Volume 987 - 25 May 2024
JFM Papers
Modelling the far-field effect of drag-induced dissipation in wave–structure interaction: a numerical and experimental study
- Alexis Mérigaud, Benjamin Thiria, Ramiro Godoy-Diana, Gaële Perret
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- Published online by Cambridge University Press:
- 17 May 2024, A24
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In the interaction of water waves with marine structures, the interplay between wave diffraction and drag-induced dissipation is seldom, if ever, considered. In particular, linear hydrodynamic models, and extensions thereof through the addition of a quadratic force term, do not represent the change in amplitude of the waves diffracted and radiated to the far field, which should result from local energy dissipation in the vicinity of the structure. In this work, a series of wave flume experiments is carried out, whereby waves of increasing amplitude impinge upon a vertical barrier, extending partway through the flume width. As the wave amplitude increases, the effect of drag – which is known to increase quadratically with the flow velocity – is enhanced, thus allowing the examination of the far-field effect of drag-induced dissipation, in terms of wave reflection and transmission. A potential flow model is proposed, with a simple quadratic pressure drop condition through a virtual porous surface, located on the sides of the barrier (where dissipation occurs). Experimental results confirm that drag-induced dissipation has a marked effect on the diffracted flow, i.e. on wave reflection and transmission, which is appropriately captured in the proposed model. Conversely, when diffraction becomes dominant as the barrier width becomes comparable to the incoming wavelength, the diffracted flow must be accounted for in predicting drag-induced forces and dissipation.
Surface tension and wetting at free surfaces in smoothed particle hydrodynamics
- Michael Blank, Prapanch Nair, Thorsten Pöschel
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- Published online by Cambridge University Press:
- 17 May 2024, A23
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Surface tension and wetting are dominating physical effects in microscale and nanoscale flows. We present an efficient and reliable model of surface tension and equilibrium contact angles in smoothed particle hydrodynamics for free-surface problems. We demonstrate its robustness and accuracy by simulating several three-dimensional free-surface flow problems driven by interfacial tension.
Peristaltic pumping down a porous conduit
- D. Takagi, N.J. Balmforth, Stefan G. Llewellyn Smith
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- Published online by Cambridge University Press:
- 17 May 2024, A22
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A theoretical analysis is presented of peristaltic pumping down a narrow conduit with permeable walls, motivated by the flushing action of lugworms and other marine organisms in sandy burrows. Flow in the conduit is dealt with using lubrication theory; the leakage into the surrounding medium is taken into account by exploiting slender-body theory to solve the associated Darcy problem. By adopting a model for the local force balance on the pumping surface, we bridge between the limits in which the pump operates with either fixed load or displacement. In the latter limit we characterize peristaltic waves with either fixed form or ones that partially collapse the conduit. We construct pump characteristics (the relation between the mean flux and net pressure drop) when the burrow wall is impermeable and pressures are fixed at each end, and compare the results with existing laboratory experiments performed on lugworms. We then consider how the peristaltic dynamics is changed when the wall is made permeable. Last, we consider pumping along an impermeable burrow into a leaky head shaft. The results reveal that the permeability of the conduit wall or end can greatly impact the direction and strength of the recirculating flow.
Impedance spectra of soft ionics
- Reghan J. Hill
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- Published online by Cambridge University Press:
- 17 May 2024, A21
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Impedance spectroscopy is widely adopted for probing the charge and charge mobility of soft ion-conducting media, such as synthetic membranes and biological tissue. The spectra exhibit a variety of distinctive signatures, but the physical basis of these is not well understood, e.g. models have not previously accounted for viscoelasticity, hydrodynamics or microstructural heterogeneity. This study explores a physically grounded continuum model that captures how these factors shape conductivity spectra. Nonlinear thermodynamics and linearised dynamics of a viscous electrolyte and compressible, elastic polymer network are coupled under the forcing of an oscillatory electric field. The model is solved in a one-dimensional spatially periodic unit cell, reporting conductivity and dielectric permittivity spectra, including Nyquist representations. Whereas rigid microstructures exhibit ion-diffusion-controlled relaxation, which manifests as a low-frequency dielectric ‘constant’, hydrodynamic and elastic forces contribute to a strongly diverging dielectric permittivity at low frequencies for heterogeneous anionic microstructures. The model also captures distinctive characteristics of experimentally reported impedance spectra for films bearing alternating layers of cationic and anionic charge, again highlighting the role of coupled hydrodynamic, elastic and electrical forces. Sufficiently thin and highly charged bilayers exhibit a notably low high-frequency conductivity. This is explained by strong low-frequency electrostatic polarisation and counter-ion release. The one-dimensional solutions computed herein provide a foundation for much more challenging computations in two and three dimensions.
Three-dimensional flow around and through a porous screen
- Olivier C. Marchand, Sophie Ramananarivo, Camille Duprat, Christophe Josserand
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- 16 May 2024, A20
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We investigate the three-dimensional (3-D) flow around and through a porous screen for various porosities at high Reynolds number $Re = {O}(10^4)$. Historically, the study of this problem has been focused on two-dimensional cases and for screens spanning completely or partially a channel. Since many recent problems have involved a porous object in a 3-D free flow, we present a 3-D model initially based on Koo & James (J. Fluid Mech., vol. 60, 1973, pp. 513–538) and Steiros & Hultmark (J. Fluid Mech., vol. 853, 2018 pp. 1–11) for screens of arbitrary shapes. In addition, we include an empirical viscous correction factor accounting for viscous effects in the vicinity of the screen. We characterize experimentally the aerodynamic drag coefficient for a porous square screen composed of fibres, immersed in a laminar air flow with various solidities and different angles of attack. We test various fibre diameters to explore the effect of the space between the pores on the drag force. Using PIV and hot wire probe measurements, we visualize the flow around and through the screen, and in particular measure the proportion of fluid that is deviated around the screen. The predictions from the model for drag coefficient, flow velocities and streamlines are in good agreement with our experimental results. In particular, we show that local viscous effects are important: at the same solidity and with the same air flow, the drag coefficient and the flow deviations strongly depend on the Reynolds number based on the fibre diameter. The model, taking into account 3-D effects and the shape of the porous screen, and including an empirical viscous correction factor that is valid for fibrous screens may have many applications including the prediction of water collection efficiency for fog harvesters.
Role of volatility and thermal properties in droplet spreading: a generalisation to Tanner's law
- Zhenying Wang, George Karapetsas, Prashant Valluri, Chihiro Inoue
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- Published online by Cambridge University Press:
- 17 May 2024, A15
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Droplet spreading is ubiquitous and plays a significant role in liquid-based energy systems, thermal management devices and microfluidics. While the spreading of non-volatile droplets is quantitatively understood, the spreading and flow transition in volatile droplets remains elusive due to the complexity added by interfacial phase change and non-equilibrium thermal transport. Here we show, using both mathematical modelling and experiments, that the wetting dynamics of volatile droplets can be scaled by the spatial–temporal interplay between capillary, evaporation and thermal Marangoni effects. We elucidate and quantify these complex interactions using phase diagrams based on systematic theoretical and experimental investigations. A spreading law of evaporative droplets is derived by extending Tanner's law (valid for non-volatile liquids) to a full range of liquids with saturation vapour pressure spanning from $10^1$ to $10^4$ Pa and on substrates with thermal conductivity from $10^{-1}$ to $10^3\ {\rm W}\ {\rm m}^{-1}\ {\rm K}^{-1}$. In addition to its importance in fluid-based industries, the conclusions also enable a unifying explanation to a series of individual works including the criterion of flow reversal and the state of dynamic wetting, making it possible to control liquid transport in diverse application scenarios.
Fragmentation of colliding liquid rims
- K. Tang, T.A.A. Adcock, W. Mostert
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- Published online by Cambridge University Press:
- 16 May 2024, A18
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We present direct numerical simulations of the splashing process between two cylindrical liquid rims. This belongs to a class of impact and collision problems with a wide range of applications in science and engineering, and motivated here by splashing of breaking ocean waves. Interfacial perturbations with a truncated white noise frequency profile are introduced to the rims before their collision, whose subsequent morphological development is simulated by solving the two-phase incompressible Navier–Stokes equation with the adaptive mesh refinement technique, within the Basilisk software environment. We first derive analytical solutions predicting the unsteady interfacial and velocity profiles of the expanding sheet forming between the two rims, and develop scaling laws for the evolution of the lamella rim under capillary deceleration. We then analyse the formation and growth of transverse ligaments ejected from the lamella rims, which we find to originate from the initial corrugated geometry of the perturbed rim surface. Novel scaling models are proposed for predicting the decay of the ligament number density due to the ongoing ligament merging phenomenon, and found to agree well with the numerical results presented here. The role of the mechanism in breaking waves is discussed further and necessary next steps in the problem are identified.
Unifying constitutive law of vibroconvective turbulence in microgravity
- Ze-Lin Huang, Jian-Zhao Wu, Xi-Li Guo, Chao-Ben Zhao, Bo-Fu Wang, Kai Leong Chong, Quan Zhou
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- 16 May 2024, A14
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We report the unified constitutive law of vibroconvective turbulence in microgravity, i.e. $Nu \sim a^{-1} Re_{os}^\beta$ where the Nusselt number $Nu$ measures the global heat transport, $a$ is the dimensionless vibration amplitude, $Re_{os}$ is the oscillational Reynolds number and $\beta$ is the universal exponent. We find that the dynamics of boundary layers plays an essential role in vibroconvective heat transport and the $Nu$-scaling exponent $\beta$ is determined by the competition between the thermal boundary layer (TBL) and vibration-induced oscillating boundary layer (OBL). Then a physical model is proposed to explain the change of scaling exponent from $\beta =2$ in the TBL-dominant regime to $\beta = 4/3$ in the OBL-dominant regime. Our finding elucidates the emergence of universal constitutive laws in vibroconvective turbulence, and opens up a new avenue for generating a controllable effective heat transport under microgravity or even microfluidic environment in which the gravity effect is nearly absent.
Coexistence of dual wing–wake interaction mechanisms during the rapid rotation of flapping wings
- Long Chen, Jianghao Wu
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- 16 May 2024, A16
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Insects flip their wings around each stroke reversal and may enhance lift in the early stage of a half-stroke. The possible lift-enhancing mechanism of this rapid wing rotation and its strong connection with wake vortices are still underexplored, especially when unsteady leading-edge vortex (LEV) behaviours occur. Here, we numerically studied the lift generation and underlying vorticity dynamics during the rapid rotation of a low aspect ratio flapping wing at a Reynolds number (${\textit {Re}}$) of 1500. Our findings prove that when the outboard LEV breaks down, an advanced rotation can still enhance the lift in the early stage of a half-stroke, which originates from an interaction with the breakdown vortex in the outboard region. This interaction, named the breakdown-vortex jet mechanism, results in a jet and thus a higher pressure on the upwind surface, including a stronger wingtip suction force on the leeward surface. Although the stable LEV within the mid-span retains its growth and location during an advanced rotation, it can be detrimental to lift enhancement as it moves underneath the wing. Therefore, for a flapping wing at ${\textit {Re}}\sim 10^3$, the interactions with stable and breakdown leading-edge vortices lead to the single-vortex suction and breakdown-vortex jet mechanisms, respectively. In other words, the contribution of wing–wake interaction depends on the spanwise location. The current work also implies the importance of wing kinematics to this wing–wake interaction in flapping wings, and provides an alternative perspective for understanding this complex flow phenomenon at ${\textit {Re}}\sim 10^3$.
The viscous force and torque on a closed irrotational surface
- John E. Sader, D.I. Pullin
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- 16 May 2024, A19
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The force and torque on a solid body in a viscous potential flow are often taken to be independent of viscosity. Joseph et al. (Eur. J. Mech. B/Fluids, vol. 12, 1993, pp. 97–106; J. Fluid Mech., vol. 265, 1994, pp. 1–23) proved that this holds for (i) the force (not the torque) in any two-dimensional flow, and (ii) the drag force experienced by a purely translating three-dimensional body. The remaining components of the force and torque, along with general three-dimensional flows, were not considered. Importantly, the flow was assumed to be unbounded and irrotational everywhere. We eliminate this rarely satisfied assumption and consider the viscous force and torque experienced by any closed surface where the flow is irrotational locally; this can include a body's surface. Any vorticity distribution is permitted away from the closed irrotational surface. In so doing, we complete the analysis of Joseph et al. for all components of the viscous force and torque in two and three dimensions and enable application to real flows that inevitably contain regions of vorticity.
Stability of Stuart vortices in rotating stratified fluids
- Yuji Hattori, Makoto Hirota
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- 16 May 2024, A12
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The linear stability of the Stuart vortices, which is a model of arrays of vortices often observed in the atmosphere and the oceans, in rotating stratified fluids is investigated by local and modal stability analysis. As in the case of the two-dimensional (2-D) Taylor–Green vortices, five types of instability appear in general: the pure-hyperbolic instability, the strato-hyperbolic instability, the rotational-hyperbolic instability, the centrifugal instability and the elliptic instability. The condition for each instability and the estimate of the growth rate derived by Hattori & Hirota (J. Fluid Mech., vol. 967, 2023, A32) are shown to also be useful for the Stuart vortices, which supports their applicability to general flows. The properties of each instability depend on stratification and rotation in a way similar to the case of the 2-D Taylor–Green vortices. For the Stuart vortices, however, the centrifugal instability and the elliptic instability become more dominant than the three hyperbolic instabilities in comparison to the 2-D Taylor–Green vortices; this is explained by the larger ratios of the maximum vorticity and the strain rate at the elliptic stagnation points to the strain rate at the hyperbolic stagnation points. Direct correspondence between the modal and local stability results is further established by comparing unstable modes to solutions to the local stability equations; this is useful for identifying the types of modes since the mechanism of instability is readily known in the local stability analysis. This helps us to discover the modes of the ring-type elliptic instability, which have been predicted only theoretically.
Investigating the parametric dependence of the impact of two-way coupling on inertial particle settling in turbulence
- Soumak Bhattacharjee, Josin Tom, Maurizio Carbone, Andrew D. Bragg
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- Published online by Cambridge University Press:
- 16 May 2024, A17
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Tom et al. (J. Fluid Mech., vol. 947, 2022, p. A7) investigated the impact of two-way coupling (2WC) on particle settling velocities in turbulence. For the limited parameter choices explored, it was found that (i) 2WC substantially enhances particle settling compared with the one-way coupled case, even at low mass loading $\varPhi _m$ and (ii) preferential sweeping remains the mechanism responsible for the particles settling faster than the Stokes settling velocity in 2WC flows. However, significant alterations to the flow structure that can occur at higher mass loadings mean that the conclusions from Tom et al. (J. Fluid Mech., vol. 947, 2022, p. A7) may not generalise. Indeed, even under very low mass loadings, the influence of 2WC on particle settling might persist, challenging the conventional assumption. We therefore explore a much broader portion of the parameter space, with simulations covering cases where the impact of 2WC on the global fluid statistics ranges from negligible to strong. We find that, even for $\varPhi _m=7.5\times 10^{-3}$, 2WC can noticeably increase the settling for some choices of the Stokes and Froude numbers. When $\varPhi _m$ is large enough for the global fluid statistics to be strongly affected, we show that preferential sweeping continues to be the mechanism that enhances particle settling rates. Finally, we compare our results with previous numerical and experimental studies. While in some cases there is reasonable agreement, discrepancies exist even between different numerical studies and between different experiments. Future studies must seek to understand this before the discrepancies between numerical and experimental results can be adequately addressed.
Boundary-layer instability on a highly swept fin on a cone at Mach 6
- Madeline M. Peck, Koen J. Groot, Helen L. Reed
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- Published online by Cambridge University Press:
- 16 May 2024, A13
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The growth and characteristics of linear, oblique instabilities on a highly swept fin on a straight cone in Mach 6 flow are examined. Large streamwise pressure gradients cause doubly inflected cross-flow profiles and reversed flow near the wall, which necessitates using the harmonic linearized Navier–Stokes equations. The cross-flow instability is responsible for the most-amplified disturbances, however, not all disturbances show typical cross-flow characteristics. Distinct differences in perturbation structure are shown between small ($\sim$3–5 mm) and large ($\sim$10 mm) wavelength disturbances at the unit Reynolds number $Re' = 11 \times 10^6$ m$^{-1}$. As a result, amplification measurements based solely on wall quantities bias a most-amplified disturbance assessment towards larger wavelengths and lower frequencies than would otherwise be determined by an off-wall total-energy approach. A spatial-amplification energy-budget analysis demonstrates (i) that wall-normal Reynolds-flux terms dictate the local growth rate, despite other terms having a locally larger magnitude and (ii) that the Reynolds-stress terms are responsible for large-wavelength disturbances propagating closer to the wall compared with small-wavelength disturbances. Additionally, the effect of free-stream unit Reynolds number and small yaw angles on the perturbation amplification and energy budget is considered. At a higher Reynolds number ($Re' = 22 \times 10^6$ m$^{-1}$), the most-amplified wavelength shrinks. Perturbations do not behave self-similarly in the thinner boundary layer, and the shift in most-amplified wavelength is due to decreased dissipation relative to the lower-Reynolds-number case. Small yaw angles produce a streamwise shift in the boundary layer and disturbance amplification. The yaw results quantify a potential uncertainty source in experiments and flight.
Starting vortices generated by an arbitrary solid body with any number of edges
- Edward M. Hinton, A. Leonard, D.I. Pullin, John E. Sader
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- 14 May 2024, A11
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The starting vortex generated at the trailing edge of a flat plate, that is impulsively translated at fixed angle of attack, is a widely studied canonical problem. Recent work that examined the effect of plate rotation on this starting vortex found that two new and distinct vortex sheet types can arise. We generalise this work to study the starting vortex generated at any sharp and straight edge of an arbitrary body under a general time-dependent two-dimensional motion. The dimensionless velocity field of the attached flow near any sharp edge is assumed to take the form, $\hat {z}^{-1/2} f(T) + g(T) + o (1)$, where $\hat {z}$ is the dimensionless position referenced to the edge, $f(T)$ and $g(T)$ are functions of dimensionless time, $T$, associated with the local flow perpendicular and parallel to the edge, respectively. This enables starting vortices to be generally calculated and their types related by simply inspecting the forms of $f(T)$ and $g(T)$. We elucidate the physics underlying all three vortex types and show that these vortices are generated by pure translation of the sharp edge. Several case studies are explored, including the leading/trailing edge vortices of a flat plate which can simultaneously be of different type (relevant to low-speed aircraft), the vortex formed by translation of a semi-infinite flat plate and the trailing-edge vortex of Joukowski aerofoils. With the ability to calculate the vortices at all edges, the theory is used to develop a general formula for the lift force of a flat plate which can find application in practice.
Flow reversal and multiple states in turbulent Rayleigh–Bénard convection with partially isothermal plates
- Jin Hu, Shengqi Zhang, Zhenhua Xia
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- 13 May 2024, A9
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This paper examines turbulent Rayleigh–Bénard convection in a two-dimensional square cavity with partially isothermal conducting plates on the horizontal walls. The study reveals that controlling the relative locations of the partially isothermal plates can accelerate or completely suppress the reversals of large-scale circulation. The heat transfer efficiency, which is characterised by the time-averaged Nusselt number, is generally higher than that of the traditional Rayleigh–Bénard convection, and can be further enhanced when the reversal is fully suppressed. The reversal in our cases is mainly caused by the competition between the two alternately growing ‘corner’ vortices, fed by the detaching plumes from the hot/cold plates. This differs from those reported in traditional Rayleigh–Bénard convection. Fourier mode decomposition of the kinetic energy, reflecting the diverse contributors, in the reversing cases further emphasises the distinction between the current system and traditional Rayleigh–Bénard convection. In addition, multiple states were observed where the conducting plates were positioned at specific relative locations and had different initial conditions. It has been observed that the difference in Nusselt numbers between the anticlockwise and clockwise states increases linearly with the distance between the upper cold and lower hot plates. Moreover, the analysis of the buoyancy moment and the stability of the primary roll structure suggests that the higher heat transfer efficiency between the two states is strongly linked to a more stable primary roll structure. This study presents a new approach for controlling flow reversal and improving heat transfer efficiency by modifying the non-global conducting boundary and initial conditions.
Freeze-out of perturbation growth for shocked heavy fluid layers by eliminating reverberating waves
- Zhouyang Cong, Xu Guo, Zhangbo Zhou, Wan Cheng, Ting Si
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- 13 May 2024, A10
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The shock wave accelerating a heavy fluid layer can induce reverberating waves that continuously interact with the first and second interfaces. In order to manipulate the perturbation growths at fluid-layer interfaces, we present a theoretical framework to eliminate the reverberating waves. A model is established to predict the individual freeze-out (i.e. stagnation of perturbation growth) for the first and second interfaces under specific flow conditions determined based on the shock dynamics theory. The theoretical model quantifies the controllable parameters required for freeze-out, including the initial amplitudes of the first and second interfaces, the interface coupling strength and the maximum initial layer thickness preventing the second interface's phase reversal. The effectiveness of the model in predicting individual freeze-out for the first and second interfaces is validated numerically over a wide range of initial conditions. The upper and lower limits of initial amplitudes for the freeze-out of the whole fluid-layer width growth are further predicted. Within this amplitude range, a slightly higher initial amplitude for the second interface is specified, effectively arresting the growth of the entire fluid-layer width before the phase reversal of the second interface.
Turbulence and mixing from neighbouring stratified shear layers
- Chih-Lun Liu, Alexis K. Kaminski, William D. Smyth
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- 13 May 2024, A8
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Studies of Kelvin–Helmholtz (KH) instability have typically modelled the initial mean flow as an isolated stratified shear layer. However, geophysical flows frequently exhibit multiple layers. As a step towards understanding these flows, we examine the case of two adjacent stratified shear layers using both linear stability analysis and direct numerical simulations. With sufficiently large layer separation, the characteristics of instability and mixing converge towards the familiar KH turbulence, and similarly when the separation is near zero and the layers add to make a single layer, albeit with a reduced Richardson number. Here, our focus is on intermediate separations, which produce new and complex phenomena. As the separation distance $D$ increases from zero to a critical value $D_c$, approximately half the thickness of the shear layer, the growth rate and wavenumber both decrease monotonically. The minimum Richardson number is relatively low, potentially inducing pairing, and shear-aligned convective instability (SCI) is the primary mechanism for transition. Consequently, mixing is relatively strong and efficient. When $D\sim D_c$, billow length is increased but growth is slowed. Despite the modest growth rate, mixing is strong and efficient, engendered primarily by secondary shear instability manifested on the braids, and by SCI occurring on the eyelids. Shear-aligned vortices are driven in part by buoyancy production; however, shear production and vortex stretching are equally important mechanisms. When $D>D_c$, neighbouring billow interactions suppress the growth of both KH instability and SCI. Strength and efficiency of mixing decrease abruptly as $D_c$ is exceeded. As turbulence decays, layers of marginal instability may arise.
Towards the understanding of convective dissolution in confined porous media: thin bead pack experiments, two-dimensional direct numerical simulations and physical models
- Marco De Paoli, Christopher J. Howland, Roberto Verzicco, Detlef Lohse
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- Published online by Cambridge University Press:
- 16 May 2024, A1
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We consider the process of convective dissolution in a homogeneous and isotropic porous medium. The flow is unstable due to the presence of a solute that induces a density difference responsible for driving the flow. The mixing dynamics is thus driven by a Rayleigh–Taylor instability at the pore scale. We investigate the flow at the scale of the pores using Hele-Shaw type experiment with bead packs, two-dimensional direct numerical simulations and physical models. Experiments and simulations have been specifically designed to mimic the same flow conditions, namely matching porosities, high Schmidt numbers and linear dependency of fluid density with solute concentration. In addition, the solid obstacles of the medium are impermeable to fluid and solute. We characterise the evolution of the flow via the mixing length, which quantifies the extension of the mixing region and grows linearly in time. The flow structure, analysed via the centreline mean wavelength, is observed to grow in agreement with theoretical predictions. Finally, we analyse the dissolution dynamics of the system, quantified through the mean scalar dissipation, and three mixing regimes are observed. Initially, the evolution is controlled by diffusion, which produces solute mixing across the initial horizontal interface. Then, when the interfacial diffusive layer is sufficiently thick, it becomes unstable, forming finger-like structures and driving the system into a convection-dominated phase. Finally, when the fingers have grown sufficiently to touch the horizontal boundaries of the domain, the mixing reduces dramatically due to the absence of fresh unmixed fluid. With the aid of simple physical models, we explain the physics of the results obtained numerically and experimentally. The solute evolution presents a self-similar behaviour, and it is controlled by different length scales in each stage of the mixing process, namely the length scale of diffusion, the pore size and the domain height.
A closure mechanism for screech coupling in rectangular twin jets
- Jinah Jeun, Gao Jun Wu, Sanjiva K. Lele
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- 13 May 2024, A5
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The twin-jet configuration allows two different scenarios to close the screech feedback. For each jet, there is one loop involving disturbances which originate in that jet and arrive at its own receptivity point in phase (self-excitation). The other loop is associated with free-stream acoustic waves that radiate from the other jet, reinforcing the self-excited screech (cross-excitation). In this work, the role of the free-stream acoustic mode and the guided-jet mode as a closure mechanism for twin rectangular jet screech is explored by identifying eligible points of return for each path, where upstream waves propagating from such a point arrive at the receptivity location with an appropriate phase relation. Screech tones generated by these jets are found to be intermittent with an out-of-phase coupling as a dominant coupling mode. The instantaneous phase difference between the twin jets computed by the Hilbert transform suggests that a competition between out-of-phase and in-phase coupling is responsible for the intermittency. To model wave components of the screech feedback while ensuring perfect phase locking, an ensemble average of leading spectral proper orthogonal decomposition modes is obtained from several segments of large-eddy simulation data that correspond to periods of invariant phase difference between the two jets. Each mode is then extracted by retaining relevant wavenumber components produced via a streamwise Fourier transform. Spatial cross-correlation analysis of the resulting modes shows that most of the identified points of return for the cross-excitation are synchronised with the guided jet mode self-excitation, supporting that it is preferred in closing rectangular twin-jet screech coupling.
Spatially evolving cascades in wall turbulence with and without interface
- A. Cimarelli, G. Boga, A. Pavan, P. Costa, E. Stalio
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- 13 May 2024, A4
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Direct numerical simulations of channel flow and temporal boundary layer at a Reynolds number $Re_{\tau } = 1500$ are used to assess the scale-by-scale mechanisms of wall turbulence. From the peak of turbulence production embedded at the small scales of the near-wall region, spatially ascending reverse cascades are generated that move through self-similar eddies growing in size with the wall distance. These fluxes are followed by spatially ascending forward cascades through detached eddies thus reaching sufficiently small scales where eventually scale energy is dissipated. This phenomenology is shared by both boundary layer and channel flow and is recognized as a robust physical feature characterizing wall turbulence in general. Specific features related to the flow configuration are indeed identified in the outer region. In particular, the central region of channels is characterized by a generalized Richardson energy cascade where large scales are in equilibrium with small scales at different wall distances through a combined forward cascade and spatial flux. On the contrary, the interface region of boundary layers is characterized by an almost two-dimensional physics where spatially ascending reverse cascades sustain long and wide interface structures with a forward cascade that survives only in the wall-normal scales. The overall scenario consists in a variety of scale motions that while protruding from the turbulent core towards the external region, squeeze at the interface thus sustaining vertical shear in a thin layer. The observed multidimensional physics sheds light on the complex interactions between outer entrainment and near-wall self-sustaining mechanisms with possible repercussions for theories.