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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↗

arXiv2022

The effect of isolated ridges and grooves on static menisci in rectangular channels

We present theoretical and numerical results that demonstrate the sensitivity of the shape of a static meniscus in a rectangular channel to localised geometric perturbations in the form of narrow ridges and grooves imposed on the channel walls. The Young--Laplace equation is solved for a gas/liquid interface with fixed contact angle using computations, analytical arguments and semi-analytical solutions of a linearised model for small-amplitude perturbations. We find that the local deformation of the meniscus's contact line near a ridge or groove is strongly dependent on the shape of the perturbation. In particular, small-amplitude perturbations that change the channel volume induce a change in the pressure difference across the meniscus, resulting in long-range curvature of its contact line. We derive an explicit expression for this induced pressure difference directly in terms of the boundary data. We show how contact lines can be engineered to assume prescribed patterns using suitable combinations of ridges and grooves.

physics.flu-dyn↗

arXiv2021

Linear instability and resonance effects in large-scale opposition flow control

Opposition flow control is a robust strategy that has been proved effective in turbulent wall-bounded flows. Its conventional setup consists of measuring wall-normal velocity in the buffer layer and opposing it at the wall. This work explores the possibility of implementing this strategy with a detection plane in the logarithmic layer, where control could be feasible experimentally. We apply control on a channel flow at $Re_τ= 932$, only on the eddies with relatively large wavelengths ($λ/ h > 0.1$). Similarly to the buffer layer opposition control, our control strategy results in a virtual-wall effect for the wall-normal velocity, creating a minimum in its intensity. However, it also induces a large response in the streamwise velocity and Reynolds stresses near the wall, with a substantial drag increase. When the phase of the control lags with respect to the detection plane, spanwise-homogeneous rollers are observed near the channel wall. We show that they are a result of a linear instability. In contrast, when the control leads with respect to the detection plane, this instability is inactive and oblique waves are observed. Their wall-normal profiles can be predicted linearly as a response of the turbulent channel flow to a forcing with the advection velocity of the detection plane. The linearity, governing the flow, opens a possibility to affect large scales of the flow in a controlled manner, when enhanced turbulence intensity or mixing is desired.

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↗

arXiv2025

Stability of trapped fluid clusters in two-phase porous media flow

A key challenge in multiphase flow through porous media is to understand and predict the conditions under which trapped fluid clusters become mobilized. Here, we investigate the stability of such clusters in two-phase flow and present a simple, quasistatic model that accurately determines the critical Bond number (that is, the critical ratio between the average pressure gradient of the flow and the surface tension) for the onset of cluster mobilization. The model is derived by combining elementary geometrical considerations with mass conservation and a mechanical equilibrium condition, resulting in a system of coupled differential equations. Our derivation sheds new light on the mechanisms that govern cluster stability. In addition, since the number of equations equals the number of cluster openings, our model is significantly faster than direct numerical simulations of the same problem and enables efficient exploration of the system's parameter space. Using this approach, we highlight a discrepancy with the prediction of current mean-field theories, which predict that the largest stable cluster size scales in proportion to $r/\text{Bo}^α$, where $r$ is a typical pore size, $\text{Bo}$ is the Bond number and $α$ is a fixed exponent. We discuss the mechanisms that explain the breakdown of the mean field theories, and we show that a scaling law of this form can only exist if $α$ is allowed to depend on a broad set of flow and geometric parameters.

physics.flu-dyn↗

arXiv2013

A stochastic view of isotropic turbulence decay

A stochastic EDQNM approach is used to investigate self-similar decaying isotropic turbulence at high Reynolds number ($400 \leq Re_λ\leq 10^4$). The realistic energy spectrum functional form recently proposed by Meyers & Meneveau is generalised by considering some of the model constants as random parameters, since they escape measure in most experimental set-ups. The induced uncertainty on the solution is investigated building response surfaces for decay power-law exponents of usual physical quantities. Large-scale uncertainties are considered, the emphasis being put on Saffman and Batchelor turbulence. The sensitivity of the solution to initial spectrum uncertainties is quantified through probability density functions of the decay exponents. It is observed that initial spectrum shape at very large scales governs the long-time evolution, even at high Reynolds number, a parameter which is not explicitly taken into account in many theoretical works. Therefore, a universal asymptotic behavior in which kinetic energy decays as $t^{-1}$ is not detected. But this decay law is observed at finite Reynolds number with low probability for some initial conditions.

physics.flu-dyn↗

arXiv2010

Geometry of Valley Growth

Although amphitheater-shaped valley heads can be cut by groundwater flows emerging from springs, recent geological evidence suggests that other processes may also produce similar features, thus confounding the interpretations of such valley heads on Earth and Mars. To better understand the origin of this topographic form we combine field observations, laboratory experiments, analysis of a high-resolution topographic map, and mathematical theory to quantitatively characterize a class of physical phenomena that produce amphitheater-shaped heads. The resulting geometric growth equation accurately predicts the shape of decimeter-wide channels in laboratory experiments, 100-meter wide valleys in Florida and Idaho, and kilometer wide valleys on Mars. We find that whenever the processes shaping a landscape favor the growth of sharply protruding features, channels develop amphitheater-shaped heads with an aspect ratio of pi.

physics.flu-dyn↗

arXiv2018

Flows and dynamos in a model of stellar radiative zones

Stellar radiative zones are typically assumed to be motionless in standard models of stellar structure but there is sound theoretical and observational evidence that this cannot be the case. We investigate by direct numerical simulations a three-dimensional and time-dependent model of stellar radiation zones consisting of an electrically-conductive and stably-stratified anelastic fluid confined to a rotating spherical shell and driven by a baroclinic torque. As the baroclinic driving is gradually increased a sequence of transitions from an axisymmetric and equatorially-symmetric time-independent flow to flows with a strong poloidal component and lesser symmetry are found. It is shown that all flow regimes characterised with significant non-axisymmetric components are capable of generating self-sustained magnetic field. As the value of the Prandtl number is decreased and the value of the Ekman number is decreased flows become strongly time-dependent with progressively complex spatial structure and dynamos can be generated at lower values of the magnetic Prandtl number.

physics.flu-dyn↗

arXiv2018

Thrifty swimming with shear-thinning

Microscale propulsion is integral to numerous biomedical systems, for example biofilm formation and human reproduction, where the surrounding fluids comprise suspensions of polymers. These polymers endow the fluid with non-Newtonian rheological properties, such as shear-thinning and viscoelasticity. Thus, the complex dynamics of non-Newtonian fluids presents numerous modelling challenges, strongly motivating experimental study. Here, we demonstrate that failing to account for "out-of-plane" effects when analysing experimental data of undulatory swimming through a shear-thinning fluid results in a significant overestimate of fluid viscosity around the model swimmer C. elegans. This miscalculation of viscosity corresponds with an overestimate of the power the swimmer expends, a key biophysical quantity important for understanding the internal mechanics of the swimmer. As experimental flow tracking techniques improve, accurate experimental estimates of power consumption using this technique will arise in similar undulatory systems, such as the planar beating of human sperm through cervical mucus, will be required to probe the interaction between internal power generation, fluid rheology, and the resulting waveform.

physics.flu-dyn↗

arXiv2022

Role of Oxygen Functionalities in Graphene Oxide Architectural Laminate Subnanometer Spacing and Water Transport

Active research in nanotechnology contemplates the use of nanomaterials for engineering applications. However, a primary challenge is understanding the effects of nanomaterial properties on industrial device performance and translating unique nanoscale properties to the macroscale. One emerging example is graphene oxide (GO) membranes for separation processes. Thus, here we investigate how individual GO properties can impact layered GO characteristics and water permeability. GO chemistry and morphology were controlled with easy-to-implement photo-reduction and sonication techniques and were quantitatively correlated offering a valuable tool to speed up the characterization process. For example, one could perform chemical analysis and concurrently obtain morphology information or vice versa. Chemical GO modification allows for fine control of GO oxidation state and GO laminate nanoarchitecture enabling controlled synthesis of a GO architectural laminate (GOAL). The GOAL can be considered as the selective layer of the membrane created by interconnected sub-nanometer channels, characterized by a length and a height (i.e., GO spacing), through which water molecules permeate. Water permeability was measured for eight GOAL characterized by different GO chemistry and morphology, and indicate that GO nanochannel height dictates water transport. The simulations indicate a no-slip Darcy-like water transport regime inside the GOAL due to the presence of basal oxygen functionalities. The experimental and simulation evidence presented in this letter help create a clearer picture of water transport in GO and can be used to rationally design more effective and efficient GO membranes.

physics.flu-dyn↗

arXiv2018

Equilibrium contact angle and adsorption layer properties with surfactants

The three-phase contact line of a droplet on a smooth surface can be characterized by the Young-Dupré equation. It relates the interfacial energies with the macroscopic contact angle $θ_e$. On the mesoscale, wettability is modeled by a film-height-dependent wetting energy $f(h)$. Macro- and mesoscale description are consistent if $γ\cos θ_\mathrm{e} =γ+f(h_\mathrm{a})$ where $γ$ and $h_\mathrm{a}$ are the liquid-gas interface energy and the thickness of the equilibrium liquid adsorption layer, respectively. Here, we derive a similar consistency condition for the case of a liquid covered by an insoluble surfactant. At equilibrium, the surfactant is spatially inhomogeneously distributed implying a non-trivial dependence of $θ_\mathrm{e}$ on surfactant concentration. We derive macroscopic and mesoscopic descriptions of a contact line at equilibrium and show that they are only consistent if a particular dependence of the wetting energy on the surfactant concentration is imposed.This is illustrated by a simple example of dilute surfactants, for which we show excellent agreement between theory and time-dependent numerical simulations.

physics.flu-dyn↗

arXiv2018

Multi-Ring Deposition Pattern of Drying Droplets

We propose a theory for the multi-ring pattern of the deposits that are formed when droplets of suspension are dried on a substrate. Assuming a standard model for the stick-slip motion of the contact line, we show that as droplets evaporate, many concentric rings of deposits are formed, but are taken over by a solid-circle pattern in the final stage of drying. An analytical expression is given to indicate when ring-pattern changes to solid-circle pattern during an evaporation process. The results are in qualitative agreement with existing experiments, and the other predictions on how the evaporation rate, droplet radius and receding contact angle affect the pattern are all subject to experimental test.

cond-mat.soft↗