Vortex models have been used for decades as computationally efficient tools to investigate unsteady aerodynamics. However, their utility for separated flows—particularly when such flows are subjected to incident disturbances—has been hindered by the tradeoff between the model's physical fidelity and its expectation for fast prediction (e.g., relative to computational fluid dynamics). In this work, it is shown that physical fidelity and speed can be simultaneously achieved by assimilating measurement data into the model to compensate for unrepresented physics. The underlying inviscid vortex model captures the transport of vortex structures with a standard collection of regularized vortex elements that interact mutually and with an infinitely thin flat plate. In order to maintain a low-dimensional representation, with fewer than $O\left(100\right)$ degrees of freedom, an aggregation procedure is developed and utilized in which vortex elements are coalesced at each time step. A flow state vector, composed of vortex element properties as well as the critical leading-edge suction parameter, is advanced within an ensemble Kalman filter (EnKF) framework. In this framework, surface pressure is used to correct the states of an ensemble of randomly initiated vortex models. The overall algorithm is applied to several scenarios of an impulsively started flat plate, in which data from a high-fidelity Navier-Stokes simulation at Reynolds number 500 are used as a surrogate for the measurements. The assimilated vortex model efficiently and accurately predicts the evolving flow as well as the normal force in both the undisturbed case (a separated flow) as well as in the presence of one or more incident gusts, despite lack of a priori knowledge of the gust's characteristics.

We derive an amplitude equation that captures the effect of small but arbitrary topography on small-amplitude surface gravity waves. The robustness of this reduced model is demonstrated by numerical simulations that compare it with the fully nonlinear water wave equations. The amplitude equation is seen to accurately capture intricate and complex wave dynamics, compared with the fully nonlinear equations, while being much faster than the latter. Consequently, the model offers great potential for various surface wave-topography interaction investigations, especially when a large number of simulations are needed to obtain wave statistics, a process that is much slower if attempted using the full set of equations.

We numerically investigate the temporal aspects of turbulent spot spreading in a plane Couette flow for transitional Reynolds numbers between 300 and 450. We focus our study on the spreading along the streamwise direction and on the shape of turbulent spots. Studying the topology of turbulent spots and the associated large-scale flows, we suggest a decomposition of the streamwise growth rate. On one hand, the quadrupolar large-scale flow heads for the spot along the streamwise direction and act against the growth. The associated growth rate is negative. On the other hand, we also define a positive growth rate associated to inside large-scale flow which enables the convection of the streaks. The sum of these two growth rates is compared to the spot streamwise growth rate and shows good agreement. The resulting shape of the spot is then discussed. A scenario gathering all these elements provides a better understanding of the growth dynamics and of the shape of a turbulent spot in a plane Couette flow. This scenario should be relevant to other shear flows.

The evaporation of water in a rectangular microchannel at low pressures was studied experimentally and numerically to demonstrate the interplay between the heat transfer and fluid dynamics during evaporation of the liquid at low pressures. The three-dimensional flow below the interface was quantified using scanning particle image velocimetry. Temperatures in the fluids on the centerline in both phases as well as the liquid temperatures along the interface were measured with a fine thermocouple. A numerical simulation, which accounted for the transport of mass, momentum, and energy in the fluids as well as those at the interface, was developed and validated with the measured experimental data. Once good agreement between the model and the experimentally obtained parameters was achieved, the model was used to examine some aspects of the evaporation phenomenon which could not be understood from the experiments alone. An important result from this work has shown that a buoyancy driven flow in the liquid water competes with a thermocapillary flow at the interface and does not allow the thermocapillary flow to spread over the interface. This is suggested to be a possible answer to the the question of why a thermocapillary flow in water, in contrast to many other liquids, does not always exist.

We solve a design optimization problem for a deterministic lateral displacement (DLD) device to sort same-size biological cells by their deformability, in particular to sort red blood cells by their viscosity contrast between the fluid in the interior and the exterior of the cells. A DLD device optimized for efficient cell sorting enables rapid medical diagnoses of several diseases such as malaria since infected cells are stiffer than their healthy counterparts. The device consists of pillar arrays in which pillar rows are tilted and hence are not orthogonal to the columns. This arrangement leads cells to have different final vertical displacements depending on their deformability and therefore it vertically separates the cells. The pillar cross section, the tilt angle of the pillar rows, and the center-to-center distances between pillars are free design parameters. For a given pair of viscosity-contrast values of the cells, we seek optimal DLD designs by fixing the tilt angle and the center-to-center distances. So the only design parameter is the pillar cross section. We propose an objective function such that a design minimizing it provides efficient cell sorting. The objective function is evaluated by simulating the cell flows through a device using our two-dimensional model [Kabacaoğlu et al., J. Comput. Phys. 357, 43 (2018)]. We solve the optimization problem using a stochastic optimization algorithm. Since the algorithm converges in $O\left(1000\right)$ iterations and our high-fidelity DLD model is expensive to evaluate the objective function, we propose a low-fidelity DLD model that enables fast solution of the problem. Finally, we present several scenarios where solving the optimization problem finds designs that can separate cells with similar viscosity-contrast values. These designs have cross sections that have features similar to a triangle.

Analytical results for the apparent slip between two spheres in a simple biviscous model of a shear-thinning fluid are presented. Velocity profiles and apparent slip lengths along the surfaces are analyzed in order to characterize the physical mechanism. It is shown that in this non-Newtonian model, the effect of shear thinning limited to high-shear rates in the interstitial regions between close spheres can be alternatively interpreted as the onset of an apparent shear-rate-dependent slippage effect. The results of the theory compare well with experiments from the literature showing the presence of surface slip on a particle approaching a planar wall. In terms of implications for suspensions rheology, the present results bridge the “hidden” solvent shear-thinning theory [Vázquez-Quesada et al., Phys. Rev. Lett. 117, 108001 (2016)] with slip-based models presented recently [Kroupa et al., Phys. Chem. Chem. Phys. 19, 5979 (2017)] as a possible explanation for the mechanism behind the shear thinning in hard-sphere non-Brownian suspensions.

This work aims at predicting continuum breakdown in high-speed, chemically reacting wake flows using breakdown parameters obtained from the generalized Champan-Enskog (GCE) theory. Previous efforts have addressed the mathematical development of these mechanism driven breakdown parameters and their utility in predicting continuum breakdown in high Mach number compressing flows. Here we present a specieswise perturbation parameter, based on the 2-norm in Hilbert space of the first-order GCE perturbation, which can be used to assess the extent to which the underlying equilibrium Maxwell-Boltzmann (MB) distribution of a given species has been perturbed. This parameter is derived for the one-, two-, and three-temperature models, and is applicable to multicomponent, chemically reacting flowfields. All transport mechanisms that can lead to distortion of the specieswise equilibrium MB distribution function—translational, rotational and vibrational heat fluxes, mass and thermal diffusion fluxes, and stress tensor components including bulk viscosity and relaxation pressure terms—are simultaneously incorporated into this perturbation parameter that can be computed for each species. This parameter and the mechanism-based GCE breakdown parameters are used to assess continuum breakdown in the forebody and wake region of a cylinder subjected to hypersonic flow. The influence of altitude, freestream velocity, and cylinder surface reactions on continuum breakdown is analyzed. Regions of continuum breakdown are observed in the shock, boundary layer, as well as in the wake. Most notably, the surface chemistry at the cylinder wall forebody can lead to the formation of breakdown regions in the wake that are detached from the cylinder surface.

We present an extensive study of Boussinesq thermal convection including a temperature-dependent internal heating source, based on numerical three-dimensional simulations. The temperature dependence mimics triple-$\alpha$ nuclear reactions and the fluid geometry is a rotating spherical shell. These are key ingredients for the study of convective accreting neutron star oceans. A dimensionless parameter ${\mathrm{Ra}}_n$, measuring the relevance of nuclear heating, is defined. We explore how flow characteristics change with increasing ${\mathrm{Ra}}_n$ and give an astrophysical motivation. The onset of convection is investigated with respect to this parameter and periodic, quasiperiodic, chaotic flows with coherent structures, and fully turbulent flows are exhibited as ${\mathrm{Ra}}_n$ is varied. Several regime transitions are identified and compared with previous results on differentially heated convection. Finally, we explore (tentatively) the potential applicability of our results to the evolution of thermonuclear bursts in accreting neutron star oceans.

We analyze hindered settling speed versus volume fraction $\varphi$ for dispersions of monodisperse spherical particles sedimenting under gravity, using data from 15 different studies drawn from the literature, as well as 12 measurements of our own. We discuss and analyze the results in terms of popular empirical forms for the hindered settling function, and compare to the known limiting behaviors. A significant finding is that the data fall onto two distinct branches, both of which are well described by a hindered settling function of the Richardson-Zaki form $H\left(\varphi \right)={(1-\varphi )}^n$ but with different exponents: $n=5.6\pm 0.1$ for Brownian systems with Péclet number $\mathrm{Pe}<{\mathrm{Pe}}_c$, and $n=4.48\pm 0.04$ for non-Brownian systems with $\mathrm{Pe}>{\mathrm{Pe}}_c$. The crossover Péclet number is ${\mathrm{Pe}}_c\approx {10}^8$, which is surprisingly large.

Direct numerical simulations are performed to investigate the spatial evolution of dual-plane jet flows with different separation lengths between the two jets. Based on the scaling law and the probability density function of the turbulent/nonturbulent interface of a single plane jet, the jet-interaction length scale $X_{*}$ is introduced. It is shown that for different separation lengths, the streamwise evolutions of various statistics along the centerline all scale with $X_{*}$. This finding may explain the linear relationship between the location of the merge point and the separation length. Of particular interest is the evolution of the probability distributions and energy spectra of the streamwise velocity fluctuations in the developing region. Similar to the case of grid-generated turbulence, the probability distribution of the velocity fluctuations can also be non-Gaussian in a dual-plane jet flow. For all flow configurations considered, close to the inlet (e.g., $X/X_{*}\simeq 1.0)$ where the two jets have not yet joined together, the skewness of the streamwise velocity fluctuations is negative. In contrast, at a further downstream location (e.g., $X/X_{*}\simeq 2.0)$, where the turbulence intensity and mean pressure reach their maximum values, the skewness takes a positive value instead. Our study suggests that there are two different physical mechanisms responsible for the formation of the intense oscillations of the velocity fluctuations. The negative value of the skewness in the upstream region is caused by the large-scale movement of the contrarotary vortices, whereas the streamwise position of the positive skewness appears to be correlated to the location of peak intensity near (or after) the merging of the jets.

A turbulent planar jet is analyzed theoretically by adopting the Lie theory of continuous transformation groups on turbulent statistical model equations. We show that at the infinite-Reynolds-number limit, the planar jet, in analogy to the turbulent axisymmetric wake, obeys the non-Kolmogorov dissipation law $\epsilon \sim C_{\epsilon }{\left(\overline{k}\right)}^{3/2}/l$, where the dissipation coefficient $C_{\epsilon }$ varies with the local and global Reynolds numbers ${\text{Re}}_l$ and ${\text{Re}}_0$, respectively. In the planar jet, $C_{\epsilon }\sim {({\text{Re}}_0/{\text{Re}}_l)}^m$, with $m=-2+2a_1/a_2$ preferably lying in $[-2,1]$, where $a_1$ and $a_2$ are dilation symmetry group parameters. When $m\in [-2,0)\cup (0,1]$, the planar jet follows nontrivial power-law similarity scalings, while when $m=-2$ it may scale exponentially. The production $P$ of turbulent kinetic energy $\overline{k}$ in this study is considered as $P=-\overline{u^{\prime }{v}^{\prime }}\partial \overline{u}/\partial y-(\overline{u^{\prime 2}}-\overline{v^{\prime 2}})\partial \overline{u}/\partial x$, where $-\overline{u^{\prime }{v}^{\prime }},-\overline{u^{\prime 2}}$, and $-\overline{v^{\prime 2}}$ are Reynolds stresses. Thus, the laws support $\overline{k}\sim {\left(\overline{u}\right)}^2\nsim -\overline{u^{\prime }{v}^{\prime }}$ when $m\ne 0,\overline{u}$ being the mean streamwise velocity. The power-law scaling of the turbulent jet half-width and centerline mean streamwise velocity for $m=1$ agree well with the recent experimental results. The entrainment coefficient, which is constant in streamwise distance when $m=0$ (Kolmogorov dissipation), varies with streamwise distance when $m\in [-2,0)\cup (0,1]$. It scales nonlinearly as an exponent $-1/3$ of streamwise distance for $m=1$, which agrees with the recent experimental observation of Cafiero and Vassilicos (G. Cafiero and J. C. Vassilicos, arXiv:1803.10488).

We investigate the effect of hydrodynamic dispersion on convection in porous media by performing direct numerical simulations (DNS) in a two-dimensional Rayleigh-Darcy domain. Scaling analysis of the governing equations shows that the dynamics of this system are not only controlled by the classical Rayleigh-Darcy number based on molecular diffusion, ${\text{Ra}}_m$, and the domain aspect ratio, but also controlled by two other dimensionless parameters: the dispersive Rayleigh number ${\text{Ra}}_d=H/{\alpha }_t$ and the dispersivity ratio $r={\alpha }_l/{\alpha }_t$, where $H$ is the domain height and ${\alpha }_t$ and ${\alpha }_l$ are the transverse and longitudinal dispersivities, respectively. For $\mathrm{\Delta }={\text{Ra}}_d/{\text{Ra}}_m>O\left(1\right)$, the influence from the mechanical dispersion is minor; for $\mathrm{\Delta }\lesssim 0.02$, however, the flow pattern is determined by ${\text{Ra}}_d$ while the convective flux is $F\sim c\left({\text{Ra}}_d\right){\text{Ra}}_m$ for large ${\text{Ra}}_m$. Our DNS results also show that the increase of mechanical dispersion, i.e., decreasing ${\text{Ra}}_d$, will coarsen the convective pattern by increasing the plume spacing. Moreover, the inherent anisotropy of mechanical dispersion breaks the columnar structure of the megaplumes at large ${\text{Ra}}_m$, if ${\text{Ra}}_d<5000$. This results in a fan-flow geometry that reduces the convective flux.

Star-nosed moles sniff for prey underwater by rapidly exhaling and inhaling bubbles that in turn capture odors on their surface. While the sniff lasts only a tenth of a second, speed alone cannot explain how the star-nosed mole so reliably sucks the bubble back in before pinch-off occurs. In this combined experimental and theoretical study, we elucidate how the unique shape of the nose stabilizes underwater bubbles. The fleshy arms of the mole's star are separated by an average of ${16}^{\circ }\pm 9^{\circ }$ increments. We laser-cut plastic stars of various angles between the arms and tilt them by hand to find the angle at which a trapped sessile bubble is released. A bubble trapped beneath the star bulges through the gaps, enabling the plastic star to retain the bubble when tilted up to $7^{\circ }$, which is 40% greater than that of a flat plastic sheet. Using a semiempirical model, we show two regimes where a bubble escapes. If the gap width is wider than the capillary length, buoyancy forces pull the bubble up through the gap. If the gap width is too small, the bubble does not sufficiently anchor itself in place. We show order of magnitude agreement between biological measurements, plastic star experiments, and theory, suggesting we correctly identified the mechanism for the star retaining bubbles. This study may lead to new ways of stabilizing centimeter-scale bubbles for underwater chemical sensing.

We investigate velocity variations inside and surrounding a gravity-driven drop impacting on and moving through a confining orifice, wherein the effects of edge geometry (round vs sharp edged) and surface wettability (hydrophobic vs hydrophilic) of the orifice are considered. Using refractive-index matching and time-resolved particle image velocimetry, we quantify the redistribution of energy in the drop and the surrounding fluid during the drop's impact and motion through a round-edged orifice. The measurements show the importance of (a) the drop kinetic energy transferred to and dissipated within the surrounding liquid and (b) the drop kinetic energy due to internal deformation and rotation during impact and passage through the orifice. While a rounded orifice edge prevents contact between the drop and orifice surface, a sharp edge promotes contact immediately upon impact, changing the near-surface flow field as well as the drop passage dynamics. For a sharp-edged hydrophobic orifice, the contact lines remain localized near the orifice edge, but slipping and pinning strongly affect the drop propagation and outcome. For a sharp-edged hydrophilic orifice, on the other hand, the contact lines propagate away from the orifice edge and their motion is coupled with the global velocity fields in the drop and the surrounding fluid. By examining the contact line propagation over a hydrophilic orifice surface with minimal drop penetration, we characterize two stages of drop spreading that exhibit a power-law dependence with variable exponent. In the first stage, the contact line propagates under the influence of impact inertia and gravity. In the second stage, inertial influence subsides and the contact line propagates mainly due to wettability.

We investigate the mechanism of particle entrainment for dense, dry, collisional granular flows driven by gravity through a set of uniform-unsteady experiments. The flow evolves in time from a rest to a fully developed condition, but without any variability in the longitudinal direction. Using a high speed camera and particle tracking algorithms, we measure the time evolution of the flow depth, the normal-to-bed velocity profile and the granular concentration. We compare these with the predictions of a simple theory, obtained by solving for the time evolution of the momentum balance in the flow direction. In doing this, the velocity profile is assumed to maintain in time the same shape it has in a fully developed flow. This is obtained from the approximate analytical integration of an extended kinetic theory for dry, dense collisional flows of dissipative spheres. The proposed model relies only on measured physical properties of the particles, without any ad hoc calibrated parameter.

We examine swimmers comprising of two rigid spheres which oscillate periodically along their axis of symmetry, considering when the spheres oscillate both in phase and in antiphase, and study the effects of fluid viscoelasticity on the swimmers' motion. These swimmers display reciprocal motion in Newtonian fluids and consequently, no net swimming is achieved over one cycle in such fluids. Conversely, in viscoelastic fluids, we find that the effect of viscoelasticity acts to propel the swimmers forward in the direction of the smaller sphere when the two spheres are of different sizes. Finally, we compare the motion of rigid spheres oscillating in viscoelastic fluids with elastic spheres in Newtonian fluids where we find similar results.

The lateral migration of a suspended vesicle (a model of red blood cells) in a bounded shear flow is investigated numerically at vanishing Reynolds number (the Stokes limit) using a boundary integral method. We explore, among other parameters, the effect of the viscosity contrast $\lambda ={\eta }_{\mathrm{in}}/{\eta }_{\mathrm{out}}$, where ${\eta }_{\mathrm{in}},{\eta }_{\mathrm{out}}$ denote the inner and the outer fluids' viscosities. It is found that a vesicle can either migrate to the center line or towards the wall depending on $\lambda$. More precisely, below a critical viscosity contrast ${\lambda }_c$, the terminal position is at the center line, whereas above ${\lambda }_c$, the vesicle can be either centered or off-centered depending on initial conditions. It is found that the equilibrium lateral position of the vesicle exhibits a saddle-node bifurcation as a function of the bifurcation parameter $\lambda$. When the shear stress increases the saddle-node bifurcation evolves towards a pitchfork bifurcation. A systematic analysis is first performed in two dimensions (due to numerical efficiency), and the overall picture is confirmed in three dimensions. This study can be exploited in the problem of cell sorting and can help understand the intricate nature of the dynamics and rheology of confined suspensions.

A permanent magnetohydrodynamics (MHD) channel flow past a stationnary sphere is investigated, with a static magnetic field transversally applied and no-slip conditions taken into account. The sphere is subject to laminar flow conditions with the Reynolds number ranging from the Stokes regime up to values corresponding to the inertial regime $({\mathrm{Re}}_{\mathrm{p}}=130$ at most for the particle Reynolds number). The maximum value of the Hartmann number is $\mathrm{Ha}=200$. After a brief review of the existing literature of three-dimensional (3-D) MHD flows past an obstacle, a 3-D numerical approach is developed, which is systematically compared to asymptotic predictions (Ha = 0, $\mathrm{Ha}\to \infty )$. Atypical flow patterns are made evident, especially characterized by the gradual emergence of Hunt's wake for a sufficiently large particle Stuart number $N_p$. Some original correlations are put forward for the wake length and the drag coefficient. Finally, an original scaling law highlighting the significant influence of the outer magnetic field on the transition between different MHD flow regimes is drawn up.

The power output of wind farms depends strongly on spatial turbine arrangement, and the resulting turbulent interactions with the atmospheric boundary layer. Wind farm layout optimization to maximize power output has matured for small clusters of turbines, with the help of analytical wake models. On the other hand, for large farms approaching a fully developed regime in which the integral power extraction by turbines is balanced through downward transport of the mean kinetic energy, the influence of turbine layout is much less understood. The main goal of this work is to study the effect of turbine layout on the power output for large wind farms approaching a fully developed regime. For this purpose we employ an experimental setup of a scaled wind farm with 100 porous disk models, of which 60 are instrumented with strain gauges. Our experiments cover a parametric space of 56 different layouts for which the turbine-area density is constant, focusing on different turbine arrangements including nonuniform spacings. The strain-gauge measurements are used to deduce surrogate power and unsteady loading on turbines for each layout. Our results indicate that the power asymptote at the end of the wind farm depends on the layout in different ways. Firstly, for layouts with a relatively uniform spacing we find that the power asymptote in the fully developed regime reaches approximately the same value, similarly to the prediction of available analytical models. Secondly, we show that the power asymptote in the fully developed regime can be lowered by inefficient turbine placement, for instance when a large number of the turbines are located in the near wake of upwind turbines. Thirdly, our experiments indicate that an uneven spacing between turbines can improve the overall power output for both the developing and fully developed part of large wind farms. Specifically, we find a higher power asymptote for a turbine layout with a significant streamwise uneven spacing (i.e., a large streamwise spacing between pairs of closely spaced rows that are slightly staggered). Our results thereby indicate that such a layout may promote beneficial flow interactions in the fully developed regime for conditions with a strongly prevailing wind direction.