# Latest papers in fluid mechanics

### Effect of spanwise domain size on direct numerical simulations of airfoil noise during flow separation and stall

It is well established that a large spanwise domain size is required for accurate numerical simulations of flow past an airfoil in stall. A number of numerical experiments support this conclusion with regard to aerodynamic and turbulence statistics. However, very little has been reported concerning the effect of the span length on aeroacoustic results. In this paper, a detailed investigation is carried out into the influence of spanwise domain length on the prediction of airfoil stall noise when spanwise periodic boundary conditions are applied. This study is based on direct numerical simulations of an NACA0012 airfoil at Re∞ = 50 000 and M∞ = 0.4 at near- and full-stall conditions. There are three main findings in this paper. First, the far-field acoustics are found to be highly sensitive to the choice of spanwise domain length. In the full-stall case, a span length equal to 20% of the airfoil chord over-predicts the radiated noise by more than 10 dB at low-to-medium frequencies relative to a case with one chord length in span. Discrepancies are found to occur for acoustic wavelengths shorter than the spanwise domain size. Under near-stall conditions, the changes caused by the small spanwise domain are noticeably milder. Second, the lower noise predictions from the large span simulation at low frequencies are attributed to the spanwise breakup of large scale flow structures and reduced spanwise coherence near the trailing edge. Third, a more destructive source phase relationship is observed with a large span for medium frequencies, which was inhibited by the periodic forcing in the small span case.

### Harnessing random low Reynolds number flow for net migration

Author(s): Takeru Morita, Toshihiro Omori, Yohei Nakayama, Shoichi Toyabe, and Takuji Ishikawa

Random noise in low Reynolds number flow has rarely been used to obtain net migration of microscale objects. In this study, we numerically show that net migration of a microscale object can be extracted from random directional fluid forces in Stokes flow, by introducing deformability and inhomogeneo...

[Phys. Rev. E 101, 063101] Published Wed Jun 03, 2020

### Energetics and mixing efficiency of lock-exchange gravity currents using simultaneous velocity and density fields

Author(s): Partho Mukherjee and Sridhar Balasubramanian

Gravity currents, a genre of stratified shear flow, are a tremendous source of turbulence and mixing in ocean and atmosphere. Using high-resolution laser diagnostics, large-, intermediate- and small-scale flow features of an evolving current are measured in laboratory experiments. From this, the turbulent fluxes, mixing efficiency, and eddy diffusivity are quantified, which helps in inferring the state of turbulence inside the current. The results add new insights into modeling of stratified shear flows.

[Phys. Rev. Fluids 5, 063802] Published Wed Jun 03, 2020

### Dynamic one-equation-based subgrid model for large-eddy simulation of stratified turbulent flows

Author(s): R. Ranjan, M. K. Venkataswamy, and S. Menon

The locally dynamic one-equation based subgrid-scale is extended for large-eddy simulation of stably stratified turbulent flows. It is comprehensively assessed by simulating turbulent channel flow for a range of Reynolds and Richardson numbers. It captures all the key flow features, such as suppression of vertical turbulent transport, presence of internal waves and pycnocline, and decrease of the friction coefficient and Nusselt number. The turbulence statistics show good agreement with the reference results thus demonstrating its applicability to stratified flows with variable mean shear.

[Phys. Rev. Fluids 5, 064601] Published Wed Jun 03, 2020

### Transition from non-swirling to swirling axisymmetric turbulence

Author(s): Zecong Qin, Hugues Faller, Bérengère Dubrulle, Aurore Naso, and Wouter J. T. Bos

Axisymmetric turbulence is shown to exhibit a critical transition between two flow states. This transition is triggered by the anisotropy of the forcing of the system.

[Phys. Rev. Fluids 5, 064602] Published Wed Jun 03, 2020

### Eulerian and Lagrangian analysis of coherent structures in separated shear flow by time-resolved particle image velocimetry

We investigate the turbulent shear flow that separates from a two-dimensional backward-facing step. We aim to analyze the unsteady separated and reattaching shear flow in both the Eulerian and Lagrangian frameworks in order to provide complementary insight into the self-sustaining coherent structures and Lagrangian transport of the entrainment process. The Reynolds number is Reh = 1.0 × 103, based on the incoming free-stream velocity and step height. The separated and reattaching shear flow as well as the recirculation region beneath is measured by time-resolved planar particle image velocimetry. As a result, time sequences of velocity vector fields in a horizontal–vertical plane in the center of the step model are obtained. In the Eulerian approach, a set of temporally orthogonal dynamic modes are extracted, and each one represents a single-frequency vortex pattern that neutrally evolves in time. The self-sustaining coherent structures are represented by reduced-order reconstruction of the identified high-amplitude dynamic modes, showing the basic unsteady flapping motion of the shear layer and the vortex rolling-up, pairing, and shedding processes superimposed on it. On the other hand, trajectories of passive fluid tracers depict the Lagrangian fluid transport by the entrainment process in the separated shear flow and identify the time-dependent vortex rolling-up process as well as complex vortex interactions. The contours of the finite-time Lyapunov exponent reveal the unsteady Lagrangian coherent structures that significantly shape the vortex patterns and contribute substantial parts to the fluid entrainment in the shear flow.

### On a non-linear droplet oscillation theory via the unified method

Presently, the oscillation of a liquid droplet in a dynamically negligible outer medium subject to surface tension and small viscosity is investigated. By using the potential flow assumption, the unified transform method by Fokas is employed to reduce the corresponding free boundary problem formulated on a time-dependent domain into a nonlinear system of integro-differential equations (IDEs). This new system depends on one less spatial variable and is now defined on a time-independent domain. Most importantly, the resulting set of equations governs the general droplet oscillation with arbitrarily large deviations from the spherical shape. As the nonlinearity of the above IDE system up to now prevented an analytical solution, the Poincaré expansion technique is employed, retaining terms up to the second order. By decomposing the unknowns into normal modes, these equations are uncoupled and the resulting ordinary differential equations for the mode amplitudes are solved, and the results are compared to those of previous works. It should be stressed that the present analysis is limited to small viscosity, or, in other words, for small Ohnesorge numbers. The reason for this is that, inside of the droplet, a potential flow is assumed and the viscous effect is taken into account only at the droplet surface by the jump condition of momentum. This is only reasonable for a small viscosity and a short time. Otherwise, vorticity is generated at the interface and diffuses toward the inside of the droplet.

### Three-dimensional vortical structures generated by plasma synthetic jets in crossflow

In the present study, phase-locked tomographic particle image velocimetry measurements are performed to obtain the complex three-dimensional vortex system created by the interaction of plasma synthetic jets with external crossflow. Three orifice configurations (round, transverse slot, and longitudinal slot) are investigated. For the round orifice case, the vortex system consists of a starting vortex ring surrounding the jet head, a hanging vortex pair residing in the two lateral sides of the jet body, several shear layer vortices bridging the two legs of the hanging vortex pair, and a hairpin vortex induced by the low-speed secondary jet. For the slot orifice cases, the above vortex system is also present; nevertheless, the interconnections of the vortices are further intersected by the rib vortices that are branched out of the elongated vortex ring during axis switching. The counter-rotating vortex pair observed in the far field is essentially evolving from the hanging vortex pair in the near field.

### Fluvial instabilities

Fluvial instabilities originate from an interplay between the carrier fluid and the erodible loose boundary at their interface, manifesting a variety of sedimentary architectures with length scales spanning from a few millimeters to hundreds of meters. This review sheds light on the current state-of-the-science of the subject, explaining the fluvial instabilities from three broad perspectives. They are micro-scale, meso-scale, and macro-scale instabilities. The interactions between the near-bed hydrodynamics and the sediment dynamics in generating various kinds of instabilities, including their natures and driving mechanisms, are thoroughly appraised in the light of laboratory experimental results, field observations, and theoretical backgrounds. Besides, this review addresses the current challenges, delineating key points as a future research scope.

### Instabilities and layering of a heated laboratory anticyclone

Author(s): M. J. Burin, J. Sommeria, and S. Viboud

We present the first laboratory-based results on thermohaline vortex decay. Anticyclonic vortices 1m in diameter were generated within a stratified tank on a rotating platform. Besides an m=2 baroclinic instability, if heated, initially convective edge features yield at later times to diffusive convection and layering: the presumed beginnings of a thermohaline staircase.

[Phys. Rev. Fluids 5, 063801] Published Tue Jun 02, 2020

### Motion of buoyant point vortices

Author(s): Jeffrey R. Carpenter and Anirban Guha

A general Hamiltonian description for the trajectories of any number of interacting buoyant vortices in a homogeneous ambient fluid is presented. It constitutes an idealized description of coherent vortex structures in environmental flows where buoyancy forces are relevant for the evolution of such structures. The addition of buoyancy to this simple system results in the earlier appearance of chaos in the motion of buoyant vortex structures.

[Phys. Rev. Fluids 5, 064702] Published Tue Jun 02, 2020

### Single-particle Lagrangian statistics from direct numerical simulations of rotating-stratified turbulence

Author(s): D. Buaria, A. Pumir, F. Feraco, R. Marino, A. Pouquet, D. Rosenberg, and L. Primavera

Turbulent fluid flows such as those in the ocean and the nocturnal atmosphere are strongly affected by Earth’s rotation and a stable density stratification. Using direct numerical simulations of the governing equations, the Lagrangian dispersion of particles in such flows is investigated. The anisotropy of various Lagrangian statistics is quantified, and different flow regimes are identified based on underlying linear and nonlinear physical processes. Comparisons with theory are made when appropriate.

[Phys. Rev. Fluids 5, 064801] Published Tue Jun 02, 2020

### Improving the k–[math]–[math]–Ar transition model by the field inversion and machine learning framework

Accurate simulation of transition from the laminar to the turbulent flow is of great importance in industrial applications. In the present work, the framework of field inversion and machine learning has been applied to improve the four-equation k–ω–γ–Ar transition model. The low-speed transitional flows past two airfoils were numerically simulated. Based on the experimental transition locations, the regularizing ensemble Kalman filtering (EnKF) was performed to obtain the distributions of space-varied correction terms for the first mode time scale in the transitional flows over a natural-laminar-flow (NLF) airfoil, NLF(1)-0416. Then, two machine learning methods, random forest (RF) and artificial neutral network (NN), were adopted to construct the mapping from the mean flow variables to the correction terms. Finally, the learned models were embedded into the original solver. The results show that the regularizing EnKF can efficiently obtain the posterior distribution of the correction terms only by the transition locations. Meanwhile, both the RF- and NN-augmented transition models can predict more accurate transition locations past NLF(1)-0416 at both interpolated and extrapolated angles of attack. Moreover, the RF-augmented model can predict more accurate transitional flows on both the windward and leeward sides of NACA0012 at the same angle of attack. It indicates that the discrepancies within the model are learned and reduced. The modified model has good applicability and generalization ability. Furthermore, by analyzing the relative importance of the features in the RF model, it is found that the streamwise pressure gradient plays the most important role in the physical information and interpretation of the learned model.

### Moist-convective thermal rotating shallow water model

We show how the moist-convective rotating shallow water model, where the moist convection and the related latent heat release are incorporated into the standard rotating shallow water model of the atmosphere, can be improved by introducing, in a self-consistent way, horizontal gradients of potential temperature and changes of the latter due to the condensation heating, radiative cooling, and ocean-atmosphere heat fluxes. We also construct the quasi-geostrophic limit of the model in mid-latitudes and its weak-gradient limits in the equatorial region. The capabilities of the new model are illustrated by the examples of convection-coupled gravity waves and equatorial waves produced by the relaxation of localized pressure and potential temperature anomalies in the presence of moist convection.

### A computational fluid dynamics approach for full characterization of muffler without and with exhaust flow

Compared to the linear frequency domain method, the transient Computational Fluid Dynamics (CFD) method is more effective when analyzing the effect of complex flow in the muffler on its acoustic characteristics. However, most of the existing CFD methods focus on the calculation of the transmission loss (TL) for the muffler only. The other evaluation parameters, such as noise reduction (NR), are rarely investigated. In this paper, a CFD approach was developed systematically for charactering TL, NR, and transfer matrix (TM) of the muffler in the cases without and with exhaust flow. In the proposed approach, only one mesh model with a correction pipe is needed based on two simulation runs. The non-reflective boundary was used as the termination of the correction pipe in the calculation for the TL, while the reflective pressure boundary was set on the correction pipe end in the calculation for the NR. The TM was then derived from the time-domain pressure and mass velocity obtained in the previous runs for calculating TL and NR. The proposed CFD approach was applied to two simple expansion chambers, and the computational predictions of TL, NR, and TM were validated successfully both with the measured results and the analytical results. In conclusion, the proposed CFD approach is effective for full characterization (TL, NR, and TM) of exhaust mufflers without and with exhaust flow.

### An efficient selective cell-based smoothed finite element approach to fluid-structure interaction

This paper describes an efficient and simple selective cell-based smoothed finite element method (CS-FEM) for partitioned fluid–structure interaction. Depending on a fractional-step fluid solver, a selective smoothed integration scheme is proposed for the Navier–Stokes equations in stationary and deforming domains. A simple hourglass stabilization is then introduced into the under-integrated smoothed Galerkin weak form of the fractional-step algorithm. As a result, the computational efficiency is considerably boosted in comparison with existing CS-FEM formulation. Meanwhile, the CS-FEM is applied to spatially discretize the elastodynamics equations of nonlinear solids as usual. After discussing the mesh moving strategy, the gradient smoothing is performed in each individual interface element to evaluate the fluid forces acting on oscillating rigid and flexible bodies. The block Gauss–Seidel procedure is employed to couple all interacting fields under the arbitrary Lagrangian–Eulerian description. Several numerical examples are presented to demonstrate the desirable efficiency and accuracy of the proposed methodology.

### Dynamics of the passive pulsation of a surface-attached air bubble subjected to a nearby oscillating spark-generated bubble

The dynamics of a spark-generated bubble (a discharge short circuit) generated in proximity to a stationary air bubble attached to a plate is experimentally investigated by high-speed photography. Numerous interesting and complex interactions occur during the two bubble coupling pulsation owing to the deformation properties or “free surface” characteristics supplied to the plate by the attached air bubble. Complex bubble jetting behaviors, such as bubble splitting, jets away from the plate, variable directional jets, and multidirectional jets are observed. Passive pulsation of the air bubble is observed in response to the spark bubble. Moreover, five types of bubble behaviors are summarized: bubble coalescence, the air bubble skirt phenomenon, the “mountain”-shaped bubble, and the “cup cover”-shaped air bubble with or without splitting. To develop a better understanding of the coupling interactions between the two bubbles during their oscillations, four types of bubble volume–time curves are summarized using the image outline identification code established to obtain information regarding the bubble shape. The complex phenomena during the two-bubble interactions, such as the bubble jetting direction, air bubble shapes, and volume–time curves, are summarized as graphs and are highly dependent on the bubble size ratio, dimensionless cavitation bubble oscillation time, and initial displacement parameter.

### Oblique elastic plate impact on thin liquid layer

The present study is concerned with possible mechanisms of air entrainment in a thin liquid layer caused by oblique impact of a deformable body on the layer. The two-dimensional unsteady problem of oblique elastic plate impact is considered within the thin-layer approximation for the first time. The plate deflection is described by the Euler beam equation. The plate edges are free of stresses and shear forces. The plate deflections are comparable with the liquid layer thickness. It is revealed in this paper that, for a stiff plate, the initial impact by the trailing edge makes the plate rotate with the leading plate edge entering water before the wetted part of the plate arrives at this edge. The air cavity trapped in such cases can be as long as 40% of the plate length. For a flexible plate, the impact does not cause the plate rotation. However, the dry part of the plate in front of the advancing wetted region is deflected toward the liquid layer also trapping the air. The numerical results are presented for elastic and rigid motions of the plate, hydrodynamic pressure in the wetted part of the plate, position of this wetted part, and the flow beneath the plate.

### Deformation and burst of a liquid droplet with viscous surface moduli in a linear flow field

Author(s): Natasha Singh and Vivek Narsimhan

We investigate conditions for the breakup of a droplet with viscous surface moduli, under the assumption of weak flow and negligible Marangoni forces. The viscous interface is treated as a homogenous fluid obeying the Boussinesq–Scriven constitutive law. We observed that the presence of surface shear viscosity stabilizes the droplet, while that of surface dilational viscosity destabilizes it. The destabilizing effect of surface dilational viscosity appears similar to surfactant convection effects, while the stabilizing impact of surface shear viscosity appears similar to surfactant dilution.

[Phys. Rev. Fluids 5, 063601] Published Mon Jun 01, 2020

### Shape evolution of compound droplet in combined presence of electric field and extensional flow

Author(s): Somnath Santra, Devi Prasad Panigrahi, Sayan Das, and Suman Chakraborty

We study the unique morphodynamics of a compound droplet resulting from the interplay between an imposed electric field and an extensional flow. The nonintuitive findings include the interconversion of shape-evolution patterns of the compound droplet system depending on the background flow strength, electric field strength, electrophysical properties, and here unveiled post-breakup dynamics. We also show that including an electric field causes an intricate dependence of extensional viscosity on the electrical properties of the inner droplet - a paradigm not prevalent in pure extensional flow.

[Phys. Rev. Fluids 5, 063602] Published Mon Jun 01, 2020