $\mathrm{\Phi }(0\le \mathrm{\Phi }<\frac{\pi }{9})$ and to ${\left(\text{Ra}\text{sin}\mathrm{\Phi }\right)}^{1/4}$ at large $\mathrm{\Phi }(\frac{\pi }{9}\le \mathrm{\Phi }\le \frac{\pi }{2})$. In contrast, the Reynolds number based on the global root-mean-square velocity shows a continuous decrease with $\mathrm{\Phi }$ due to the reduction in buoyancy fluxes, which convert the available potential energy into kinetic energy. Though the buoyancy flux decreases, convection persists through irreversible mixing, which is the dominant mechanism in inclined thermal convection.

The amplitude modulation phenomena, defined originally by Mathis et al. [J. Fluid Mech. 628, 311 (2009)], corresponds to a unique nonlinear interaction between Reynolds number $\left({\text{Re}}_{\tau }\right)$ dependent large-scale motions and ${\text{Re}}_{\tau }$-invariant inner-scale motions observed in canonical wall-bounded flows. While similar nonlinear interactions have been quantified previously in non-canonical wall-bounded flows, linking them solely to amplitude modulation is questionable due to the fact that each non-canonical effect is associated with distinct variations in the energies of both the large and inner scaled motions. This study revisits analysis of nonlinear triadic interactions, with consideration to various non-canonical effects, by analyzing published hot-wire datasets acquired in the large Melbourne wind tunnel. It is found that triadic interactions, across the entire turbulence scale hierarchy, may become statistically significant with increasing intensity of non-canonical effects such as wall roughness, pressure gradients, and spanwise or wall-normal forcing (when compared relative to their respective canonical baseline cases at matched ${\text{Re}}_{\tau }$). This stands in contrast to previous observations made in canonical flows, where only the interaction between inner scales and inertia-dominated large scales was considered dynamically significant for increasing ${\text{Re}}_{\tau }$. The implications of these findings are discussed for near-wall flow prediction models in non-canonical flows, which should take into account all nonlinear interactions coexisting in wall-bounded flows.

In this paper, we provide the semianalytical solution of the temperature and flow fields of a fluid confined in a narrow space between two parallel plates. The temperature increase is triggered by photothermal effects of fluids and/or boundaries due to the absorption of a focused Gaussian beam irradiated perpendicular to the fluid film, and then the temperature variation induces the flow fields through a buoyancy force and/or thermo-osmotic slip. The semianalytical solution to this optothermal fluidic system is validated by comparing with the results of numerical simulation, and is applied to typical optothermal fluidic problems. In particular, the optothermal trap of nanoparticles observed in our previous experiment [Tsuji et al., Electrophoresis 42, 2401 (2021)] is investigated in terms of thermophoretic force and flow drag that are obtained semianalytically. The semianalytical solution can be shared through open-source codes that are available to researchers without the background of fluid mechanics.

A detailed description of coupled heat and momentum transfer in a one-dimensional porous medium saturated by a supercritical fluid subject to a heat flux at one of its boundaries is reported in this study. The derivation is performed with an asymptotic analysis of the linearized macroscopic mass, momentum, and energy equations, assuming a van der Waals supercritical fluid and the mean-field theory, considering Darcy's law for momentum transfer. Three regimes of heat transfer separated by two crossovers are highlighted. The first regime, far enough from the critical point (CP), corresponds to the classical piston effect (PE), as in a plain fluid. While nearing the CP, a first crossover is found, giving rise to a second regime in which the PE in the bulk fluid is supplemented by a temperature gradient that results from a pressure gradient buildup. Below this crossover, the critical speeding up by thermocompression of the bulk stops and a porous saturation of the characteristic heat transfer timescale is reached. Closer to the CP, a second crossover is identified that corresponds to the presence of a viscous pressure drop in the whole domain. Below this second crossover, the PE is faded away and, in this third regime, heat transfer returns to a classical diffusive process. The two crossovers are characterized by a single parameter that is the ratio between the acoustic time (i.e., the sound wave travel time through a pore) and the pore-scale viscous diffusion time, namely, the acoustic pore Reynolds number.

This paper demonstrates the efficient extraction of unstable recurrent flows from two-dimensional turbulence by using nonlinear triads to diagnose recurrence in direct numerical simulations. Nearly recurrent episodes are identified from simulations and then converged using a standard Newton-GMRES-hookstep method, however with much greater diversity than previous studies which performed this “recurrent flow analysis.” Unstable periodic and relative periodic orbits are able to be identified which span larger values of dissipation rate, i.e., corresponding to extreme bursting events. The triad variables are found to provide a more natural way to weight the greater variety of spatial modes active in such orbits than a standard Euclidian norm of complex Fourier amplitudes. Moreover, the triad variables build in a reduction of the continuous symmetry of the system which avoids the need to search over translations when obtaining relative periodic orbits. Armed with these orbits we investigate optimal weightings when reconstructing the statistics of turbulence and suggest that, in fact, a simple heuristic weighting based on the solution instability provides a very good prediction, provided enough dynamically relevant orbits are included in the expansion.

This paper briefly reprises, with added commentary, a talk I gave on transport and flows within living cells at an APS-DFD meeting. Directed transport is especially important in large cells, such as eggs where developmental factors need to be properly localized, and early embryos whose organelles and genetic material must be properly positioned before cell division. I discuss two cases—a nematode single-cell embryo and a fruit fly egg cell—where advances in mathematical modeling and large-scale simulation of fluid-structure interactions have helped us understand fundamental mechanisms of force transduction and self-organization within the cell.

Cloud droplets grow via vapor condensation and collisional aggregation. Upon reaching approximately $\approx 100\mu \mathrm{m}$, their inertia allows them to capture smaller droplets during descent, initiating rain. Here we show that raindrop formation is not primarily governed by gravity or thermal diffusion, but by a critical range of drop sizes ($3–30\mu \mathrm{m}$) where collisions are largely ineffective and controlled by van der Waals and electrostatic interactions. We identify four pathways to rain. The coalescence pathway, which is slow, involves the broadening of the drop size distribution across the $3–30\mu \mathrm{m}$ low-efficiency gap through collisions, until enough large individual droplets achieving efficient collisions have formed. The mixing pathway, which is faster, requires mixing at the cloud top with drop-free, cold, humid air to create locally supersaturated conditions that grow droplets above the low-efficiency gap. The electrostatic pathway bypasses the gap through a static vertical field creating attractive interactions between droplets. The turbulence pathway relies on air turbulence to bring the droplets together at an increased rate, but we show that this pathway is unlikely. For all dynamical mechanisms, we demonstrate that the initiation time for rainfall occurs at the crossover between the broadening of the drop size distribution and the emergence of individual droplets large enough to trigger the onset of the rainfall cascade.

Two different adjoint-based approaches are developed here for gust mitigation of two-dimensional or three-dimensional wing models in oscillatory heaving-pitching motion. One approach is based on a full-order model (FOM), i.e., Navier-Stokes equations, where noncylindrical calculus is implemented for moving boundary effect, and the other is based on a global reduced-order model (ROM), which models fluid flow and moving solid boundary in a global framework. When the lift performance was affected by either streamwise or transverse gusts, an objective function was designed to reduce the oscillation and keep the same lift to maintain a stable flight in gust. The goal was achieved by the optimal control of wing motions using the adjoint-FOM approach or the adjoint-ROM approach. In the study, the streamwise gust was successfully mitigated by reducing the amplitude of the heaving-pitching motion, and the transverse gust was mitigated by reducing the oscillation amplitude and decreasing the mean angle of attack at the same time. The adjoint-FOM approach provides better accuracy and can handle stronger gusts at the cost of longer computational time. The adjoint-ROM approach has lower accuracy and can only handle two-dimensional cases with weaker gusts, but it has its own advantage of requiring much less computational time and makes real-time control possible.