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arXiv2022

Interaction between near-wall streaks and large-scale motions in turbulent channel flows

The interactions between the near-wall streaks and the large-scale motions (LSMs) of the outer region of wall-bounded turbulent flows are investigated. The co-supporting hypothesis of Toh & Itano (2005) is checked in full-scale channels at low to moderate Reynolds numbers, from two points of view. To study the top-down influence of the outer structures on the spanwise motion of the near-wall streaks, a method inspired by particle-image velocimetry is used to track the spanwise position of the streaks. Their spanwise advection velocity is found to be affected by the hierarchy of large-scale circulations in the logarithmic layer, but their spanwise streak density is only weakly related to the LSMs. The evidence suggests that a top-down influence exists and drives the drift of the streaks in the spanwise direction, as suggested by Toh & Itano (2005), but that the hypothesized streak accumulation rarely occurs. Numerical experiments at Re_tau about 535 are then performed to clarify the role of the near-wall streaks in the generation and preservation of the outer LSMs. The results show that the merger of the near-wall streaks is only weakly correlated with the generation of the LSMs, and that removing the near-wall roots of the LSMs does not affect the evolution of their outer region. It is concluded that the bottom-up influence from the near-wall streaks is not essential for the LSM generation and preservation, also weakening the evidence for the co-supporting hypothesis.

physics.flu-dyn↗

arXiv2025

On the Linear Stability of Partially and Fully Saturated Atmospheres to Moist Convection

We present a linear analysis of a minimal model of moist convection under a variety of atmospheric conditions. The stationary solutions that we analyze include both fully saturated and partially unsaturated atmospheres in both unconditionally and conditionally unstable cases. We find that all of the solutions we consider are linearly unstable via exchange of stability when sufficiently driven. The critical Rayleigh numbers vary by over an order of magnitude between unconditionally unstable and conditionally unstable atmospheres. The unsaturated atmospheres are notable for the presence of linear gravity wave-like oscillations even in unstable conditions. We study their eigenfunction structure and find that the buoyancy and moisture perturbations are anticorrelated in $z$, such that regions of negative buoyancy have positive moisture content. We suggest that these features in unsaturated atmospheres may explain the phenomenon of gravity wave shedding by moist convective plumes.

physics.flu-dyn↗

arXiv2024

Inhomogeneity-induced wavenumber diffusion

Inertia-gravity waves are scattered by background flows as a result of Doppler shift by a non-uniform velocity. In the WKB regime, the scattering process reduces to a diffusion in spectral space. Other inhomogeneities the waves encounter, such as density variations, also cause scattering and spectral diffusion. We generalise the spectral diffusion equation to account for these inhomogeneities. We apply the result to the rotating shallow water system, for which height inhomogeneities arise from velocity inhomogeneities through geostrophy, and to the Boussinesq system for which buoyancy inhomogeneities arise similarly. We compare the contributions that height and buoyancy variations make to the spectral diffusion with the contribution of the Doppler shift. In both systems, we find regimes where all contributions are significant. We support our findings with exact solutions of the diffusion equation and with ray tracing simulations in the shallow water case.

physics.flu-dyn↗

arXiv2024

Machine-learning wall-model large-eddy simulation accounting for isotropic roughness under local equilibrium

We introduce a wall model (WM) for large-eddy simulation (LES) applicable to rough surfaces with Gaussian and non-Gaussian distributions for both transitionally and fully rough regimes. The model is applicable to arbitrary complex geometries where roughness elements are assumed to be underresolved. The wall model is implemented using a feedforward neural network, with the geometric properties of the roughness topology and near-wall flow quantities serving as input. The optimal set of non-dimensional input features is identified using information theory, selecting variables that maximize information about the output while minimizing redundancy among inputs. The model incorporates a confidence score based on Gaussian process modeling, enabling the detection of low model performance for unseen rough surfaces. The model is trained using a direct numerical simulation roughness database comprising approximately 200 cases. The roughness geometries for the database are selected from a large repository through active learning. This approach ensures that the rough surfaces incorporated into the database are the most informative. The model performance is evaluated both a-priori and a-posteriori in WMLES of turbulent channel flows with rough walls. Over 120 channel flow cases are considered, including untrained roughness geometries, roughness Reynolds numbers, and grid resolutions for both transitionally- and fully-rough regimes. The results show that the rough-wall model predicts the wall shear stress within 15% accuracy. The model is also assessed on a high-pressure turbine blade with two different rough surfaces. The WM predicts the skin friction and the mean velocity deficit within 10% accuracy except the region with shock waves.

physics.flu-dyn↗

arXiv2024

Reynolds number effects on turbulent flow in curved channels

In this work, we study the flow in curved channels, an archetypal configuration that allows insights into problems featuring turbulence bounded by curved walls. Besides its relevance to many engineering applications, it exhibits a rich physics due to the presence of turbulence superimposed to large-scale structures driven by centrifugal instabilities. The resulting secondary motions, which depend on the channel geometry and Reynolds number, break symmetry between the convex and the concave surface. We investigate the effects of curvature by focusing on two cases of mildly and strongly curved channel, in which shear and inertia are supposed to control the general features of the flow, respectively. For each geometry, we examine systematically the effects of the Reynolds number: we run a campaign of direct numerical simulations covering flow regimes from laminar up to moderately high value of Reynolds number - based on bulk velocity and channel height - of 87000. Our analysis pivots around the friction coefficient, which is the macroscopic observable of the flow, and explores how the large-scale structures change their shape and role on turbulence for increasing Reynolds numbers. Special attention is paid to the longitudinal large-scale structures (resembling Dean vortices), and how their dynamics of splitting and merging is influenced by curvature. In addition, we also observe and characterise transverse large-scale structures populating the convex wall of strongly curved channels, which are originated by streamwise instabilities and contribute to the negative production of turbulence kinetic energy.

physics.flu-dyn↗

arXiv2025

Principles of hydrodynamic particle manipulation in internal Stokes flow

Manipulation of small-scale particles across streamlines is the elementary task of microfluidic devices. Many such devices operate at very low Reynolds numbers and deflect particles using arrays of obstacles, but a systematic quantification of relevant hydrodynamic effects has been lacking. Here, we explore an alternate approach, rigorously modeling the displacement of force-free spherical particles in vortical Stokes flows under hydrodynamic particle-wall interaction. Certain Moffatt-like eddy geometries with broken symmetry allow for systematic deflection of particles across streamlines, leading to particle accumulation at either Faxen field fixed points or limit cycles. Moreover, particles can be forced onto trajectories approaching channel walls exponentially closely, making quantitative predictions of particle capture (sticking) by short-range forces possible. This rich, particle size-dependent behavior suggests the versatile use of inertial-less flow in devices with a long particle residence time for concentration, sorting, or filtering.

physics.flu-dyn↗

arXiv2024

Three-dimensional coherent structures in a curved pipe flow

Dean's approximation for curved pipe flow, valid under loose coiling and high Reynolds numbers, is extended to study three-dimensional travelling waves. Two distinct types of solutions bifurcate from the Dean's classic two-vortex solution. The first type arises through a supercritical bifurcation from inviscid linear instability, and the corresponding self-consistent asymptotic structure aligns with the vortex-wave interaction theory. The second type emerges from a subcritical bifurcation by curvature-induced instabilities and satisfies the boundary region equations. Despite the subcritical nature of the second type of solutions, it is not possible to connect their solution branches to the zero-curvature limit of the pipe. However, by continuing from known self-sustained exact coherent structures in the straight pipe flow problem, another family of three-dimensional travelling waves can be shown to exist across all Dean numbers. The self-sustained solutions also possess the two high-Reynolds-number limits. While the vortex-wave interaction type of solutions can be computed at large Dean numbers, their branch remains unconnected to the Dean vortex solution branch.

physics.flu-dyn↗

arXiv2024

Migration and deformation of a droplet enclosing an active particle

The encapsulation of active particles, such as bacteria or active colloids, inside a droplet gives rise to nontrivial shape dynamics and droplet motility. To understand this behavior, we derive an asymptotic solution for the fluid flow about a deformable droplet containing an active particle, modeled as a Stokes-flow singularity, in the case of small shape distortions. Offsetting of the active particle from the center of the drop breaks symmetry and leads to excitation of large number of shape modes as well as particle and drop displacement. Flows due to common singularity representations of active particles, such as Stokeslets, rotlets, and stresslets, are computed and compared to results for non-deformable droplets enclosing active particles. The effect of interfacial properties is also investigated. Surfactants adsorbed at the droplet interface immobilize the interface and arrest the droplet motion. Our results highlight strategies to steer the flows of active particles and create autonomously navigating containers.

cond-mat.soft↗

arXiv2013

Electrocapillary instability of magnetic fluid peak

The paper presents an experimental study of the capillary electrostatic instability occurring under effect of a constant electric field on a magnetic fluid individual peak. The peaks under study occur at disintegration of a magnetic fluid layer applied on a flat electrode surface under effect of a perpendicular magnetic field. The electrocapillary instability shows itself as an emission of charged drops jets from the peak point in direction of the opposing electrode. The charged drops emission repeats periodically and results in the peak shape pulsations. It is shown that a magnetic field affects the electrocapillary instability occurrence regularities and can stimulate its development. The critical electric and magnetic field strengths at which the instability occurs have been measured; their dependence on the peak size is shown. The hysteresis in the system has been studied; it consists in that the charged drops emission stops at a lesser electric (or magnetic) field strength than that of the initial occurrence. The peak pulsations frequency depending on the magnetic and electric field strengths and on the peak size has been measured.

physics.flu-dyn↗

arXiv2013

Hydrodynamic Instabilities Provide A Generic Route To Spontaneous Biomimetic Oscillations In Chemomechanically Active Filaments

Non-equilibrium processes which convert chemical energy into mechanical motion enable the motility of organisms. Bundles of inextensible filaments driven by energy transduction of molecular motors form essential components of micron-scale motility engines like cilia and flagella. The mimicry of cilia-like motion in recent experiments on synthetic active filaments supports the idea that generic physical mechanisms may be sufficient to generate such motion. Here we show, theoretically, that the competition between the destabilising effect of hydrodynamic interactions induced by force-free and torque-free chemomechanically active flows, and the stabilising effect of nonlinear elasticity, provides a generic route to spontaneous oscillations in active filaments. These oscillations, reminiscent of prokaryotic and eukaryotic flagellar motion, are obtained without having to invoke structural complexity or biochemical regulation. This minimality implies that biomimetic oscillations, previously observed only in complex bundles of active filaments, can be replicated in simple chains of generic chemomechanically active beads.

cond-mat.soft↗

arXiv2012

Oscillations and translation of a free cylinder in a confined flow

An oscillatory instability has been observed experimentally on an horizontal cylinder free to move and rotate between two parallel vertical walls of distance H; its characteristics differ both from vortex shedding driven oscillations and from those of tethered cylinders in the same geometry. The vertical motion of the cylinder, its rotation about its axis and its transverse motion across the gap have been investigated as a function of its diameter D, its density s, of the mean vertical velocity U of the fluid and of its viscosity. For a blockage ratio D/H above 0.5 and a Reynolds number Re larger then 14, oscillations of the rolling angle of the cylinder about its axis and of its transverse coordinate in the gap are observed together with periodic variations of the vertical velocity. Their frequency f is the same for the sedimentation of the cylinder in a static fluid (U = 0) and for a non-zero mean flow (U 6= 0). The Strouhal number St associated to the oscillation varies as 1/Re with : St.Re = 3 $\pm$ 0.15. The corresponding period 1/f is then independent of U and corresponds to a characteristic viscous diffusion time over a distance ~ D, implying a strong influence of the viscosity. These characteristics differ from those of vortex shedding and tethered cylinders for which St is instead roughly constant with Re and higher than here.

physics.flu-dyn↗

arXiv2013

Structure-dependent mobility of a dry aqueous foam flowing along two parallel channels

The velocity of a two-dimensional aqueous foam has been measured as it flows through two parallel channels, at a constant overall volumetric flow rate. The flux distribution between the two channels is studied as a function of the ratio of their widths. A peculiar dependence of the velocity ratio on the width ratio is observed when the foam structure in the narrower channel is either single staircase or bamboo. In particular, discontinuities in the velocity ratios are observed at the transitions between double and single staircase and between single staircase and bamboo. A theoretical model accounting for the viscous dissipation at the solid wall and the capillary pressure across a film pinned at the channel outlet predicts the observed non-monotonic evolution of the velocity ratio as a function of the width ratio. It also predicts quantitatively the intermittent temporal evolution of the velocity in the narrower channel when it is so narrow that film pinning at its outlet repeatedly brings the flow to a near stop.

physics.flu-dyn↗

arXiv2013

Stability of viscous long liquid filaments

We study the collapse of an axisymmetric liquid filament both analytically and by means of a numerical model. The liquid filament, also known as ligament, may either collapse stably into a single droplet or break up into multiple droplets. The dynamics of the filament are governed by the viscosity and the aspect ratio, and the initial perturbations of its surface. We find that the instability of long viscous filaments can be completely explained by the Rayleigh-Plateau instability, whereas a low viscous filament can also break up due to end pinching. We analytically derive the transition between stable collapse and breakup in the Ohnesorge number versus aspect ratio phase space. Our result is confirmed by numerical simulations based on the slender jet approximation and explains recent experimental findings by Castrejon-Pita et al., PRL 108, 074506 (2012).

physics.flu-dyn↗

arXiv2013

Helical swimming in Stokes flow using a novel boundary-element method

We apply the boundary-element method to Stokes flows with helical symmetry, such as the flow driven by an immersed rotating helical flagellum. We show that the two-dimensional boundary integral method can be reduced to one dimension using the helical symmetry. The computational cost is thus much reduced while spatial resolution is maintained. We review the robustness of this method by comparing the simulation results with the experimental measurement of the motility of model helical flagella of various ratios of pitch to radius, along with predictions from resistive-force theory and slender-body theory. We also show that the modified boundary integral method provides reliable convergence if the singularities in the kernel of the integral are treated appropriately.

physics.flu-dyn↗

arXiv2013

Spatial and temporal scales of force and torque acting on wall-mounted spherical particles in open channel flow

Data from direct numerical simulation of open channel flow over a geometrically rough wall at a bulk Reynolds number of 2900, generated by Chan-Braun et al. ["Force and torque acting on particles in a transitionally rough open-channel flow", J. Fluid Mech. 684, 441--474 (2011), 10.1017/jfm.2011.311] are further analysed with respect to the time and length scales of force and torque acting on the wall-mounted spheres. For the two sizes of spheres in a square arrangement (11 and 49 wall units in diameter, yielding hydraulically smooth and transitionally rough flow, respectively), the spatial structure of drag, lift and spanwise torque is investigated. The auto-correlation and spectra in time as well as the space-time correlation and convection velocities are presented and discussed. It is found that the statistics of spanwise particle torque are similar to those of shear stress at a smooth wall. Particle drag and lift are shown to differ from spanwise particle torque, exhibiting considerably smaller time and length scales; the convection velocities of drag and lift are somewhat larger than those of spanwise torque. Furthermore, correlations between the flow field and particle-related quantities are presented. The spatial structure of the correlation between streamwise velocity and drag/spanwise torque features elongated shapes reminiscent of buffer-layer streaks. The correlation between the pressure field and the particle drag exhibits two opposite-signed bulges on the upstream and downstream sides of a particle.

physics.flu-dyn↗

arXiv2013

Note on the hydrodynamic description of thin nematic films: strong anchoring model

We discuss the long-wave hydrodynamic model for a thin film of nematic liquid crystal in the limit of strong anchoring at the free surface and at the substrate. We rigorously clarify how the elastic energy enters the evolution equation for the film thickness in order to provide a solid basis for further investigation: several conflicting models exist in the literature that predict qualitatively different behaviour. We consolidate the various approaches and show that the long-wave model derived through an asymptotic expansion of the full nemato-hydrodynamic equations with consistent boundary conditions agrees with the model one obtains by employing a thermodynamically motivated gradient dynamics formulation based on an underlying free energy functional. As a result, we find that in the case of strong anchoring the elastic distortion energy is always stabilising. To support the discussion in the main part of the paper, an appendix gives the full derivation of the evolution equation for the film thickness via asymptotic expansion.

physics.flu-dyn↗

arXiv2018

Vortex interaction with a rough wall formed by a hexagonal lattice of posts

An experimental study is reported which investigates the head-on collision of a laminar vortex ring of diameter D (ReΓ= 3000) on a fakir-like surface composed of circular posts of height h*=0.068 located on a planar bed. Lattices of the posts in hexagonal and random distribution (average porosity of e = 0.94 in the layer) are compared to each other with respect to the plain wall. Prior to impact, the vortex ring develops the early state of natural azimuthal instabilities of different mode numbers N=5-7 competing with each other. While impacting with the rough wall, a secondary ring is observed which is pushed outwards and is not wrapped around the primary ring as in flat wall impact. Between both rings of opposite sign vorticity, a strong fluid rebound is induced. The hexagonal lattice causes the rapid growth of further secondary vortex structures in a regular mode number N=6 arrangement at the outer edge of the primary ring in form of six lobes which are aligned with the orientations of preferential pathways in the layer. At the outer tip of the lobes radial wall-jets are generated. Rotating the fakir geometry around the centre of impact also rotates the jets location and direction accordingly. A surface with random lattice of the posts at the same average number density is not able to repeat this observation and no regular secondary flow pattern is visible until full breakdown of the ring. The results show that a tailored arrangement of such posts can be used for near-wall flow control when patterns of preferred pathways in the posts layer lock-on with existing instability modes such as in impacting jet flows or in turbulent boundary layer flows.

physics.flu-dyn↗

arXiv2011

An exact axisymmetric spiral solution of incompressible 3D Euler equations

Spiral structure is one of the most common structures in the nature flows. A general steady spiral solution of incompressible inviscid axisymmetric flow was obtained analytically by applying separation of variables to the 3D Euler equations. The solution, depending on 3 parameters, describes the spiral path of the fluid material element on the Bernoulli surface, whereas some new exact solutions were obtained to be bounded within the whole region. The first one is a continued typhoon-like vortex solution, where there are two intrinsic length scales. One is the radius of maximum circular velocity $r_m$, the other is the radius of the vortex kernel $r_k=\sqrt{2}r_m$. The second one is a multi-planar solution, periodically in $z$-coordinate. Within each layer, the solution is a umbrella vortex similar to the first one. The third one is also a multi-planar solution in $z$-coordinate. In each layer, it is a combination of two independent solutions like the Rankine vortex, which is also finite but discontinued for either vertical or horizontal velocity. The fourth one is a multi-paraboloid vortex solution finite for $z$-coordinate but infinite for $r$-coordinate. Besides, some classical simple solutions (Rankine vortex, Batchelor vortex, Hill spherical vortex, etc.) were also obtained. The above explicit solutions can be applied to study the radial structure of the typhoon, tornados and mesoscale eddies. Both the solutions and approaches used here could also be applied to other complex flows by the Navier-Stokes equations.

physics.flu-dyn↗