A key aspect in understanding pressure-driven flows of non-Newtonian fluids in narrow and confined geometries is the relationship between the flow rate and pressure drop. Using the Lorentz reciprocal theorem, we derive a closed-form expression for the flow rate-pressure drop relation of complex fluids in narrow channels of arbitrary shape, which holds for a wide class of viscoelastic and shear-thinning constitutive models. For the weakly non-Newtonian limit, our theory provides the first-order non-Newtonian correction for the flow rate-pressure drop relation solely using the corresponding Newtonian solution, eliminating the need to solve the non-Newtonian flow problem.

Even after one century of research on particle resuspension the multiphysics mechanism for it remains unclear. In this Letter we show evidence for the inter-particle collision in a monolayer deposit with an intermediate surface coverage. Previously, the inter-particle collision was neglected in monolayer deposits and was considered only in multilayer beds due to lack of evidence. This experimental work indicates that particle cluster resuspension plays an important role in the early stage of resuspension. This explains the strong bimodal character of the resuspension curve, which shows the remaining particle fraction as a function of the flow velocity.

Flow and retention of polymer in porous media result in an unexpected reduction in medium permeability. Our experiment and simulation of polymer retention show that these changes are a direct consequence of pore blockage and diversion of flow through the medium. Despite the complex changes in flow after polymer retention, we introduce a simple scaling for the distribution of pore-level velocities based on the bulk permeability of the medium.

Due to their sizeable Kolmogorov n-width, travel-wave problems have brought critical challenges to conventional model reduction techniques. This study aims to provide new insights into this problem by exploiting the Radon cumulative distribution transform (R-CDT) that emerged in the sector of computer vision science. By virtue of the unique property that nonlinear invertible R-CDT renders both traveling and scaling components into amplitude modulations, a substantial model-reduction is achieved in the R-CDT space, while sustaining high accuracy. The method is parameter-free and data-driven, which lends itself to problems regardless of the dimensions or boundary conditions.

The Rayleigh-Taylor (RT) instability occurs at the interface between two fluids of different densities when the lighter fluid pushes against the heavier. For example, RT instability fingers are evident in the Crab Nebula. It plays a critical role in all known forms of fusion. The variable density model (VDM), which is comprised of a set of partial differential equations, best models the flow in the mixing layer. This paper shows that the VDM can be exactly transformed into the inhomogeneous, incompressible, forced Navier-Stokes equations.

In 1935, G. I. Taylor invoked rotational symmetry to derive a remarkable formula for the turbulent dissipation rate. That derivation, though ingenious, leaves it unclear if the formula truly conforms with rotational symmetry. We use the machinery of Lie groups to furnish a rigorous derivation of Taylor’s formula under rotational symmetry and also under a symmetry not considered by Taylor, reflectional symmetry.

We study the dynamics of a microswimmer near a wall with arbitrary curvature using theory and lattice Boltzmann simulations. The results are presented using several measures with experimental relevance. Extending the previous works on swimmer dynamics near a flat wall, we comprehensively explore the swimmer dynamics near flat, concave, and convex walls. We find that swimmers exhibit a greater affinity towards a concave boundary compared to a convex boundary. In addition, the combined effect of convex and concave walls is studied by confining the swimmer in an annulus.

We study how helical swimmers move across a viscosity gradient, motivated by the need to understand how such heterogenous environments affect the motion of microorganisms. We find that the swimmer’s speed can be either decreased or increased while crossing the viscosity gradient, depending on the orientation of the tail and the gradient of viscosity. Our experimental findings are sustained by good agreement with a resistive-force based model.

The combustion of aluminum particle clusters in shocked flows is studied with two-dimensional numerical simulations. These simulations examine, for the first time, aspects of the vaporization and burning of molten aluminum particle clusters that are markedly different from an isolated burning aluminum particle. The flame-structure around a particle within a cluster is found to vary along the flow direction: particles at the cluster front end undergo kinetically limited combustion with the formation of a wake flame, while particles located downstream in the cluster burn with an envelope flame indicating combustion limited by transport and mixing.

We previously derived the two-temperature Navier-Stokes system (a set of compressible Navier-Stokes equations with the translational and internal temperatures) for a polyatomic gas with slow relaxation of the internal modes from the ellipsoidal statistical model of the Boltzmann equation. In this paper, the appropriate boundary conditions for the two-temperature Navier-Stokes system are derived. The results are presented in a form that is applicable to practical applications immediately.

Developing stages of horizontal convection observed during transitions from conduction to thermally equilibrated convection states are studied with visualization experiments imposing horizontally differential heating at the top of low-temperature water. Due to the absence of destabilizing thermal sources, convective rolls, which are localized on the horizontal plane on which differential heating is imposed, are formed only by the baroclinic torque driving force against a braking force due to stable temperature stratification. We find a nondimensional parameter for the balance of the braking force relaxing with time and the baroclinic torque driving force.

A cavitation bubble is harmful to machines as it issues a fast microjet when it collapses near the boundary. This work focusses on a bubble located in a corner of a wall and a free surface, where both boundaries alter the jet direction. We present a simplified model to describe the jet direction as a function of the bubble location, which agrees with that measured in high-speed observation. This may give some insight for avoiding cavitation-induced damage in practical designs.

Minimizing the contact between impacting droplets and solid substate is useful in many applications, for example, anti-icing. This study shows that a simple crater-like decoration on a substate can reduce contact area and time simultaneously and cut the overall contact up to 75%. The novel simulation model used in this study has been validated with experiments and shows a great advantage in accurately measuring the dynamic wetting area between liquid and substrate, which can only be inferred with much difficulty in experiments.

An efficient actuation method for millimetric droplets is described: Single droplets are driven on a liquid infused surface by a small bead that acts as a carrier, like a rickshaw. When the bead is moved at a fixed velocity the droplet follows its trajectory, up to a critical value of the velocity at which the bead and the droplet lose contact. The critical velocity is predicted from a balance between the bead/droplet adhesion force and the friction acting on the droplet where it is in contact with the substrate.

When a light fluid is continuously released from the top (as a fountain) or from the bottom (as a plume) into a box with a top opening, a buoyant layer of constant thickness and density forms under the ceiling at steady state. Both configurations have been investigated using theoretical approaches and small scale air-helium experiments. As a practical application, for a fixed buoyant flux, the fountain and the plume configurations have been compared with respect to their mixing efficiency.

Particles falling uniformly through a Rayleigh-Bénard cell have a profound influence on the stability of the system. Mechanically, they exert a stabilizing effect akin to that of the solid phase in a porous medium. Their temperature, however, can markedly affect the undisturbed temperature distribution of the fluid phase with unexpected effects on the stability threshold.

We study the long-wave instability of a falling film of the Oldroyd-B fluid. The weighted residual method is adopted to model the film dynamics in both linear and nonlinear regimes. The mechanism of the viscoelastic effect on the instability is explored within the framework of the Whitham wave hierarchy theory. We further analyze the film evolution and the traveling waves by means of nonlinear simulations.

Active flow control with microjets in crossflow is a promising technology to improve the performance of many engineering flows. Predicting effective placement for the microjets at the surface of the aerodynamic model remains an unsolved challenge due to the complex interactions between the jets and the main flow. We propose and demonstrate a fully experimental, model-free approach using a solenoid array and a genetic algorithm to find a highly effective actuator pattern for drag reduction in the flow over a simplified fuselage afterbody, deploying thousands of actuator configurations in a single experiment and reaching a configuration that achieves a 10% reduction in drag.

Drying of droplets on inclined surfaces is relevant to applications such as ink-jet printing, spray coating, and crime-scene reconstruction. We develop a lubrication-theory based model to investigate the effect of substrate inclination on the evaporation of pure-solvent and particle-laden droplets on smooth and rough inclined substrates. We find that the effect of inclination on evaporation mainly depends on substrate roughness and the Bond number. Our predictions qualitatively agree with previous experimental work and our model can be easily extended to more complex situations such as multiple droplets evaporating on inclined substrates.

We study the relaxation dynamics of a fluid-filled blister between an elastic sheet and a porous substrate using laboratory experiments and a mathematical model. The dynamics are controlled by the deformation of the elastic sheet, the viscous stresses in the pores, and the capillary pressure at the liquid-air interface due to imbibition. We identify two regimes of drainage, where for thick sheets and more permeable substrates, drainage is primarily due to the stresses in the deformed elastic sheet, and for thin sheets and less permeable substrates, drainage is driven by the imbibition of the liquid into the pore space.

Rigid plate-like particles displaying interfacial slip can attain a constant orientation in a shear flow when the slip length is sufficiently large. But actual thin particles such as single-layer graphene are prone to bending deformations when exposed to shear stress. To study the effect of bending deformation on the particle’s stable orientation, we develop a two-dimensional fluid-structure interaction model. We find that (i) a stable alignment occurs even for relatively flexible particles, and that (ii) edges effects on the shape of the plate are important for values of the length-to-thickness aspect ratio as large as 100.

Clustering of small rigid spherical particles in particle accumulation structures (PAS) of various shapes is found with highly resolved numerical simulations in a thermocapillary liquid bridge at a Prandtl number of 68. The intricate Kolmogorov–Arnold–Moser (KAM) structure of the fluid flow is unraveled for several Reynolds numbers for flows periodic in time and space. For these flows, a rich variety of periodic and quasiperiodic attractors for particles nearly density-matched to the fluid is found near closed streamlines and KAM tori approaching the free surface closely. A large parametric study finds the PAS dependence on particle size, particle-to-fluid density ratio, and Reynolds number.

When a high-speed gas flow destabilizes a liquid jet into a spray (atomization), the gas-liquid interface undergoes instabilities that play a key role in the breakup events. We use high-speed backlit imaging to track the maxima of such interfacial perturbations as they get stretched and accelerated by the gas phase. The spatial gradients of the local ensemble-averaged velocity statistics exhibit two regimes with respect to the gas Reynolds numbers that are in good agreement with changes in atomization regimes.

For the first time, the lift force on a pair of obstacles placed side-by-side within a granular flow is studied experimentally. Attraction or repulsion exists between the obstacles depending on the flow velocity and the distance separating them. We found an interesting empirical relation between the lift force and the flow velocity around the obstacles. Our analysis supports the idea that the granular system behaves like a pair of hot intruders within a Newtonian fluid flow with temperature-dependent viscosity.

A droplet exposed to a high-speed gas flow is subject to a violent fragmentation, dominated by a widespread mist of multiscale structures that introduce significant complexities in numerical studies. The present work focuses on capturing all stages of the aerodynamic breakup of a waterlike droplet under the shear-induced entrainment regime. The numerical investigation is conducted within a physically consistent multiscale framework, which provides insight into the mist dynamics and the distribution of the produced secondary droplets under different postshock conditions.

Liquid-gas front propagation in disordered media exhibits unique behavior during a repeated series of drainage-imbibition displacements. Such complex behavior in a disordered media can be simplified to a single mesa-shaped defect, which provides new insight into the collective behavior at the macro-scale. We show how the morphological difference in imbibition and drainage is affected by the capillary number and wetting properties.

Since industrial fluidized-bed reactors typically operate with polydispersed particles, approximating such reactors as the superposition of corresponding monodispersed fluidized beds would greatly simplify their design and operation. To examine the validity of this superposition, we evaluate the effects of bidispersity by comparing three-dimensional liquid-solid monodispersed and segregated bidipsersed fluidized beds. This work demonstrates that, despite the clear segregation into layers that behave like monodispersed beds, the transition region is governed by complex bidispersed mechanisms that cannot be explained in terms of the particle behavior in the segregated layers.

The formation of an axisymmetric monolayer of dense particles at a liquid interface is explored in order to study the interaction between numerous objects of different sizes randomly distributed on a liquid surface. The individual motion of each bead cannot be solved but the overall clustering can be described statistically. The clustering dynamics of this system with a long-range interaction varies during the aggregation process. The cluster-size distribution evolves with a self-similar mechanism and we observe a well-defined transition between two aggregating regimes that we can characterize.

The kinetic energy in two-dimensional turbulence evolves towards larger sizes, eventually condensing into quasi-steady states of a few vortices at the scale of the simulation domain. When this happens in decaying turbulence, the flow initially segregates into a background of fast-moving small vortices and a system of larger ones that move more slowly. The slow component is shown here to form a low-energy ‘stochastic crystal’ in which vortices of opposite sign locally screen each other. Screening has long been conjectured for turbulence, and its mechanism is documented here, but global ordering is believed to be a new observation.

We extend the bridging Partially-Averaged Navier-Stokes (PANS) equations model to variable-density flow and develop a scale-dependent closure for complex flows. This includes $a$ $priori$ testing to develop guidelines for the efficient selection of parameters controlling the model resolution (range of resolved scales). Accuracy of the model is evaluated with simulations of two benchmark transitional problems: the Taylor-Green Vortex and Rayleigh-Taylor flow. The results show that the model can accurately and efficiently predict the selected flows while resolving only a fraction of the turbulence field.

We conduct direct numerical simulations of the viscous-stirring von Karman turbulence which show that it undergoes quasiperiodic cycles. The quasiperiodicity can be explained by energy exchange between toroidal and poloidal components. The proposed scenario of the quasiperiodic energy cycle may persist at higher Reynolds numbers and in inertial-stirring von Karman flow.

Wall-attached dynamic free-slip surfaces effectively shift the near-wall transverse vorticity field and associated turbulent shearing motions away, creating a locally relaminarized zone in the near-wall region of the turbulent boundary layer.

Turbulence in a nocturnal stably stratified flow draining from a mountain range was captured using a probe system consisting of sonic and hot-film anemometers that communicate with each other through a neural network for optimal operation without any human intervention. This unique ‘Combo’ system allowed probing turbulence continuously down to energy dissipation scales, at Taylor Reynolds number greater than 1200. The data analyses, together with direct numerical simulation, reveal that, contrary to the Kolmogorov Self-Similarity Hypothesis, turbulence at dissipation scales is anisotropic, suggesting a new line of inquiry on turbulence in stable atmospheric boundary layers.

Correlations between the properties of a rough surface and their associated drag are a very useful tool in engineering. Here, we assess the effect of different scales of roughness by numerically simulating the flow over surfaces constructed by band-passing the spectral content of a scanned grit-blasted surface. Although the velocity fluctuations are found overall to be resilient to the changes, we find existing drag correlations to be only qualitatively useful, while dispersive stresses (associated with mean flow inhomogeneity) are shown to depend on the roughness spectral content.

Modification to the structure of wall-bounded turbulence due to the presence of porous walls has been investigated in the low and high supersonic regime. For sufficiently high degrees of wall permeability, streamwise-traveling surface waves are triggered and stay confined in the buffer layer region. These waves yield a sinusoidal modulation of the near-wall turbulent ejection and burst events.

To study the dynamical properties of plane Couette turbulence, this paper describes unstable periodic orbits (UPOs) in a large eddy simulation (LES) system with a Smagorinsky-type eddy viscosity model. At a moderately high Reynolds number, the UPO of the present study possesses spanwise vortices in the central region of the channel, which seem to be caused by a streak instability. These stretched vortices are shown to enhance transfer of the streamwise turbulent momentum, as in developed near-wall turbulence.

The effect of Coriolis forces on the turbulent flow in an elliptical pipe subjected to spanwise rotation has been studied using direct numerical simulations (DNS). In response to the system rotation, large-scale secondary flows appear in the cross-stream plane as a pair of counter-rotating vortices, which significantly impact the turbulence statistics and structures of the flow. The characteristics of the turbulence field is investigated in both physical and spectral spaces through analyses of the first- and second-order statistical moments, as well as the budget balance of the Reynolds stress transport equation and coherent flow structures.

For three decades there have been speculations about the existence of conformal invariance in two-dimensional turbulence and possible implications thereof. These speculations have been confirmed by numerical experiments. However, there is a scarcity of relevant analytical studies on this topic. In our work we analyze the underlying equation for the one-point probability density function of a scalar in two-dimensional turbulence. We derive conditions under which the probability measure is conformally invariant and show that with this transformation certain statistics of non-homogeneous fields can be derived based on solutions of the homogeneous one.

In a turbulent jet flow, finite-time Lyapunov exponents gauge the exponentially fast spreading of fluid parcels. To observe their fine structure, we moved our Particle Image Velocimetry and Laser-Induced Fluorescence cameras with the mean flow. The resulting remarkable shapes in the figure are linked to the organization of a dispersed fluorescent tracer.

The Reynolds-averaged Navier-Stokes (RANS) unclosed terms can be reconstructed by the local artificial neural network (LANN) based on the local coordinate system which is orthogonal to the curved wall. The LANN model performs better than the Global artifical neural network (GANN), Spalart-Allmaras (SA), and Shear Stress Transport (SST) $k-\omega$ models in the predictions of the average velocity, wall-shear stress, and average pressure in the flows over periodic hills. The LANN framework has a great potential to be applied to complex wall-bounded turbulent flows over curved walls.

Two interwoven helical vortices of the same circulation and pitch display a rich variety of dynamics. Using simplified models of straight vortices, ring vortices, and helical filaments, we introduce dynamical systems of a few degrees of freedom which we analyze in terms of orbits in phase spaces structured by hyperbolic and elliptic points. Possible inviscid motions, namely leapfrogging, overtaking and fluttering, are systematically described as a function of vortex pitch, core size, and initial configuration.

This experimental study characterizes vortex shedding from a sinusoidally pitching hydrofoil at high Reynolds number, reveals the effects of pitching amplitude, reduced frequency, and Reynolds number on the dynamic force responses beyond the linear inviscid theory, and sheds light on the correlation between vortex shedding regimes and dynamic force responses for a high Reynolds number pitching hydrofoil.

Oscillating large-scale flows observed in atmospheres are driven by turbulently generated internal gravity waves. We experimentally investigate this mechanism by studying the interaction between a turbulent layer and a stratified layer. The wave field is described, and a wave-driven flow is observed and analyzed, although it exhibits no oscillating dynamics.

In temperate lakes, early springs typically lead to a weak thermal stratification involving water both above and below the temperature at which the density maximum occurs. This implies that mixing of two parcels with the same density, but different temperature, can lead to the creation of denser fluid: a phenomenon known as cabbeling. Here we document the nature of the three-dimensionalization of shear instability at moderate Reynolds number in the cabbeling regime of freshwater.

The present study explores the influence of conduit tilt as well as top and side wall confinements on planar hydraulic jumps by means of extensive experiments and theoretical analysis. The observations are consolidated as a phase diagram that identifies the natural jump regime bounded by full bore flow, subcritical flow, and supercritical flow throughout the conduit and also shows the presence of multiple hydrodynamic states for a certain range of input parameters. Upslope flow is found to exhibit unique instabilities and undergo a hysteretic excursion to regain the initial stable configuration. The jump induced hysteretic flow in sloping conduits is reported for the first time.

The resolvent framework for the Navier-Stokes equations with the Boussinesq approximation was applied to a stratified turbulent boundary layer. The results show that despite using only a very limited range of representative scales, the resolvent model was able to reproduce the relative magnitude of turbulence intensities and the balance of the energy budget as well as provide meaningful analysis of structures in the flow. The resolvent response modes were able to predict the relative variation in turbulence intensities as a function of wall-normal distance and Richardson number (Ri${}_{\tau }$) for the Ri${}_{\tau }$ under consideration in this study.

In thin films flowing down the underside of an inclined planar substrate, surface topology is known to evolve towards a spanwise structuring of rivulets. While experiments imply a connection between long-term spanwise structuring and primary instabilities (PI) of the film surface at low Reynolds number (Re), this connection is not conclusive if a larger parameter space of Re and Kapitza number (Ka) is considered. Using an integral boundary layer model for falling liquid films and varying imposed initial conditions, Re, Ka, and wall inclination, we numerically investigate long-term rivulet evolution and its connection to PI, obtaining excellent concordance with previous experimental data.