# Latest papers in fluid mechanics

### Theoretical analysis and numerical simulations of turbulent jets in a wave environment

A thorough understanding of the mixing and diffusion of turbulent jets released in a wave flow field is still lacking in the literature. This issue is undoubtedly of interest because, although stagnant ambient conditions are well known, they are almost never present in real coastal environmental problems, where the presence of waves or currents is common. As a result, jets cannot be analyzed without considering the surrounding environment, which is only rarely under stagnant conditions. The aim of the present research is to analyze from a theoretical point of view a pure jet vertically discharged in a wave motion field. Specifically, starting from the fundamental Navier–Stokes equations governing the problem joined to the continuity equation, the equations of motion and the integral equations of momentum, energy, and moment of momentum are derived. Therefore, the laws of variation of the jet length and velocity scales are deduced. Results from experiments and numerical simulations of a jet issuing in a wave environment demonstrate the validity of the proposed laws.

### Interaction between rarefaction wave and viscous fingering in a Langmuir adsorbed solute

Author(s): Chinar Rana and Manoranjan Mishra

The evolution of dissolved species in a porous medium is determined by its adsorption on the porous matrix through the classical advection-diffusion processes. The extent to which the adsorption affects the solute propagation in applications related to chromatography and contaminant transport is lar...

[Phys. Rev. E 101, 033101] Published Mon Mar 02, 2020

### Statistics of relative velocity for particles settling under gravity in a turbulent flow

Author(s): Akshay Bhatnagar

We study the joint probability distributions of separation R and radial component of the relative velocity VR of particles settling under gravity in a turbulent flow. We also obtain the moments of these distributions and analyze their anisotropy using spherical harmonics. We find that the qualitativ...

[Phys. Rev. E 101, 033102] Published Mon Mar 02, 2020

### Solitary waves on superconfined falling liquid films

Author(s): Gianluca Lavalle, Nicolas Grenier, Sophie Mergui, and Georg F. Dietze

Solitary waves on the surface of a vertically falling liquid film in contact with an extremely confined counter-current gas flow are studied numerically. As the gas velocity is increased, traveling waves display a secondary oscillatory instability and then a catastrophic instability. The periodic amplitude modulations produced by the oscillatory instability intensify mixing and can be tuned through the gas velocity. The catastrophic instability leads to wave reversal and liquid arrest.

[Phys. Rev. Fluids 5, 032001(R)] Published Mon Mar 02, 2020

### Theoretical and numerical analysis of density perturbation development induced by high velocity impact

The problem of high velocity impact between two solid plates where one of them has a non-uniformly disturbed density field is studied. The nature of an initial perturbation here differs from one considered in the classical Richtmyer–Meshkov instability (RMI). We consider the instability that develops from the initial perturbations of the density field with a flat interface between plates, while RMI is triggered by a shock passing through the corrugated interface. The structure of perturbation fields generated in the plates due to impact and the interface evolution are studied via the analytic linear and nonlinear models for normal modes using the Euler equations for compressible fluids and appropriate boundary conditions. Such analysis reveals three different regimes in which the generated disturbances can develop depending on the direction of the perturbation wave vector. The obtained theoretical findings are in good quantitative agreement with our detailed numerical simulations.

### Viscoelastic laminar drag bounds in pipe flow

The velocity and friction properties of laminar pipe flow of a viscoelastic solution are bounded by the corresponding values for two Newtonian fluids, namely, the solvent and a fluid with a viscosity identical to the total viscosity of the solution. The lower friction factor for the flow of the solution when compared to the latter is tracked to an increased strain rate needed to enhance viscous dissipation. Finally, we show analytically that the effective viscosity varies similarly to the radial diagonal component of the conformation tensor as observed numerically in turbulent flows and give a lucid interpretation of shear-thinning through a sequence of underlying constitutive physical phenomena.

### Mechanism for vorticity in a secondary flow within a pipe: Vortex-induced vortex

Vortex-induced vortex theory, commonly used for a flow past a disturbed bluff body, is applied in this paper to analyze an incompressible flow through a circular-section pipe with the occurrence of a secondary flow. The disturbed flow field is solved based on the Stokes equations by introducing a vortex or vortex pair uniformly distributed along the axial direction and periodically varying along the azimuthal direction as a result of the secondary flow with the assumption of inertial force being neglected and the viscous force being dominant in the vicinity of the pipe walls. Two kinds of boundary cases are considered to simulate the introduced vorticity distributed on and near the walls, and two sign laws for vorticity are also derived and verified for the present internal flow. For original pipe flow with a specific velocity distribution, such as a paraboloid of revolution at lower Reynolds numbers, these two sign laws are all positive upstream but negative downstream and they physically reveal the intrinsic relationships of the vorticity sign among different vorticity components, which are generated inherently with specific signs in secondary flows. Furthermore, two basic viscous force mechanisms are identified: a direct effect for vorticity generated on the walls due to shear flows and an indirect effect for vorticity induced by a vortex with former vorticity near the walls. Examples to demonstrate these two sign laws under geometric disturbances at a laminar Reynolds number of 200 and physical meaning are also presented briefly.

### Effect of interfacial mass transport on inertial spreading of liquid droplets

In this work, the early time dynamics of low-viscosity liquid drops spreading in their saturated vapor on partially wetting surfaces are investigated by lattice Boltzmann numerical simulations. Attention is paid to the effect of vapor transport through condensation on the spreading process. We observe that the condensation current resulting from the slight supersaturation of the liquid vapor near the dynamic wetting meniscus contributes to the motion and affects the spreading dynamics. Our results indicate that, in order to properly capture the initial dynamics of inertial spreading of a relatively volatile liquid drop, it is important to account for the vapor transport through condensation in the immediate vicinity of the contact line. A direct qualitative and quantitative comparison with experimental data of spontaneously wetting liquid drops is presented.

### Instantaneous pressure determination from unsteady velocity fields using adjoint-based sequential data assimilation

A sequential data assimilation (DA) method is developed for pressure determination of turbulent velocity fields measured by particle image velocimetry (PIV), based on the unsteady adjoint formulation. A forcing term F, which is optimized using the adjoint system, is added to the primary Navier–Stokes (N–S) equations to drive the assimilated flow toward the observations at each time step. Compared with the conventional unsteady adjoint method, which requires the forward integration of the primary system and the backward integration of the adjoint system, the present approach integrates the primary-adjoint system all the way forward, discarding the requirement of data storage at every time step, being less computationally resource-consuming, and saving space. The pressure determination method of integration from eight paths [J. O. Dabiri et al., “An algorithm to estimate unsteady and quasi-steady pressure fields from velocity field measurements,” J. Exp. Biol. 217, 331 (2014)] is also evaluated for comparison. Using synthetic PIV data of a turbulent jet as the observational data, the present DA method is able to determine the instantaneous pressure field precisely using the three-dimensional velocity fields, regardless of the observational noise. For the two-dimensional three-component (3C) or two-component (2C) velocity fields, which are not sufficient for pressure determination by the integration method due to the lack of off-plane derivatives, the present DA method is able to reproduce pressure fields whose statistics agree reasonably well with those of the referential results. The 3C and 2C velocity fields yield quite similar results, indicating the possibility of pressure determination from only planar-PIV measurements in turbulent flows. The tomography PIV measurements are also used as observational data, and a clear pressure pattern is obtained with the present DA method.

### Identifying improved microchannel configuration with triangular cavities and different rib structures through evaluation of thermal performance and entropy generation number

Exploration of newer geometrical structures for microsinks stems from the desire to achieve better cooling at a lower pressure drop for more compact electronic devices. In this study, a three-dimensional conjugate heat transfer analysis is performed for a novel microchannel heat sink (MCHS) with disruptive structures in an otherwise rectangular channel. Each of these structural units has a pair of triangular cavities (TCs) on the opposite side walls and one in between the rib positioned symmetrically about the vertical mid-plane. Different units with diamond rib, rectangular rib (RR), backward triangular rib (BTR), and forward triangular rib (FTR) are analyzed. A notable finding of this work is identifying a rib as a disruption leading to thinning of the boundary layer on the side walls in the channel behind the rib. Another important contribution of a rib in both TC-RR and TC-BTR units is shown to promote chaotic advection due to having a longitudinal downstream vortex in each quadrant. The benefit of the lowest wall temperature is evident from the predicted results. Simple thermodynamic models are developed to establish that the minimization of entropy generation number (EGN) leads to the lowest temperature of the channel material for removing a given heat flux by the MCHS, and the maximization of the thermal performance (TP) implies achievement of the lowest pumping power. The corresponding numerical results are exploited for identifying the geometrical parameters over Reynolds number ranging from 197 to 595 that maximize the TP and closely minimize the EGN. The TC-FTR configuration is seen to yield the highest TP of about 1.78 at an intermediate value of Re around 400 along with low EGN of nearly 0.45. Results show that a microchannel with TC-BTR combination yields the highest heat transfer rate with a maximum pressure drop penalty leading to its poor TP. Thus, TC-RR turns out to be the choice in case a low wall temperature happens to be a critical requirement. A small sacrifice in it makes TC-FTR the choice for having the highest TP leading to a compact design.

### On the influence of two-dimensional hump roughness on laminar–turbulent transition

The presence of large surface irregularities such as humps, where the height is similar to the local boundary-layer (BL) displacement thickness, introduces regions of localized strong streamwise gradients in the base flow quantities. These large gradients can significantly modify the spatial development of incoming disturbances that lead to laminar–turbulent transition in wall-bounded flows [e.g., Tollmien–Schlichting (TS) waves]. Techniques such as Parabolized Stability Equations (PSE) are not suited for BL instability analysis in such regions: their formulation assumes that streamwise variations of base flow and disturbance quantities are small, allowing a marching procedure for their resolution. On the other hand, the Adaptive Harmonic Linearized Navier–Stokes (AHLNS) equations can handle these large streamwise gradients by using a fully elliptic system of equations, similar to Linearized Navier–Stokes (LNS), Harmonic LNS (HLNS), or Direct Numerical Simulation (DNS). Moreover, in AHLNS (as in PSE), a wave-like character of the instabilities is assumed, leading to a significant reduction in the number of streamwise grid points required compared with LNS, HLNS, or DNS computations. In the present study, an efficient combination of PSE and AHLNS is used to investigate the effect of height, length, and shape of a single hump placed on a flat plate in a two-dimensional flow field at Ma∞ = 0.5 without pressure gradient. The effect of this hump on the spatial evolution of TS waves, in terms of N-factors, is presented. An expected laminar–turbulent transition onset, via the eN methodology, is also described. It is shown that the shape of the surface irregularity, together with the height and length, plays an important role for the location of laminar–turbulent transition onset in convectively unstable flows.

### Nonlinear evolution of perturbations in high Mach number wall-bounded flow: Pressure–dilatation effects

We characterize the nonlinear evolution of perturbations in a high Mach number Poiseuille flow and contrast the behavior against an equivalent incompressible flow. The focus is on the influence of pressure–dilatation on (i) internal energy evolution, (ii) kinetic–internal energy exchange, and (iii) kinetic energy spectrum evolution. We perform direct numerical simulations of plane Poiseuille flow at different Mach numbers subject to a variety of initial perturbations. In all high-speed cases considered, pressure dilatation leads to energy equipartition between wall-normal velocity fluctuations (dilatational kinetic energy) and pressure fluctuations (a measure of internal energy). However, the effect of pressure–dilatation on the kinetic energy spectral growth can be varied. In cases wherein pressure–dilatation is larger than the turbulent kinetic energy production, spectral growth is considerably slow relative to an equivalent low Mach number case. When pressure–dilatation is smaller than production, the spectral growth is only marginally affected. As a consequence, in a high-speed Poiseuille flow, the spectral growth rate varies with the wall-normal distance depending on the local pressure effects. These findings provide valuable insight into the nonlinear aspects of breakdown toward turbulence in high speed wall-bounded shear flows.

### Surface wave mechanism for directional motion of droplet on an obliquely vibrated substrate

The directional motion of a two-dimensional droplet on an obliquely vibrated substrate is studied numerically. The time dependent droplet profile is decomposed by using a proper orthogonal decomposition (POD) method. Two dominant POD modes of the capillary wave are identified. The first mode is quasi-harmonic, which leads to an apparent wetted area difference between uphill and downhill stages of the substrate vibration (ΔS). It plays a key role in the directional motion. The second mode is weak but contributes to ΔS subtly. The two modes qualitatively match the proposed “swaying” and “spreading” modes. Our decomposition directly reveals the connection between ΔS and the surface waves.

### A comparative study on the large-scale-resolving capability of wall-modeled large-eddy simulation

Wall-modeled large-eddy simulation (WMLES) could be a useful predictive tool in high-Reynolds-number wall-bounded turbulent flows that are ubiquitous in nature and engineering, but its capability to resolve large-scale energy-containing outer motions has yet to be assessed comprehensively. In this study, moderately high-Reynolds-number turbulent channel flows up to Reτ ≈ 5200 are simulated by WMLES with various subgrid-scale (SGS) models and wall models in comparison with direct-numerical simulation data. The main objective is to assess the predictive capability of WMLES in the context of the turbulence kinetic energy spectrum in the outer region. Four classical eddy-viscosity-type SGS models are compared, i.e., the Smagorinsky model, the Lagrangian dynamic model, the Lagrangian scale-dependent (LASD) model, and the Vreman model. It is shown that the performance of the LASD model is superior to others in predicting one-point statistics as well as kinetic energy spectra. Three types of wall models are involved, i.e., the equilibrium wall model, the slip-wall model, and the integral wall model. We find that the wall model does not significantly affect prediction of turbulence fluctuations in the outer region. Although near-wall turbulent motions are not fully resolved in WMLES, we clearly show that the spectral characteristics of large-scale energy-containing turbulent motions in the outer region can reasonably be predicted with appropriate models. We also provide a preliminary discussion on the effects of domain setup and grid resolution. The difference in the spectral energy distribution between full- and half-channel flows is also reported.

### Multiplicity of stable orbits for deformable prolate capsules in shear flow

Author(s): Xiao Zhang and Michael D. Graham

The orbital dynamics of an inertialess deformable prolate capsule in unbounded shear flow are numerically investigated. In certain parameter regimes, the capsule can adopt multiple stable orbits, depending on the initial orientation. A corresponding multiplicity in the rheological properties is predicted for a dilute suspension of such capsules.

[Phys. Rev. Fluids 5, 023603] Published Fri Feb 28, 2020

### Shapes and stability of viscous rotating drops in a compressional/extensional flow

Author(s): Sumit Malik, Olga M. Lavrenteva, and Avinoam Nir

Simultaneous effects of rotation and compression or extension of a viscous drop are studied numerically in terms of deformation, stationarity, and stability of the drop. The problem is modeled in terms of creeping flow and is solved using the boundary integral method. The region of stability of the deformed drop under various effects is presented.

[Phys. Rev. Fluids 5, 023604] Published Fri Feb 28, 2020

### Integration through transients for inelastic hard sphere fluids

Author(s): W. Till Kranz, Fabian Frahsa, Annette Zippelius, Matthias Fuchs, and Matthias Sperl

Granular flows naturally occur at high densities and significant shear rates. A kinetic theory, applicable at high densities and arbitrary shear rates, predicting the viscosity of an inelastic hard sphere fluid over many orders of magnitude is proposed. It explains the origin of Newtonian, shear thinning, as well as shear thickening behavior, i.e., Bagnold scaling in granular fluids.

[Phys. Rev. Fluids 5, 024305] Published Fri Feb 28, 2020

### Flow topology dynamics in a three-dimensional phase space for turbulent Rayleigh-Bénard convection

Author(s): F. Dabbagh, F. X. Trias, A. Gorobets, and A. Oliva

A very hard turbulent regime of the classical Rayleigh-Bénard convection problem is accessed using direct numerical simulations (5.7 billion grid points) with the aim of obtaining a deeper understanding of the small-scale dynamics and flow topology. The outcomes attest to the strong self-growth of strain production augmented by vortex contraction, and the linear amplification of vortex stretching relevant to the strain-dominated structures.

[Phys. Rev. Fluids 5, 024603] Published Fri Feb 28, 2020

### Turbulent transition of a gaseous mixing zone induced by the Richtmyer-Meshkov instability

Author(s): Yannick Bury, Pierre Graumer, Stéphane Jamme, and Jérôme Griffond

A new experiment analyses the process driving the fast transition towards turbulence of an impulsively accelerated then decelerated interface between gases of different densities, when the timescale of this transitional process is of the same order as that of the resulting turbulence. This transition to turbulence is revealed as the imprint of the initial condition is lost and the dynamical spectral content covers a wide range of scales compatible with a self-similar trend.

[Phys. Rev. Fluids 5, 024101] Published Thu Feb 27, 2020

### Particle trapping in merging flow junctions by fluid-solute-colloid-boundary interactions

Author(s): Sangwoo Shin, Jesse T. Ault, Kazumi Toda-Peters, and Amy Q. Shen

Experiments and numerical simulations show how colloidal particles can be trapped permanently in merging flow channels. When two merging colloidal streams contain different solutes, interactions between the particles, solutes, channel wall, and the inlet fluid flow induce a near-wall vortex that leads to stable particle trapping. A unique particle trapping mechanism, potentially found in a wide range of common flow systems, is documented and characterized.

[Phys. Rev. Fluids 5, 024304] Published Thu Feb 27, 2020