doi:10.1017/jfm.2024.387 Liu et al. Turbulence and mixing from neighbouring stratified shear layers
JFM Papers
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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- 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.
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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- 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.
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.
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.
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 ${\textit {Re}}\sim 10^3$.
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.
Fragmentation of colliding liquid rims
- K. Tang, T.A.A. Adcock, W. Mostert
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- 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.
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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- 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.
Impedance spectra of soft ionics
- Reghan J. Hill
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- 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.
Surface tension and wetting at free surfaces in smoothed particle hydrodynamics
- Michael Blank, Prapanch Nair, Thorsten Pöschel
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- 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.
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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- 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.
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.
A study of streamline geometries in subsonic and supersonic regions of compressible flow fields
- Zhong Wei Tian, Kai Cui
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- 20 May 2024, A26
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The geometrical properties of streamlines, such as the curvatures, directions and positions, are studied in steady inviscid compressible flow fields via differential geometry theories and conservation laws. The influences of the streamline geometries on the flow speeds and pressures are also identified and discussed. By transforming the streamlines to fill the domain and satisfy the boundary conditions, a unified geometry-based solver, the streamline transformation method, is proposed for both subsonic and supersonic regions. The governing equations and boundary conditions along streamlines and shock waves are also derived. This method is verified by numerical results of three typical flow fields, including the subsonic channel flow, the supersonic downstream of attached shock waves and especially the subsonic/supersonic downstream of detached bow shock waves. Both two-dimensional planar and axisymmetric flow fields are considered. Compared with the results from computational fluid dynamics, good agreements are achieved by this method, while fewer computational resources, by an order of magnitude, are consumed. Features of these flow fields are also analysed from a geometrical perspective, such as flow speeds and pressures deviated by the wall curvatures, and three-dimensional effects in the after-shock flow fields. For a hyperbolic-shaped bow shock wave, the stand-off distances and the transitions from subsonic to supersonic regions are also discussed. As indicated by the accuracy, efficiency and applicability in a wide range of flow speeds, the streamline transformation method would be a potential candidate for the theoretical analysis and inverse design of high-speed flow fields, especially where the subsonic regions exist downstream of strong shock waves.
Peristaltic pumping down a porous conduit
- D. Takagi, N.J. Balmforth, Stefan G. Llewellyn Smith
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- 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.
Bubble-induced entrainment at viscoplastic–Newtonian interfaces
- M. Zare, I.A. Frigaard, G.A. Lawrence
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- 20 May 2024, A28
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The passage of single air bubbles through the horizontal interface between viscoplastic and Newtonian fluids, considering various combinations of densities and viscosities for the fluid layers, is studied computationally. The primary focus is on the quantity of liquid transferred from the lower layer (viscoplastic fluid) to the upper layer (Newtonian fluid) as a result of the bubble's ascent, a factor with significant implications for the turbidity of methane-emitting lakes and water bodies. The entrainment characteristics are observed to vary considerably with the bubble shape, within the lower layer and as the bubble approaches the interface. The results show that at Bond number $(Bo)>1$ and moderate Archimedes ($Ar$), prolate-shaped bubbles crossing the interface undergo elongation in the direction of their poles. This elongation is further accentuated when the viscosity of upper layer is less than the plastic viscosity of the lower layer. The bubble is found to break up when leaving the lower layer, of a critical capillary number, $Ca_c \approx 5$. The results show a significant reduction in the volume of entrainment compared with the Newtonian counterpart. This suggests disturbances caused by the rising bubble at the interface dissipate over a smaller region. Four distinct entrainment regimes are identified, mainly indicating the height to which the entrained fluid can be transported away from the interface. In contrast to Newtonian fluids, the volume of entrainment increases by decreasing the viscosity of the upper layer. Interestingly, the heavy viscoplastic fluid that has been dragged up into the light Newtonian fluid does not recede with time.
Turbulent kinetic energy budget of sediment-laden open-channel flows: bedload-induced wall-roughness similarity
- Hélder Guta, David Hurther, Julien Chauchat
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- 20 May 2024, A25
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New experiments in highly turbulent, steady, subcritical and uniform water open-channel flows have been carried out to measure the mean turbulent kinetic energy (TKE) budget of sediment-laden boundary layer flows with two sizes (dp = 3 mm and 1 mm) of Plexiglas particles $({\rm relative\ density}\ = 1.192)$. The experiments covered energetic sediment transport conditions (Shields number of $0.35 < \theta < 1.2$) ranging from non-capacity to full-capacity flows in bedload-to-suspension-dominated transport modes (suspension number of $0.5 < {w_s}/{u_\ast } < 1.3$ where ${w_s}$ is the settling velocity and $u_*$ is the friction velocity) and for weakly to highly inertial, finite size turbulence-particle conditions (Stokes number of 0.1 < St < 3.5 and dp/η > 10 where $\eta$ is the Kolmogorov length scale). It was shown that the effects of sediments on the TKE budget are very pronounced in all large particle experiments for which a bedload layer of several grain diameter thickness is developed above the channel bed. When compared with the corresponding reference clear-water flows, the TKE shear-production rate for the 3 mm particle flows is strongly reduced in the wall region corresponding to the bedload layer. This turbulence damping is seen to increase with sediment load until full capacity for flows with constant Shields value, as well as with Shields number value. Inside this damped TKE shear-production zone, a distinct peak of maximal turbulence production appears to coincide with the upper edge of the bedload layer delimited by a sharp gradient in mean sediment concentration. This vertically upshifted peak of TKE production is accompanied by an enhanced net downward oriented TKE flux when compared with the reference clear-water flows. The downward diffused TKE is found to act in the bedload layer as a local energy source in reasonable balance with the sediment transport term. The mechanism behind this downward TKE transport was further analysed on the basis of coherent flow structure dynamics controlled by ejection- and sweep-type events. The agreement between the height of downward directed mean TKE flux and the height below which sweep-type events dominate the Reynolds shear-stress contribution over ejections, revealed the leading role played by sweeps in mean TKE transport. This agreement holds for all reference clear-water flows supporting the well-known wall-roughness-induced dominance of the sweep contribution in turbulent, rough clear-water boundary layer flows. Furthermore, for all 3 mm particle flows, the two referred to transition levels were significantly and similarly upshifted to the upper edge of the bedload layer. Only for these sediment-laden flows, the bedload layer thickness is seen to exceed the wall-roughness sublayer of the reference clear-water flows. This supports a strong analogy between wall-roughness effects in clear-water flows and bedload layer effects in sediment-laden flows, on the mean TKE budget induced by a similarly modified coherent flow structure dynamics. The bedload layer-controlled wall roughness is finally confirmed by the good prediction of the wall-roughness parameter ks of the logarithmic velocity distribution. An empirical formulation fitting the presented measurements is presented, valid over the range of Shields number values covered herein.
Added mass of oscillating bodies in stratified fluids
- Bruno Voisin
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- 20 May 2024, A27
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The concept of added mass is generalized to stratified fluids, accounting for the presence of internal waves. Once the added mass of a moving body is known, so is the hydrodynamic force exerted on it by the fluid, and the energy imparted by it to the fluid. As a function of frequency, added mass is complex. Its real part is associated with inertia and its imaginary part, only present in the frequency range of propagating waves, with wave damping. Owing to causality, these two parts satisfy Kramers–Kronig relations. The added masses of an elliptic cylinder of horizontal axis, typical of two-dimensional bodies, and a spheroid of vertical axis, typical of three-dimensional bodies, are deduced from their dipole strengths, themselves deduced from their representations as single layers. The wave power is shown to be a maximum, for fixed oscillation amplitude, at approximately $0.8$ times the buoyancy frequency. In the temporal domain, added mass appears as a new memory force taking the form of a convolution integral. The kernel of this integral combines algebraically decaying oscillations at the buoyancy frequency on the one hand; and an exponentially damped oscillation for the horizontal motion of the spheroid, implying short-term memory, an aperiodic algebraic decay for its vertical motion, implying long-term memory, and a constant for the motion of the cylinder, implying everlasting memory, on the other hand. A limitation of the study is its restriction to translational motion.
Effect of thermal fluctuations on spectra and predictability in compressible decaying isotropic turbulence
- Qihan Ma, Chunxin Yang, Song Chen, Kaikai Feng, Ziqi Cui, Jun Zhang
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- 21 May 2024, A29
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This study investigates the impact of molecular thermal fluctuations on compressible decaying isotropic turbulence using the unified stochastic particle (USP) method, encompassing both two-dimensional (2-D) and three-dimensional (3-D) scenarios. The findings reveal that the turbulent spectra of velocity and thermodynamic variables follow the wavenumber (k) scaling law of ${k}^{(d-1)}$ for different spatial dimensions $d$ within the high wavenumber range, indicating the impact of thermal fluctuations on small-scale turbulent statistics. With the application of Helmholtz decomposition, it is found that the thermal fluctuation spectra of solenoidal and compressible velocity components (${\boldsymbol {u}}_{s}$ and ${\boldsymbol {u}}_{c}$) follow an energy ratio of 1 : 1 for 2-D cases, while the ratio changes to 2 : 1 for 3-D cases. Comparisons between 3-D turbulent spectra obtained through USP simulations and direct numerical simulations of the Navier–Stokes equations demonstrate that thermal fluctuations dominate the spectra at length scales comparable to the Kolmogorov length scale. Additionally, the effect of thermal fluctuations on the spectrum of ${\boldsymbol {u}}_{c}$ is significantly influenced by variations in the turbulent Mach number. We further study the impact of thermal fluctuations on the predictability of turbulence. With initial differences caused by thermal fluctuations, different flow realizations display significant disparities in velocity and thermodynamic fields at larger scales after a certain period of time, which can be characterized by ‘inverse error cascades’. Moreover, the results suggest a strong correlation between the predictabilities of thermodynamic fields and the predictability of ${\boldsymbol {u}}_{c}$.
Turbulent drag reduction with streamwise-travelling waves in the compressible regime
- Federica Gattere, Massimo Zanolini, Davide Gatti, Matteo Bernardini, Maurizio Quadrio
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- 21 May 2024, A30
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The ability of streamwise-travelling waves of spanwise velocity to reduce the turbulent skin-friction drag is assessed in the compressible regime. Direct numerical simulations are carried out to compare drag reduction in subsonic, transonic and supersonic channel flows. Compressibility improves the benefits of the travelling waves, in a way that depends on the control parameters: drag reduction becomes larger than the incompressible one for small frequencies and wavenumbers. However, the improvement depends on the specific procedure employed for comparison. When the Mach number is varied and, at the same time, wall friction is changed by the control, the bulk temperature in the flow can either evolve freely in time until the aerodynamic heating balances the heat flux at the walls, or be constrained such that a fixed percentage of kinetic energy is transformed into thermal energy. Physical arguments suggest that, in the present context, the latter approach should be preferred. This provides a test condition in which the wall-normal temperature profile more realistically mimics that in an external flow, and also leads to a much better scaling of the results, over both the Mach number and the control parameters. Under this comparison, drag reduction is only marginally improved by compressibility.
Linear dynamics of a thick liquid layer subjected to an oblique temperature gradient
- Ganesh Dixit, Syed Furqan Bukhari, Ramkarn Patne
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- 22 May 2024, A32
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The present study aims to demonstrate the application of the oblique temperature gradient (OTG) to manipulate the buoyancy instabilities and resulting mixing. To accomplish this, we consider a model consisting of a liquid layer supported by a perfectly conducting bottom wall from below and the upper surface is exposed to ambient inert gas in a shallow container. The stability analysis employs the pseudospectral method and perturbation energy budget approach. The imposed OTG consists of a negative vertical temperature gradient (VTG), which leads to unstable density stratification, and a negative horizontal temperature gradient (HTG) component responsible for the Hadley circulation, which can be utilised to control instabilities. Without the HTG, a Rayleigh–Bénard mode of instability exists due to the imposed VTG termed as a VTG mode. The imposed HTG induces a linear VTG term and a quintic polynomial VTG term in the bottom wall-normal coordinate $y$. The induced linear VTG term reinforces the imposed VTG, while the induced quintic polynomial VTG term opposes the imposed VTG. For the vanishing Biot number ($Bi$), the induced quintic VTG term stabilises the VTG mode for the Prandtl number, $Pr=7$. However, for $Pr=0.01$, the Reynolds stresses associated with the Hadley circulation destabilise the VTG mode. For non-zero $Bi$, new streamwise and spanwise instability modes arise for $Pr=7$ due to the induced linear VTG term. Physical arguments show that the unstable density stratification near the gas–liquid interface caused by the synergistic effect of the imposed VTG and the induced linear VTG term lead to the existence of the predicted new modes. The present study thus shows that the strength of the HTG can be utilised to control the instability modes and critical parameters, thereby demonstrating the utility of the OTG in manipulating the buoyancy instabilities.