# Latest papers in fluid mechanics

### Controlling droplet deposition with surfactants

Author(s): Hanne Hoffman, Rick Sijs, Thijs de Goede, and Daniel Bonn

Surfactants are often added to sprays to improve spray deposition. We show how the dynamic surface tension of surfactants solutions can be evaluated from drop impact experiments, allowing for a better understanding of drop deposition in the presence of surfactants.

[Phys. Rev. Fluids 6, 033601] Published Mon Mar 15, 2021

### Structure interactions in a reduced-order model for wall-bounded turbulence

Author(s): André V. G. Cavalieri

Reduced-order models are derived for a simplified description of transition and turbulence in Waleffe and Couette flow. Twelve nonlinear ordinary differential equations model the dynamics of coherent structures in fair agreement with direct numerical simulation. Compared to previous models, these low order systems display longer turbulence lifetimes and lower transition thresholds. Two spanwise wavelengths, Lz and Lz/2, for roll and streak modes is a key feature. The models show that interaction between structures with either wavelength is crucial to maintain longer turbulence lifetimes, as a neglect of such interaction leads to order-of-magnitude lifetime reductions.

[Phys. Rev. Fluids 6, 034610] Published Mon Mar 15, 2021

### Voronoi analysis of vortex clustering in homogeneous isotropic turbulence

Clustering of fine-scale dissipative vortices is quantified using a new technique based on the Voronoi diagram. We consider datasets of numerical simulations of decaying and forced homogeneous turbulence up to [math]. Velocity gradient events are more intense and intermittent if fine-scale vortices have a higher number density. However, clustering is observed only if the vortices are thresholded according to their intensity. Therefore, a fine-scale vortex cluster is the accumulation among stronger vortices rather than the accumulation of all of the vortices in the flow. Turbulence statistics in intense vortex clusters share characteristics with those of the outside when they are renormalized by their local magnitude. This suggests that the clusters are the product of passive amplification of the swirling intensity by underlying larger-scale motions. Comparing the decaying and forced flows reveals that the large-scale forcing affects the vortex distribution although other turbulence statistics are unaffected. The rotation axes of the vortices in the cluster are not preferentially aligned for either flow, which implies that large-scale shear layers are not a vital feature of the clusters.

### Continuous adjoint complement to the Blasius equation

This manuscript is concerned with a continuous adjoint complement to two-dimensional, incompressible, first-order boundary-layer equations for a flat plate boundary layer. The text is structured into three parts. The first part demonstrates that the adjoint complement can be derived in two ways, following either a first simplify then derive or a first derive and then simplify strategy. The simplification step comprises the classical boundary-layer (BL) approximation, and the derivation step transfers the primal flow equation into a companion adjoint equation. The second part of the paper comprises the analyses of the coupled primal/adjoint BL framework. This leads to similarity parameters, which turn the partial-differential-equation (PDE) problem into a boundary value problem described by a set of ordinary-differential-equations (ODEs) and support the formulation of an adjoint complement to the classical Blasius equation. Opposite to the primal Blasius equation, its adjoint complement consists of two ODEs, which can be simplified depending on the treatment of advection. It is shown that the advective fluxes, which are frequently debated in the literature, vanish for the investigated self-similar BL flows. Differences between the primal and the adjoint Blasius framework are discussed against numerical solutions, and analytical expressions are derived for the adjoint BL thickness, wall shear stress, and subordinated skin friction and drag coefficients. The analysis also provides an analytical expression for the shape sensitivity to shear driven drag objectives. The third part assesses the predictive agreement between the different Blasius solutions and numerical results for Navier–Stokes simulations of a flat plate BL at Reynolds numbers between [math]. It is seen that the reversal of the inlet and outlet locations and the direction of the flow, inherent to the adjoint formulation of convective kinematics, poses a challenge when investigating real finite length (finite Re-number) flat plate boundary layer problems. Efforts to bypass related issues are discussed.

### Transitional pulsatile flows with stenosis in a two-dimensional channel

Although blood flows are mostly laminar, transition to turbulence and flow separations are observed at curved vessels, bifurcations, or constrictions. It is known that wall-shear stress plays an important role in the development of atherosclerosis as well as in arteriovenous grafts. In order to help understand the behavior of flow separation and transition to turbulence in post-stenotic blood flows, an experimental study of transitional pulsatile flow with stenosis was carried out using time-resolved particle image velocimetry and a microelectromechanical systems wall-shear stress sensor at the mean Reynolds number of 1750 with the Womersley number of 6.15. At the start of the pulsatile cycle, a strong shear layer develops from the tip of the stenosis, increasing the flow separation region. The flow at the throat of the stenosis is always laminar due to acceleration, which quickly becomes turbulent through a shear-layer instability under a strong adverse pressure gradient. At the same time, a recirculation region appears over the wall opposite to the stenosis, moving downstream in sync with the movement of the reattachment point. These flow behaviors observed in a two-dimensional channel flow are very similar to the results obtained previously in a pipe flow. We also found that the behavior in a pulsating channel flow during the acceleration phase of both 25% and 50% stenosis cases is similar to that of the steady flow, including the location and size of post-stenotic flow separation regions. This is because the peak Reynolds number of the pulsatile flow is similar to that of the steady flow that is investigated. The transition to turbulence is more dominant for the 50% stenosis as compared to the 25% stenosis, as the wavelet spectra show a greater broadening of turbulence energy. With an increase in stenosis to 75%, the accelerating flow is directed toward the opposite wall, creating a wall jet. The shear layer from the stenosis bifurcates as a result of this, one moving with the flow separation region toward the upper wall and the other with the wall jet toward the bottom wall. Low wall-shear stress fluctuations are found at two post-stenotic locations in the channel flow – one immediately downstream of the stenosis over the top wall (stenosis side) inside the flow separation region, and the other in the recirculation region on the bottom wall (opposite side of the stenosis).

### Wall shear stress distribution in a compliant airway tree

The airflow in the bronchi applies a shear stress on the bronchial mucus, which can move the mucus. The air–mucus interaction plays an important role in cough and in chest physiotherapy (CP). The conditions under which it induces a displacement of the mucus are still unclear. Yet, the air–mucus interaction justifies common technics of CP used to help the draining of the mucus in prevalent diseases. Hence, the determination of the distribution of the shear stress in the lung is crucial for understanding the effects of these therapies and, potentially, improves their efficiency. We develop a mathematical model to study the distribution of the wall shear stress (WSS) induced by an air flow exiting an airway tree. This model accounts for the main physical processes that determine the WSS, more particularly the compliance of the airways, the air inertia, and the tree structure. We show that the WSS distribution in the tree depends on the dynamics of the airways deformation and on the air inertia. The WSS distribution in the tree exhibits a maximum whose amplitude and location depend on the amount of air flow and on the “tissue” pressure surrounding the airways. To characterize the behavior of the WSS at the tree bifurcations, we derive new analytical criteria related to the airway size reduction in the bifurcations. Our results suggest that a tuning of the airflow and of the tissue pressure during a CP maneuver might allow to control, at least partially, the air–mucus interaction in the lung.

### Recirculation regions in wakes with base bleed

Author(s): K. Steiros, N. Bempedelis, and L. Ding

A simple potential flow model sheds light on the behavior of detached recirculation bubbles as their initial conditions vary.

[Phys. Rev. Fluids 6, 034608] Published Fri Mar 12, 2021

### Statistical properties of streamline geometry in turbulent wall-flows

Author(s): Rina Perven, Jimmy Philip, and Joseph Klewicki

This study investigates the characteristics of streamline curvature and torsion in wall-bounded turbulence using DNS data from channel and boundary layer flows. The analysis includes characterizing the curvature of probability distributions as a function of the wall-normal distance. Far from the wall, the probability density function of the curvature decays with a -4 power dependence for the extreme events that are comparable with the Kolmogorov length scale. Consistent with previous studies, these large values of curvature are hypothesized to reflect the flow in the vicinity of stagnation points in the fluctuating field.

[Phys. Rev. Fluids 6, 034609] Published Fri Mar 12, 2021

### Dynamics of freely suspended drops translating through miscible environments

Our work focuses on an experimental investigation of droplets freely rising through a miscible, more viscous liquid. We report observations of water droplets rising through glycerol and corn syrup, which are common household ingredients. Immediately after the drops are formed, they take on prolate shapes and rise with constant velocity without expanding in size. However, after a critical time predicted by our scaling arguments, the drops continually grow into oblate spheroids, and as they mix with the ambient liquid, their volume increases and their velocity decreases, eventually following power laws. We present scaling relations that explain the main observed phenomena. However, the power laws governing the rate of the volumetric increase and the velocity decrease, namely, [math] and [math], respectively, remain points of further investigation.

### Bidispersive double diffusive convection with relatively large macropores and generalized boundary conditions

This paper is concerned with the question of the beginning of convective motion in a fluid saturated porous layer, containing a salt in solution, heated below and salted above and below. This model has a single temperature and employs the Darcy theory in the micropores, the Brinkman theory, however, being utilized in the macropores. The effect of slip boundary conditions on the stability of the model is also studied. General boundary conditions regarding temperature and salt are also taken into account. It will be shown that the linear instability threshold is the same as that of nonlinear stability if the layer is salted from above, indicating that the linear theory entirely captures the physics of the onset of thermal convection. In the case of salting from below, the behavior of the transition from stationary to oscillatory convection is investigated in detail, as the boundary conditions change from prescribed temperature and salt concentration toward those of prescribed heat flux and salt flux. The nonlinear stability threshold does not coincide with that of linear instability; thus, regions of possible subcritical instability are still present. We believe that the problem presented in this paper has not been addressed before and that its study will have great scientific value and impact.

### A new universal model for friction factor in smooth pipes

Friction factor models for turbulent flow in smooth pipes express friction factor λ as a function of the bulk Reynolds number ReD and may be broadly grouped into two categories: power-law models and log-law models. While the former stem from the spectral scaling arguments applied to eddy momentum transfer close to the wall, the latter are derived from the mean velocity log law and are known to be consistent with the attached eddy model of wall turbulence structure. Interestingly, none of these models individually describes the entire range of Reynolds numbers (Re) accessed to date, without requiring adjustment of coefficients and/or exponents, i.e., these models are not universal. In this work, we present a new semi-empirical universal model that combines, without introducing any additional empirical coefficients, the essence of both power-law and log-law models. Due to this, our model successfully describes the variation of friction factor over the entire range of Reynolds numbers (more than four decades in ReD) at once. The physical basis for our model is the observation that at finite Reynolds numbers, the flow appears to be a small perturbation of the so-called ultimate regime of smooth-pipe turbulence, as far as friction is concerned; in the ultimate regime, [math] asymptotically as [math]. The new model has significant potential toward accurate estimation of friction factor or flow rate in smooth pipe flows.

### New scaling laws predicting turbulent particle pair diffusion, overcoming the limitations of the prevalent Richardson–Obukhov theory

Both the evolution of particle pair separation distance l in a turbulent flow and how different length scales affect l are major unresolved challenges. The reigning theory in this topic is that of Richardson and Obukhov (R-O theory). We propose a new theory of pair diffusion in homogeneous, isotropic turbulence hypothesizing that not only structures of size l, but much larger ones also induce significant pair separation—ignored in the R-O theory. We arrive at new scaling laws for the pair diffusivity K, leading to [math] where γ depends on the size of the inertial subrange: for a short inertial subrange, we find from our simulations that [math], and for an infinite inertial subrange, we find that [math]—these relations agree closely with data. We assert that the celebrated “R-O constant” gl is neither physically meaningful nor a constant as universally assumed; our theory leads to two new physically relevant constants: GK for pair diffusivity and Gl for pair separation—which asymptote to [math] and [math] at high Reynolds numbers. We find that the particle dispersion is smaller by an order of magnitude compared to R-O prediction; this is significant in many applications such as sprays, and, in particular, the spread of biological contagions (e.g., COVID19) which persist longer and drift farther compared to R-O prediction. We find that the turbulent dispersion does not depend on the fine structure timescale—a striking result which would greatly facilitate turbulent diffusion modeling.

### Experimental study on transformation and energy properties of depression internal solitary wave over a bottom step

Waveform deformation and breaking are widespread phenomena when internal solitary waves (ISWs) encounter changing topographies, which have been observed in many parts of oceans. In this study, experiments are performed in a series of combinations of bottom step topographies with different heights and ISWs in different amplitudes within a two-layer stratified fluid system. According to experimental results, the evolution processes of ISWs over the bottom step are classified into four typical regimes as the wave–step interaction varying from weak to strong, which are the transmission regime, transitional regime, breaking regime, and reflection regime, corresponding to the evolution patterns of steady passage, deformation, breaking, and strong reflection, respectively. To describe the intensity of wave–step interaction, a new improved interaction parameter is proposed, which takes both relative amplitude of ISWs and relative topography changes into consideration, and achieved better effectiveness in defining the boundaries between different regimes. In terms of energy properties, with the wave–step interaction becoming stronger, the transmission ratio keeps decreasing throughout all regimes, while the reflection wave starts to appear since the breaking regime and its energy keeps increasing. At the critical point between the breaking regime and reflection regime, the reflection ratio equals the transmission ratio, and the energy loss ratio reaches its maximum.

### Slat cove dynamics of low Reynolds number flow past a 30P30N high lift configuration

A three-dimensional computational fluid dynamics analysis of low Reynolds number [[math]] flow over a 30P30N three-element high lift wing is carried out using a high-order spectral element method. In this article, we study the flow in the slat cove region and the slat wake/shear layer interaction. Vortical structures, identified in the computations, are very similar to those visualized in recent experiments. For Reynolds numbers below a critical interval (found in recent experiments), Görtler vortices are observed in the slat wake, while for Reynolds numbers above the critical interval, a roll-up is observed in the slat cove and both streamwise and spanwise vortices form in the slat wake. Prior to the formation of Görtler and roll-up vortices, three-dimensional tongue- or rib-like vortex shapes, similar to those found in the wake of bluff bodies, are observed in the slat cove and promote transition to three-dimensional flow. Above the critical interval, streaks and spanwise vortices are observed to dominate the slat wake and lead to the formation of hairpin vortices which contribute to the transition to turbulence. Integral flow parameters such as lift, drag, and pressure coefficients are analyzed in the range of Reynolds numbers studied.

### Slat cove dynamics of low Reynolds number flow past a 30P30N high lift configuration

A three-dimensional computational fluid dynamics analysis of low Reynolds number [[math]] flow over a 30P30N three-element high lift wing is carried out using a high-order spectral element method. In this article, we study the flow in the slat cove region and the slat wake/shear layer interaction. Vortical structures, identified in the computations, are very similar to those visualized in recent experiments. For Reynolds numbers below a critical interval (found in recent experiments), Görtler vortices are observed in the slat wake, while for Reynolds numbers above the critical interval, a roll-up is observed in the slat cove and both streamwise and spanwise vortices form in the slat wake. Prior to the formation of Görtler and roll-up vortices, three-dimensional tongue- or rib-like vortex shapes, similar to those found in the wake of bluff bodies, are observed in the slat cove and promote transition to three-dimensional flow. Above the critical interval, streaks and spanwise vortices are observed to dominate the slat wake and lead to the formation of hairpin vortices which contribute to the transition to turbulence. Integral flow parameters such as lift, drag, and pressure coefficients are analyzed in the range of Reynolds numbers studied.

### Transmission and evaporation of cough droplets in an elevator: Numerical simulations of some possible scenarios

As the world learns to live with COVID-19 and activities/business open up, the use of elevators becomes frequent. A pertinent question is what happens if someone accidentally coughs inside the elevator. In this work, a three dimensional Euler–Lagrangian model is used to understand the transmission and evaporation of micrometer-sized droplets in such cases. The effect of turbulence created by the air puff associated with coughing has been considered. Different possible scenarios varying in the presence of air ventilation within the elevator, number of persons coughing, direction of ejection of cough droplets, and ambient relative humidity and temperature have been postulated and simulated. The results obtained show that in the presence of proper ventilation within the elevator, most of the ejected cough droplets fall to the ground before impacting other persons traveling in the same elevator. However, in the absence of proper ventilation, the turbulence created during coughing transmits the particles all across the elevator enclosure.

### Self-sustaining and propagating mechanism of localized wave packet in plane-Poiseuille flow

In this Letter, it is revealed that the convection velocity of a localized wave packet in two-dimensional plane-Poiseuille flow is determined by the solitary wave at the centerline of a vortex dipole, which is evinced by subtracting the base flow from the mean flow. The fluctuation component propagates obeying the local dispersion relation of the mean flow and oscillates with a global frequency selected by the upstream marginal absolute instability and, hence, is a traveling wave mode. The vortex dipole provides an unstable region for the fluctuation waves to grow up, and the Reynolds stress of the fluctuation waves leads to streaming components enhancing the vortex dipole. By applying localized initial disturbances, a nonzero wave-packet density is achieved at the threshold state, suggesting a first-order transition.

### Exact time scale of energy exchange in triad interactions of homogeneous isotropic turbulence

We solve analytically the period of a single triad interaction of homogeneous isotropic turbulence. Comparing with the traditional concept of the timescale of energy transfer, we found that this period is a timescale of energy exchange among the three wave vectors of a triad. Quantitatively, the timescale of energy exchange is usually longer if the equilibrium dissipation law is satisfied; however, when energy transfer is suppressed, the energy exchange becomes dominant. We extract the periods in typical numerical experiments of triad interactions and show that they are in good agreement with theoretical predictions. This picture implies that energy exchange corresponds to oscillation, while energy transfer corresponds to damping, and the damping rate is correlated with the oscillation. The present results of the timescale of energy transfer are expected to be applied in nonequilibrium turbulent flows.

### Relative motion of two neighboring points on inert and reactive scalar iso-surfaces in homogeneous turbulence

The study of the deformation and rotation of line and surface and volume elements, embedded in a mixing-reaction zone, is supposedly of a paramount importance to comprehend the evolution of inert and chemically reacting species in turbulent flows. This analysis examines the relative motion of two points on adjacent, nonmaterial, propagating, isoscalar surfaces, subject to the flow velocity, [math], and the normal displacement speed vector, [math] ([math] is the unit vector perpendicular to the isosurface). The methodology of Perry and Chong [“Topology of flow patterns in vortex motions and turbulence,” Appl. Sci. Res. 53, 357–374 (1994)], applied to the velocity gradient tensors of [math], [math], and [math], [math] serves to characterize this motion. Small-scale flow and displacement topologies clearly emerge from this description. The invariants of these two velocity gradient tensors yield the total rate of change of the normal distance between two isosurfaces, the area stretch factor, the total volumetric dilatation rate, and the nodal or focal features of the motions. The influence of the first invariant on the displacement speed and the chemical depletion is also established. A simple mathematical formalism portrays the time rate of change of an infinitesimal nonmaterial vector, [math], joining two points on adjacent isoscalar surfaces within a zone where turbulent mixing of inert and reactive species occurs. Databases of a 3D 5123 DNS of a statistically homogeneous and stationary turbulence with inert and reactive scalars undergoing random mixing in a constant density fluid are examined to illustrate the application of the previous conceptual framework. Small scales are well resolved. Various flow and displacement contributions to the two-point relative velocity components, normal and tangential to the isosurface, are compared to conclude that motions of isoscalar surfaces due to [math] are, at least, as important as those caused by [math]. In particular, the additional vorticity, [math], is one order of magnitude greater than the flow vorticity, [math], and tangential to the isoscalar surfaces, contributing significantly to their folding. While the dynamically passive scalars do not modify the conventional local flow motions, new additional topologies, induced by [math] and typified by its invariants, [math], and [math], appear and affect the displacement speed and the reaction rate. The mass entrainment rate per unit mass into a volume element between two adjacent isosurfaces is given by the first invariant, [math], and its influence on the displacement speed and the chemical reaction is explored.

### Physics-guided deep learning framework for predictive modeling of bridge vortex-induced vibrations from field monitoring

Vortex-induced vibrations (VIVs) with large amplitudes have been observed on long-span bridges worldwide. Classic semi-empirical VIV models that depend on wind tunnel tests are challenged when required to predict the VIV response of real bridges due to the complexity of real winds, high Reynolds number effects, and uncertainty of bridge structures. The prediction accuracy by these laboratory-based models may, thus, be reduced for real large-scale bridges. Emerging field monitoring systems on prototype bridges allow one to reconsider modeling of bridge VIVs with considerations of real natural winds and full-scale structures by massive monitoring data. In this research, first, we derive a general form of time-dependent ordinary differential equation based on Scanlan's semi-empirical model and field observed bridge VIVs to describe VIV dynamics. Second, guided by the formulation and field observation, we propose a deep learning framework to identify the VIV dynamics, leading to a data-driven model. We demonstrate the proposed framework on a real long-span bridge by performing long-time prediction of the VIV response under real natural winds.