Modeling the effect of subgrid-scale processes is one of the main obstacles in the accurate prediction of multiscale systems. An investigation considers how machine learning methods can be applied to model subgrid-scale processes and integrated within sequential data assimilation methods. It is found that the use of machine-learning-based closure modeling in conjunction with data assimilation improves the prediction of multiscale systems and can be considered a promising approach to numerical weather prediction tasks in the age of data.

The weights of a deep neural-network model are optimized over the governing flow equations to provide a model for the subgrid-scale stresses in a turbulent plane jet. The training, which is done in $aposteriori$ large-eddy simulations (LES), solves the adjoint Navier-Stokes equations to provide end-to-end sensitivities. Out-of-sample testing on multiple dual-jet configurations confirms that the required grid resolution is half that needed by dynamic models for comparable accuracy. The coupled formulation is generalized to train based only on the mean flow and Reynolds stresses, which are more readily available from experiments.

Investigations show that convolutional neural networks (CNNs) are able to reconstruct missing data in turbulence. Different types of input information impact the performance of the algorithm. CNNs are able to reconstruct original data with errors comparable to equation-informed tools such as nudging, even in the presence of large gaps.

Perspectives are presented on the use of machine learning to augment models of turbulent flows. Particular emphasis is placed on techniques that promote consistency of the machine learning model with the underlying physical model in view of the possibility of using sparse computational and experimental data. This is followed by a discussion of physics-informed and mathematical considerations on the choice of the feature space and imposition of constraints. Machine learning should be viewed as one tool in the turbulence modeler’s toolkit. The associated modeling endeavor requires multidisciplinary advances.

Fish swim by coordinating their shape changes with the fluid environment to produce forward swimming or turning gaits. We use model-free reinforcement learning to learn shape coordinations that lead to robust turning and forward swimming motions in the context of a simple three-link fish in a potential flow environment. We show that the optimal control policies arrived at by reinforcement learning are interpretable via shape space analysis in driftless environment and are robust to the presence of drift-related perturbations.

We use an ensemble Kalman filter (EnKF) to sequentially estimate low Reynolds number aerodynamic flows using an inviscid vortex model and distributed surface pressure readings. We look at two scenarios: an impulsively translating plate subject to flow actuation near the leading edge or placed in a cylinder wake. In each case, the ensemble transform Kalman filter (ETKF) - a deterministic version of the EnKF - is consistently more robust than the stochastic EnKF and is qualitatively better at representing the coherent structures of the true flow. We analyze the mapping from pressure discrepancies to state update through a singular value decomposition of the Kalman gain.

A rotating detonation engine displays complex nonlinear shock front propagation dynamics which impede effective dimensionality reduction. A novel optimization is used to discover separate low-rank modes and interpretable dynamics for each front’s propagation. Koopman autoencoders similarly enable separation and forecasting of shock wave interactions.

We use the background method to find an upper bound on the nondimensional temperature dissipation for Rayleigh-Bénard convection with the temperature of one boundary modulated in time. The resulting bound depends on characteristics of the temperature modulation profile and its derivative. We investigate the limits of high-frequency modulation and large Rayleigh number, and we also examine two examples of sinusoidal modulation. Asymptotically, the bound for large Rayleigh number has the same leading order behavior as the non-modulated case.

What happens to a tropical cyclone past landfall? Per the prevailing theory, tropical cyclones past landfall decay via a straightforward process in which thermodynamics plays no role. We show, contrary to this theory, that thermodynamics is crucially important and propose a conceptual framework for the post-landfall phase, culminating in the surprising discovery of the birth of a cold core. In addition to its significance for our understanding of the post-landfall phase, the birth of a cold core bears directly on the current forecasting methods for extreme weather conditions triggered by a landfalling tropical cyclone.

How do surface tension forces contribute to the energy budget in a flowing liquid with a free surface? One might expect that these forces always produce power when the fluid is flowing. Here we show, however, that there is no power term if the surface itself does not move, i.e., for a fixed control volume. The energy conservation law for a free surface in a control volume moving with a specified velocity, independent of the liquid velocity, is derived and extended to the full system energy including the bulk flow. The Laplace pressure and tangential capillary forces then appear naturally, and the power provided by the latter forces is given through the velocity of the control volume and not that of the flow.

Fish swim by undulating their body to ensure propulsion. In a steady state, thrust is balanced by the total drag force, for which the dominant terms depend on the Reynolds number and the flow regime. In this article we propose a set of simple scaling laws to determine the contribution of each mechanism to the drag exerted on the swimmer.

We present the first direct measurement of the orbits of microscale passive tracers in the unsteady flow created by an oscillating microsphere. Using a time-shared optical trap to position tracers in several concentric arcs around a driven central sphere, we find that the tracers exhibit elliptical Lissajous figures whose orientation and aspect ratio are in quantitative agreement with a scaling law that arises from a low-frequency expansion of the underlying unsteady Stokes equations. The implications of these results for the understanding of metachronal waves in ciliated microorganisms are discussed.

Colloidal migration driven by electrolyte gradients is often reported in low-salinity conditions. Applying such a concept in high salinity conditions, however, is quite challenging due to the deteriorated colloidal stability and quenched electrostatic interaction. Here, droplet migration in high salinity is induced by the gradient of a zwitterionic surfactant that also stabilizes the emulsion. The reported emulsion system and mobilization strategy allow encapsulation and enhanced delivery of chemical agents for many subsurface applications.

We consider a model microswimmer consisting of two counter-rotating spheres that has zero propulsion in a Newtonian fluid but swims in the direction of the larger sphere in a viscoelastic fluid. This is analogous to the bacteria E. coli which propels itself with a rotating flagellar bundle and counter-rotating cell body. We find that the swimmer’s thrust is due to a pressure imbalance along its body resulting from polymeric hoop stresses around the faster spinning smaller sphere that advect fluid radially inward. In contrast to previous work, our artificial swimmer is both force- and torque-free. We show that the latter condition has a profound impact on the swimming speed in an elastic fluid.

Since the seminal results of Batchelor, Morton and Turner who laid the foundations of classical convective plume theory, it has been recognized that convective thermals exhibit remarkable scaling properties. In this paper, the authors identify dynamics of strong thermals which can be drastically different from weak Boussinesq-type thermals. In general, the evolution of thermals is affected by the interplay of two processes: entrainment flux caused by thermal expansion and solid-body acceleration of the thermal centroid. As a result, depending on the density contrast between the thermal and the ambient environment, scaling laws are modified with different power-law exponents.

A series of three-dimensional computations are conducted to investigate convective flow generated by an interaction between a vertical solute gradient and a horizontal thermal gradient. The convection develops into what is called a fully developed flow which is composed of the largest number of horizontal convection layers. Within each layer there prevails an array of salt-finger vortices. The multilayered structure changes systematically with boundary values, while the convection layer bears a layer thickness, so that the positive thermal buoyancy can balance with the negative solute buoyancy.

An experimental particle tracking velocimetry is used to investigate the Lagrangian velocity and acceleration in plume-rich regions of turbulent Rayleigh-Bénard convection. The measured acceleration variances show regions with and without abounded number of plumes have different Ra-dependent power laws. Further examination reveals that turbulent flow in the plume-rich regions is governed by a mixed dynamics with contribution from both thermal plumes and turbulent background fluctuations.

Differential diffusion effects can impact chemically driven convective dissolution that occurs when a chemical reaction destabilizes an otherwise stable density stratification after dissolution of a given solute in a host phase.

The effect of surfactant on the pairwise interactions of drops in an applied uniform DC electric field is studied using a combination of numerical simulations and an analytical theory assuming small drop deformations. We show that the surfactant weakens the electrohydrodynamic flow and thus dielectrophoretic interactions play a more prominent role in the dynamics of surfactant-covered drops compared to clean drops. If drop conductivity is the same as the suspending fluid, a nondiffusing surfactant can arrest the drops’ relative motion, thereby effectively preventing coalescence.

We develop a mathematical model of a recently discovered puzzling phenomenon of levitation of droplets near heated solid surfaces at temperatures far below the Leidenfrost point. Coupled heat transfer, vapor diffusion, and Stefan flow around a spherical droplet are accounted for. Predictions of levitation height based on the model agree with the experimental measurements.

We examine the role of interfacial viscosity on the motion of a surfactant-laden droplet across the streamlines of flow when subjected to thermal gradients. Our results show that both the shear and dilatational components of the interfacial viscosity necessarily slow down the cross-streamline migration of the droplet, but the influence of dilatational viscosity is significantly more imperative. These results suggest new strategies of droplet manipulation in a direction transverse to the flow by utilizing the variation of surface tension across the droplet interface.

In this experiment we study the motion of a walking droplet on the surface of a vibrated fluid, where the drop is confined within a circular corral defined by an array of pillars that protrude through the surface of the fluid. We demonstrate that in a certain acceleration range, just below the Faraday threshold, the long-time statistics of the droplet motion correlates with the eigenmode of the corral, referred to as the Faraday-Talbot pattern.

The input-output approach is expanded to investigate actuated wall-bounded shear flows whose geometries and input signals span a range of pulse-width modulated signals common in experimental flow control studies. The model is validated through comparisons to experiments and simulations of three different plasma actuator geometries. An important benefit of this analytical method is the low computational cost associated with its use, enabling efficient parametric studies.

We introduce single-step proximal policy optimization, a deep reinforcement learning algorithm for situations where neural network optimization does not depend on state. Optimization is examined with open-loop control problems of laminar and turbulent flows (Re up to a few ${10}^4$). For turbulent flow past a square cylinder, the approach reduces drag by 30% by finding the best placement of a small control cylinder, in agreement with existing experimental data. For turbulent flow past a fluidic pinball, drag is reduced by 60% by using boat tailing actuation made up of a slowly rotating front cylinder and two oppositely rotating downstream cylinders, matching existing machine learning results.

The critical Reynolds number for a steady shear flow can be reduced with the addition of an oscillatory driving force. Optimized pulsations maximizing this reduction are determined. Percentage reductions are shown to further improve in the presence of a transverse magnetic field, in a quasi-two-dimensional framework, by tuning the frequency to ensure boundary layer inflection points remain prominent. Nonlinear simulations support the linear findings at the critical conditions.

The viscous fingering or Saffman-Taylor instability occurs when a less viscous fluid penetrates a more viscous fluid in a porous medium. Fingering patterns refer to the deformation of the interface between the invading and displaced fluids. For mixtures composed of three miscible species, the dynamic of each component varies greatly. In that case, multicomponent diffusion effects are of primary importance, and reverse diffusion could trigger the instability from a configuration that is known to be stable for binary mixtures.

Using weak nonlinear analysis, it is shown that an electric field imposed on a bilayer of fluids in the presence of gravity can only lead to subcritical instability of the interface. We see that no matter the horizontal dimension of the fluid layers or the Bond number, subcritical branching necessarily results. A simple expression for the case of deep layers reveals that the subcritical nature of the instability is contributed dominantly by electrostatic forcing, which is of $O(k)$, and diminished curvature which is of $O(k^3)$, both being enough to offset the supercritical nature offered by gravity, which is of $O(k^2)$.

We report the experimental investigation of lift generation by an initially submerged aspect ratio 4 wing that translates through the water-air interface. Many animals, such as flying fish and diving seabirds, use wings or fins to produce lift forces as they transit the water-air interface, and cross-domain underwater-aerial vehicles were recently demonstrated, but lift production of a wing egressing from water had not yet been quantified. Our results show that the lift history is markedly different for low egress velocities versus high egress velocities, with low velocities exhibiting a large oscillation in lift coefficient and high velocities exhibiting a more linear lift attenuation.

The absolute permeability of porous media is an important parameter for various technological applications ranging from ground water hydrology to hydrocarbon recovery to microfluidics. We investigate the max-flow min-cut theorem which states that the maximum flow through any network is exactly the sum of the edge weights that define the minimum cut. We hypothesize that the min-cut can be related to the absolute permeability of a network. We find correspondence between the absolute permeability measured from pore network modeling ($K_{pnm}$) to that measured from the min-cut ($K_{edm}$) and provide a means to identify structural regions that result in significant energy dissipation.

In applications superhydrophobic surfaces are often irregular and nanostructured. On such a surface, it has been found that only a part of the surface is homogeneously wetted, i.e. wetting and slippage corresponding to that of a regularly structured surface. On the remaining part, large air inclusions occurred that possess a comparatively large slip length. In order to measure the velocity profile at distances below 1µm close to the surface, an enhanced evaluation method for fluorescence correlation spectroscopy is developed in this work.

We develop a model of time-dependent diffusiophoretic compaction of colloids in a two-dimensional pore due to the gradient of a multivalent solute in tandem with a diffusioosmotic slip-driven background flow field. The model is simulated for various surface charges and particle diffusivities. We also conduct experiments varying the initial ion combinations and total solute concentration. Our results indicate that diffusiophoretic compaction can be increased or decreased by manipulating electrolyte and total solute concentrations, wall charge, and particle diffusivity; each effect can modify the particle velocity, with varying strength, in unison or in opposition to the other effects.

Most natural and industrial flows involve mixtures of nonspherical particle species. A general approach to predicting segregation over the infinite space of all possible particle shapes and sizes seems, at first glance, to be impossible. Surprisingly, we find that for a broad range of binary particle mixtures composed primarily of pairs of disks and rods with different aspect ratios, but also cylinders combined with spheres and cubes, shape plays only a minor role. Instead, the primary driver of segregation is the volume ratio of the two species.

We studied large particle segregation via experiments in a two-dimensional shear cell. Our results validated a recent equation relating particle-size segregation velocity, size ratio and shear rate, further explaining the role of size ratio on large particle segregation. Based on our observations, we showed and described the part played by particle rotation and expansion rate in large particle segregation mechanics.

Ambient conditions surrounding respiratory droplets determine their growth or shrinkage. In cold and humid weather, the droplets can grow due to the supersaturation of the vapor puff. This phenomenon can be explained by our model.

The rotational behavior of accretion disks is subject to an as yet not finally determined mechanism of angular momentum transport. Shallow water accretion disk experiments allow for replication and measurement of thesedynamics. This paper reports the set-up of an experimental prototype aswell as the measurement of angular momentum transport under the influence of MHD-like effects as they are expected to occur in an accretion disk.

Using a high-speed camera, laser imaging and ultrasound velocimetry, we study positively buoyant miscible jets. Based on the appearance of the laminar length, we classify the flow into fully turbulent and semi-turbulent regimes. We quantify the regime transition boundaries and propose empirical correlations to predict the laminar length. To have a global view of the flow, we also analyze the quasi-steady jet characteristics (jet radius, spread angle, virtual origin, velocity profiles and energy dissipation) and starting jet characteristics (penetration length and tip velocity).

A more concise and accurate generalized Taylor dispersion theory is applied to dispersion of active gyrotactic microorganisms in a plane Poiseuille flow. The joint effect of boundary conditions, cell shape anisotropy, swimming speed, and flow speed leads to the nonmonotonic variations of the phenomenological dispersion coefficients.

We propose theoretical models to describe Boussinesq and non-Boussinesq plume rise in a corner of arbitrary angle. The Boussinesq plume theory is applied to the case of a naturally ventilated room and agrees well with previous experimental/theoretical results. The non-Boussinesq plume theory compares satisfactorily with previous measurements of fire plume mass flux.

Empirical formulae describing the Darcy-Weisbach friction factor remain indispensable for applications in sciences and engineering dealing with turbulent flows. Despite their practical significance, these formulae have remained without theoretical interpretation for many decades. To close this knowledge gap we provide, using a co-spectral budget model, a clarification of the link between spectral properties of velocity fluctuations and the scaling of friction factors in turbulent pipe flows in the hydraulically smooth and fully rough regimes.

A dynamic autoregressive (DAR) random forcing model is proposed for space-time energy spectra in turbulent shear flows. This model starts with Taylor’s convection model and introduces the DAR random forcing to represent the random sweeping effect. The DAR model is further combined with linear stochastic estimation (LSE) to reconstruct the near-wall velocity fluctuations.

Wall-shear stress becomes more intermittent as the Reynolds number (Re) of a flow increases. To properly resolve wall shear stress events in direct numerical simulations thus requires finer grids at higher Re. In this work we examine the grid resolution required to resolve a given percentage of wall shear stress events as a function of Re. We find that the standard grid resolution does not capture a fraction of high intensity events which increases with Re and quantify the grid resolution needed to do so.

The accurate prediction of hypersonic flows is a key challenge for the design of reentry bodies or hypersonic aircraft. Knowledge concerning the wall-bounded turbulence is especially needed. The present work is a fundamental study of a turbulent spatially developing flat-plate boundary layer subjected to high-enthalpy effects. The influence of air chemical reactions, typical of high-speed regimes, is investigated by means of direct numerical simulations. First- and second-order statistics are accurately examined, as well as spectral content and classical correlations.

A composite drag control (CDC) combining the opposition (OC) and spanwise opposed wall-jet forcing (SOJF) methods is investigated. A maximum drag reduction of about 33% is obtained for CDC – much higher than that produced by either individual method (namely, 19% for SOJF and 23% for OC). Flow analysis shows that CDC can take advantage of both OC and SOJF methods to better suppress drag producing near-wall turbulent structures –vortices and streaks. Our results suggest prospects of employing a composite control strategy for effective skin friction drag reduction, particularly at very high Reynolds numbers.

We study turbulence induced by the Rayleigh-Taylor (RT) instability for 2D immiscible two-component flows by using a multicomponent lattice Boltzmann method. We compare our results with the extension to the 2D case of the phenomenological theory for immiscible 3D RT studied by Chertkov and collaborators. In the immiscible case, the enstrophy shows a tendency to grow as $\propto t^{3/2}$, with the highest vorticity values concentrated close to the interface. We also investigate the typical drop size evolution and the behavior of the total length of the interface in the emulsion-like state, showing the existence of a power law behavior compatible with our phenomenological predictions.

We present a numerical procedure, which we call the macroscopic forcing method (MFM), which reveals the differential operators acting upon the mean fields of quantities transported by underlying fluctuating flows. More broadly, MFM can reveal differential operators associated with turbulence closure for scalar and momentum transport. We present MFM using canonical problems with increasing complexity, from a simple parallel flow to a complex nonhomogeneous flow, and show its efficacy, which can be utilized for quantitative understanding of non-Boussinesq effects and assessment of model forms in turbulence closures.

The resistance drag force acting on the wind by ocean waves plays a critical role in weather and climate forecasting. With the aid of computer simulation, we investigate the difference between the drag force caused by open sea waves and that by coastal waves. Our results show that the increased drag in the coastal region is closely related to the slowing down of waves in a physical process called wave shoaling.

Helmholtz decomposition is applied to investigate the compressibility effect in hypersonic turbulent boundary layers. The dilatational component of flow plays an important role in the near-wall region, while the solenoidal component is dominant far from the wall. The cold wall condition significantly enhances the compressibility, and especially enhances compression motions near the wall.

A data-driven wall model for turbulent flows over periodic hills is developed using a feedforward neural network and wall-resolved large-eddy simulation data. The developed wall model employs wall-normal distance, near-wall velocities, and pressure gradients as input features, and the wall shear stresses as output labels, respectively. In the $a$ $priori$ test, the accuracy of the trained wall model is examined using periodic hill cases at different Reynolds numbers and with different hill geometries. In the $a$ $posteriori$ test, the trained wall model is applied to the flow over periodic hills and turbulent channel flows.

We propose a partially-averaged Navier-Stokes equations (PANS) closure to predict the Taylor-Green vortex (TGV) flow. The results confirm the ability of the model to efficiently predict this problem. Yet, the physical resolution of the model should guarantee that only phenomena amenable to modeling are represented by the closure. This requires resolving the vortex-reconnection process of the TGV flow.

Two- and three-dimensional turbulence display markedly different dynamics. However, within the Earth’s atmosphere both states are observed to coexist in certain circumstances. We consider a simplified system of geometrically confined turbulence where the height of the system is smaller than the horizontal lengths. This system is also known to support the coexistence of two- and three-dimensional turbulence, making it a useful proxy for the atmosphere. Our focus is on the predictability of the system, measured through the Lyapunov exponent, and we find discontinuous jumps in predictability, which has potential implications for the next generation of numerical weather prediction models.

We present experimental observations of the turbulence field generated by a rectangular fractal grid. For engineering tests in wind tunnels, the grid can be used to produce turbulent flows with high turbulence intensities and large integral length scales. Our results also add to previous knowledge of nonequilibrium dissipation scaling, which is observed in decaying turbulence, even though homogeneity and isotropy are not strictly satisfied.

The prediction of unsteady forces on an accelerating plate is improved by including the sweeping effect of the free-stream flow in the equations that approximate the inviscid evolution of the separated flow structures. This effect is represented by a similarity variable that combines the temporal variation of the length scale and angle of attack, and which introduces an implicit time scale into the vortex dynamics and force histories.

The behavior and performance of synthetic jets is closely tied to the dynamics of vortex rings, which are a dominant feature of the early jet. When a synthetic jet actuator employs a non-axisymmetric orifice, the self-induced deformations of the vortex rings are responsible for changes in the shape, momentum distribution, and entrainment rate of the jet. In this study, axis-switching of vortex rings in finite-span synthetic jets with a range of orifice aspect ratios was experimentally investigated using stereoscopic particle imaging velocimetry, and the results were compared to vortex dynamics simulations based on the Biot-Savart law to gain additional insight.

When vortex patches are subjected to externally imposed strain flows where the strain rate grows slowly in time, the system approximately preserves an adiabatic invariant related to oscillatory elliptical deformations of the vortices. Formulae are derived for the breaking of this invariant with respect to the rate and functional form of the strain ramp. The analytical results are compared to experimental data acquired using magnetized pure electron plasmas, which provide a close laboratory realization of the motion of two-dimensional ideal vortices.

We conduct wind tunnel experiments to evaluate the drag and base-pressure coefficients and velocity field in the wake of a circular cylinder with extremely low length-to-diameter (fineness) ratio for diameter-based Reynolds number in the range $2-7.7\times {10}^4$. A magnetic suspension and balance system eliminates interference from support structures. We find that the drag coefficient converges monotonically to that of a local disk without a maximum at any fineness ratio in the 0.1-0.5 range. Large-eddy simulations at Re = $4\times {10}^4$ agree with the experiments.