Turbulent Convection Research Articles

Examination of Vorticity and Divergence on a Rotating Turbulent Convection Model of Jupiter's Polar Vortices

AbstractThe correlation between divergence and vorticity has traditionally served as a signature of convection in rotating fluids. While this correlation has been observed in the JIRAM brightness temperature data for Jupiter's polar vortices, it is notably absent in the JIRAM images. This discrepancy presents a new challenge in determining whether this correlation can serve as a reliable signature of convection in rapidly rotating atmospheres. In this study, we analyzed data from a three‐dimensional simulation of Jupiter's polar vortices using a deep convection model. Our findings confirm the theoretical prediction of a negative correlation between divergence and vorticity in the northern hemisphere. Interestingly, this correlation is weaker within the cyclones compared to outside them. The skewness of upflows and downflows plays an important role in this negative correlation. We also observed that the correlation varies with height, being strongest near the interface and decaying away from it. The correlation diminishes when the resolution is reduced. Furthermore, our findings suggest that the geostrophic approximation may not be suitable for the Jovian atmosphere, particularly in the stable layer. Both tilting and stretching effects contribute to the material derivative of vorticity, with the tilting effect dominating in the unstable layer and the stretching effect prevailing in the stable layer. This suggests a transfer of vorticity from the convectively unstable layer to the stable layer. Consistent with observations, we also noted an upscale energy transfer from smaller to larger scales.

Theory of the momentum source method for synthetic turbulence

The interaction between turbulence and blade leading edges is known to have a significant impact on the aerodynamic and aeroacoustic performance of propellers. In addition to directly simulating turbulence, synthetic turbulence, such as the momentum source method, has been developed as a popular method for studying this interaction process in computational fluid dynamics and computational aeroacoustics. However, it is found that for non-periodic disturbances, although the induced velocity field is divergence-free, spurious noise may be generated in the source region and contaminate simulation results. To address this issue, the present work proposes adding a correction term so that the divergence-free condition is satisfied globally and the unwanted acoustic waves are suppressed, as an extension to our previous work for time-periodic gusts [H. Jiang, Phys. Fluids 35, 096115 (2023)]. The strength of the proposed approach lies in its simplicity, flexibility, and generality. First, it derives explicit source terms, which are straightforward for numerical implementations, to generate unsteady flow fluctuations. Second, the sources can be added inside the computational domain, saving computational costs for turbulence convection and being compatible with most existing boundary conditions. Third, the proposed method can obtain analytical expressions for the needed momentum source of the Navier–Stokes equation subject to any desired isotropic or anisotropic divergence-free turbulence fields. The method has been verified by examples of synthesizing harmonic gusts, Gaussian eddies, and random turbulence. The synthetic velocity results characterized by different spectral components are directly compared to target velocity fields, verifying the proposed approach and showing its capability. Parameters that influence the distribution of added sources are systematically investigated to identify an optimal combination for different scenarios. Finally, the model is employed to evaluate the aerodynamic interaction between an incoming turbulence and a thin airfoil. The obtained results exhibit good correspondence with analytical solutions.

Analysis of BMR Tilt from AutoTAB Catalog: Hinting toward the Thin Flux Tube Model?

One of the intriguing mechanisms of the Sun is the formation of bipolar magnetic regions (BMRs) in the solar convection zone (CZ), which are observed as regions of concentrated magnetic fields of opposite polarity on the photosphere. These BMRs are tilted with respect to the equatorial line, which statistically increases with latitude. The thin flux tube model, employing the rise of magnetically buoyant flux loops and their twist by Coriolis force, is a popular paradigm for explaining the formation of tilted BMRs. In this study, we assess the validity of the thin flux tube model by analyzing the tracked BMR data obtained through the Automatic Tracking Algorithm for BMRs. Our observations reveal that the tracked BMRs exhibit the expected collective behaviors. We find that the polarity separation of BMRs increases over their normalized lifetime, supporting the assumption of a rising flux tube from the CZ. Moreover, we observe an increasing trend of the tilt with the flux of the BMR, suggesting that rising flux tubes associated with lower flux regions are primarily influenced by drag force and Coriolis force, while in higher flux regions, magnetic buoyancy dominates. Furthermore, we observe Joy’s law dependence for emerging BMRs from their first detection, indicating that at least a portion of the tilt observed in BMRs can be attributed to the Coriolis force. Notably, lower flux regions exhibit a higher amount of fluctuations associated with their tilt measurement compared to stronger flux regions, suggesting that lower flux regions are more susceptible to turbulent convection.

Direct numerical simulations of first-mode oblique breakdown in a supersonic boundary layer under wall transpiration

Complete first-mode oblique breakdowns under wall transpirations in a Mach 2 flat-plate boundary layer are investigated by direct numerical simulations. The parameters of oblique waves are determined by linear stability analysis, while air transpiration is modeled by a wall-injection boundary condition. Wall transpiration with various blowing ratios is imposed at two distinct streamwise regions to assess its effects. When wall transpiration is located in the linear and early nonlinear region, the transition shifts upstream with increasing blowing ratios. This promotion effect arises from the destabilization of the oblique mode, steady vortex mode and higher-harmonic modes. Wall transpiration also leads to reduced skin friction and heat transfer in the transpiration and downstream turbulent regions. Through integral analysis, the impacts of transpiration on the generation mechanisms of skin friction and heat transfer are gained. The reduced skin friction and heat transfer in the transpiration region are mainly attributed to the amplified negative contributions from mean convection. In the turbulent region, the reduction of skin friction can be attributed to the heightened negative contributions from mean convection and the diminished positive contributions from turbulent convection. Concurrently, heat transfer experiences a decrease as a consequence of reduced positive contributions from spatial development and augmented negative contributions from mean convection. When wall transpiration is located in the late nonlinear region, its impacts resemble those observed when transpiration is located in the linear and early nonlinear region. However, the transition-promoting effect weakens, and the heat-transfer reduction effect becomes more pronounced.

Bridging theory and observations in stellar pulsations: the impact of convection and metallicity on the instability strips of classical and type-II cepheids

ABSTRACT The effect of metallicity on the theoretical and empirical period–luminosity relations of Cepheid variables is not well understood and remains a highly debated issue. Here, we examine empirical colour–magnitude diagrams (CMDs) of Classical and Type-II Cepheids in the Magellanic Clouds and compare those with the theoretically predicted instability strip (IS) edges. We explore the effects of incorporating turbulent flux, turbulent pressure, and radiative cooling into the convection theory on the predicted IS at various metallicities using Modules for Experiments in Stellar Astrophysics – Radial Stellar Pulsations. We find that the edges become redder with the increasing complexity of convection physics incorporated in the fiducial convection sets, and are similarly shifted to the red with increasing metallicity. The inclusion of turbulent flux and pressure improves the agreement of the red edge of the IS, while their exclusion leads to better agreement with observations of the blue edge. About 90 per cent of observed stars are found to fall within the predicted bluest and reddest edges across the considered variations of turbulent convection parameters. Furthermore, we identify and discuss discrepancies between theoretical and observed CMDs in the low-effective temperature and high-luminosity regions for stars with periods greater than ∼20 d. These findings highlight the potential for calibrating the turbulent convection parameters in stellar pulsation models or the prediction of a new class of rare, long-period, ‘red Cepheids’, thereby improving our understanding of Cepheids and their role in cosmological studies.

Numerical Study of Three-Dimensional Models of Single- and Two-Phase Nanofluid Flow through Corrugated Channels

This study delves into computational fluid dynamics (CFDs) predictions for SiO2–water nanofluids, meticulously examining both single-phase and two-phase models. Employing the finite volume approach, we tackled the three-dimensional partial differential equations governing the turbulent mixed convection flow in a horizontally corrugated channel with uniform heat flux. The study encompasses two nanoparticle volume concentrations and five Reynolds numbers (10,000, 15,000, 20,000, 25,000, and 30,000) to unravel these intricate dynamics. Despite previous research on the mixed convection of nanofluids using both single-phase and two-phase models, our work stands out as the inaugural systematic comparison of their predictions for turbulent mixed convection flow through this corrugated channel, considering the influences of temperature-dependent properties and hydrodynamic characteristics. The results reveal distinct variations in thermal fields between the two-phase and single-phase models, with negligible differences in hydrodynamic fields. Notably, the forecasts generated by three two-phase models—Volume of Fluid (VOF), Eulerian Mixture Model (EMM), and Eulerian Eulerian Model (EEM)—demonstrate remarkable similarity in the average Nusselt number, which are 24% higher than the single-phase model (SPM). For low nanoparticle volume fractions, the average Nusselt number predicted by the two-phase models closely aligns with that of the single-phase model. However, as the volume fraction increases, differences emerge, especially at higher Reynolds numbers. In other words, as the volume fraction of the nanoparticles increases, the nanofluid flow becomes a multi-phase problem, as depicted by the findings of this study.

Turbulent natural convection inside inclined enclosures: Effects of adiabatic and heat-conducting inserts

Natural convection phenomena are found in many engineering applications, ranging from building and refrigeration design to nuclear reactors. Such importance has prompted both experimental and numerical studies aiming at enhancing heat transfer characteristics. Turbulent natural convection in closed cavities, apparently simple, is a stepstone to such problems, which require mathematical and numerical tools capable of providing accurate results. This work is inserted within this framework, in which influences of insert size and type (adiabatic/heat-conducting), and cavity inclination angle are assessed for Rayleigh numbers 10 7 ≤ Ra ≤ 10 9 . The study shows that the insert is mostly detrimental to heat transfer owing to restriction to recirculation, irrespective of the cavity inclination angle. An operation envelope for the global Nusselt number for all cavity inclination angles, insert sizes and types, and Rayleigh numbers was also determined.

How aphids fly: Take‐off, free flight and implications for short and long distance migration

Abstract An introduction to high‐speed photography and its entomological impact is provided, emphasizing the importance of high frame rates and high resolution. The take‐off and free flight of Drepanosiphum platanoidis and Myzus persicae were studied in still air using high‐speed photography in HD. The wing tip and body posture were tracked to show how they are displaced during each wingbeat cycle. The important structural elements of the wing are described. The wingbeat is driven by a reinforced leading edge, the pterostigma and costa. The remainder of the coupled fore‐ and hindwing acts as a single aerofoil that deforms during flight, due to sparse venation and a lack of cross veins. During flight, aphids use a ‘near clap and fling’ mechanism with a body pitch close to 90°. Rapid acceleration about the thoracic lateral axis into wing reversal generates enough lift for take‐off, typically within the first or second wingbeat. Unique footage shows that aphids demonstrate a high degree of flight control and manoeuvrability in the lab, occasionally using forward and inverted flight, two flight modes that are otherwise poorly known. While research into the impact of turbulent convection is needed, we posit that the strength of atmospheric forces presents a formidable challenge to aphid migrants. Above the flight boundary layer, migrating aphids may not easily oppose upwardly moving air, although if used, ‘frozen flight’ may cause them to descend on average. We evaluate five devices for insect flight research.

Thermal-hydraulic performance of turbulent flows across a heated round tube installed through several perforated twisted tapes

PurposeThe purpose of this study is to advance turbulent thermal convection inside the constant heat-flux round tube inserted by multiple perforated twisted tapes.Design/methodology/approachThe novel design of this study is accomplished by inserting several twisted tapes and drilling some circular perforations near the tape edge (C1, C3, C5: solid tapes; C2, C4, C6: perforated tapes). The turbulence flow appearances and thermal convective features are examined for various Reynolds numbers (8,000–14,000) using the renormalization group (RNG) κ−ε turbulent model and Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm.FindingsThe simulated outcomes reveal that inserting more perforated-twisted tapes into the heated round tube promotes turbulent thermal convection effectively. A swirling flow caused by the twisted tapes to produce the secondary flow jets between two reverse-spin tapes can combine with the main flow passing through the perforations at the outer edge to enhance the vortex flow. The primary factors are the quantity of twisted tapes and with/without perforations, as the perforation ratio remains at 2.5 in this numerical work. Weighing friction along the tube, C6 (four reverse-spin perforated-twisted tapes) brings the uppermost thermal-hydraulic performance of 1.23 under Re = 8,000.Research limitations/implicationsThe constant thermo-hydraulic attributes of liquid water and the steady Newtonian fluid are research limitations for this simulated work.Practical implicationsThe simulated outcomes will avail the inner-pipe design of a heat exchanger inserted by multiple perforated twisted tapes to enhance superior heat transfer.Originality/valueThese twisted tapes form tiny circular perforations along the tape edge to introduce the fluid flow through these bores and combine with the secondary flow induced between two reverse-spin tapes. This scheme enhances the swirling flow, turbulence intensity and fluid mixing to advance thermal convection since larger perforations cannot produce large jet velocity or the position of perforations is too far from the tape edge to generate a separated flow. Consequently, this work contributes a valuable cooling mechanism toward thermal engineering.

Role of partial stable stratification on fluid flow and heat transfer in rotating thermal convection

The liquid iron core of the Earth undergoes vigorous convection driven by thermal and compositional buoyancy. The dynamics of convective fluid motions and heat transfer in such conditions are determined by background rotation, geometrical symmetry, and thermal interactions across the boundaries. In this study, rotating thermal convection in a horizontal fluid layer is considered to understand the fluid flow characteristics in the Earth's outer core focusing on the regions close to the rotational axis. The effects of a partial stable stratification on fluid flow and heat transfer are investigated to ascertain the physical significance of thermal core–mantle interaction on geomagnetic field generation driven by core fluid motion. It is found that even with non-linear evolution, convective instabilities retain the fundamental characteristics of linear onset modes. Mildly supercritical regimes lead to near laminar flows with the transition to turbulent convection occurring for strongly driven convection around 50–100 times enhanced buoyancy. Axial symmetry breaking and preferential damping of small-scale vortical structures are the hallmark of penetrative convection. Rapid rotation sustains small-scale helical flows in stable regions, a necessary ingredient for the sustenance of Earthlike dipolar magnetic fields. Coherent flow structures for strongly turbulent convection are obtained using reduced-order modeling. The overall total heat transfer is suppressed (up to 25%) due to the stable stratification although convective efficiency is enhanced (up to 30%) in the unstable regions favored by rapid rotation. Flow suppression is overcome under strong buoyancy forces, a relevant dynamical regime for deep-seated dynamo action in the Earth's core.

Exploring the excess of cloud condensation nuclei and rain suppression using a minimal three-dimensional Boussinesq model with bulk cloud microphysics

Over the years, there have been discussions about the possibility of air pollution affecting the process of rain formation. In this study, we have developed a simplified model that represents the atmospheric dynamics and cloud microphysics to explore the impact of pollution on rain formation. We used an existing three-dimensional minimal model consisting of five equations, for which we added a simple bulk parametrization that represents the role of cloud condensation nuclei (CCN) in cloud formation processes. We conducted numerical tests using two CCN profiles, with either one or two accumulation layers and modified their abundance to explore the effects of different CCN concentrations and distributions. We conducted four numerical tests corresponding to the two aforementioned profiles with polluted and low-polluted scenarios. The numerical simulations suggested that a layer with high CCN concentration close to the surface tends to suppress precipitation, while the same concentration distributed over two layers tends to enhance the efficiency of rain formation. The simulations also showed that CCN particles far from the surface produced higher cloud tops and longer events, consistent with previous research. Although the model includes a stable representation of precipitating turbulent convection with bulk cloud microphysics, we expect its simplicity and conservation properties to allow for deeper theoretical analyses that can help us better understand the physical processes involved in the studied phenomenon. We hope this model will serve as a tool to explore different aerosol-related scenarios within the context of minimal models.

Experimental measurement of spatio-temporally resolved energy dissipation rate in turbulent Rayleigh–Bénard convection

We report a home-built velocity-gradient-tensor-resolved particle image velocimetry (VGTR-PIV) system which spatio-temporally resolves all components of the velocity gradient tensor. This technique is applied to the paradigmatic turbulent Rayleigh–Bénard convection system in a cylindrical cell at three representative positions, i.e. centre, side and bottom regions. The VGTR-PIV system allows us to directly measure, for the first time, the spatio-temporally resolved energy dissipation rate and enstrophy in turbulent thermal convection. In the experiment, the Rayleigh number $Ra$ varied in the range $2 \times 10^8 \leqslant Ra \leqslant 8 \times 10^9$ and the Prandtl number $Pr$ was fixed at $Pr = 4.34$ . Compared with the fully resolved energy dissipation rate $\varepsilon$ , the pseudo-dissipation provides the best estimate within $3\,\%$ , the planar (two-dimensional) surrogate has a larger relative error and the one-dimensional surrogate leads to the largest error. The power-law scalings of the time-averaged energy dissipation rate with the Rayleigh number follow $\langle \varepsilon _c \rangle _t / (\nu ^3 H^{-4}) = 9.86 \times 10^{-6} Ra^{1.54 \pm 0.02}$ , $\langle \varepsilon _s \rangle _t / (\nu ^3 H^{-4}) = 9.26 \times 10^{-3} Ra^{1.25 \pm 0.02}$ and $\langle \varepsilon _b \rangle _t / (\nu ^3 H^{-4}) = 2.70 \times 10^{-2} Ra^{1.23 \pm 0.02}$ in the centre, side and bottom regions, respectively where $\nu$ is dynamic viscosity and $H$ is cell height. These scaling relations, along with our earlier measured time-averaged energy dissipation rate at the bottom wall surface $\langle \varepsilon _w \rangle _t / (\nu ^3 H^{-4}) = 9.65 \times 10^{-2} Ra^{1.25 \pm 0.02}$ (J. Fluid Mech., vol. 947, 2022, A15), provide important constraints against which theoretical models may be tested. For the centre and side locations in the convection cell, the probability density functions (p.d.f.s) of the energy dissipation rate and enstrophy both follow a stretched exponential distribution. For the bottom region, the p.d.f.s of dissipation and enstrophy exhibit a stretched exponential distribution outside the viscous boundary layer and an exponential distribution inside the viscous boundary layer. It is also found that extreme events with high dissipation are the most intermittent in the side region, whereas the bottom region is less intermittent than the cell centre.

Turbulent thermal convection across a stable liquid-liquid interface

Turbulent thermal convection across a stable liquid-liquid interface

Model for the dynamics of the large-scale circulations in two-layer turbulent convection

Model for the dynamics of the large-scale circulations in two-layer turbulent convection

Turbulent mixed convection in a horizontal cylindrical cavity with the off-lattice Boltzmann method

Large-eddy simulations (LES) of turbulent mixed convection in a horizontal concentric cylindrical cavity when cylinders are subjected to rotations are investigated in the present study. A characteristic-based finite-difference off-lattice Boltzmann method solver is employed to investigate whether rotation enhances heat transfer in a horizontal concentric cylindrical cavity configuration where buoyancy acts perpendicular to the cylinder axis. The study focuses on assessing heat transfer characteristics for different rotation intensities in both counter-rotating-cylinders (CRC) and outer-rotating-cylinder (ORC) configurations. The LES simulations are performed for Rayleigh number, Ra=106, and Reynolds numbers, Re=0,500,1000, and 5000 for air (Pr=0.71), employing a classical Smagorinsky sub-grid-scale (SGS) model. The numerical solver is verified using two benchmark problems, namely (i) Buoyancy-driven flow in a differentially heated air-filled cubic enclosure and (ii) turbulent Taylor-Couette flow. The CRC and ORC configurations are chosen for the three-dimensional simulations in this study, prompted by the notable improvement in heat transfer observed in their respective two-dimensional simulations. A thorough comparison between two- and three-dimensional mixed convection results reveals substantial influence from secondary flow in the axial direction. While three-dimensional CRC simulations exhibit a modest increase in heat transfer at Re=500, the ORC configuration experiences a decrease in heat transfer rate as the Reynolds number increases, contrasting with two-dimensional simulation trends. The CRC configuration enhances the axial motion of the flow with Reynolds number, and its magnitude is larger than that of the ORC configuration and natural convection. A significant difference between two-dimensional and three-dimensional mixed convection simulation results is observed because of considerable secondary flow. Furthermore, the flow and thermal characteristics of turbulent mixed convection are investigated using streamlines, isotherms, Q-criterion, Nusselt number variation along the cylinders, anisotropy analysis, turbulent kinetic energy (TKE), dissipation, contours of radial and axial components of velocity.

Budget equations and astrophysical nonlinear mean-field dynamos

Abstract Solar, stellar and galactic large-scale magnetic fields are originated due to a combined action of non-uniform (differential) rotation and helical motions of plasma via mean-field dynamos. Usually, nonlinear mean-field dynamo theories take into account algebraic and dynamic quenching of alpha effect and algebraic quenching of turbulent magnetic diffusivity. However, the theories of the algebraic quenching do not take into account the effect of modification of the source of turbulence by the growing large-scale magnetic field. This phenomenon is due to the dissipation of the strong large-scale magnetic field resulting in an increase of the total turbulent energy. This effect has been studied using the budget equation for the total turbulent energy (which takes into account the feedback of the generated large-scale magnetic field on the background turbulence) for (i) a forced turbulence, (ii) a shear-produced turbulence and (iii) a convective turbulence. As the result of this effect, a nonlinear dynamo number decreases with increase of the large-scale magnetic field, so that that the mean-field αΩ, α2 and α2Ω dynamo instabilities are always saturated by the strong large-scale magnetic field.

Spatio-temporal dynamics of superstructures and vortices in turbulent Rayleigh–Bénard convection

Understanding turbulent thermal convection is essential for modeling many natural phenomena. This study investigates the spatiotemporal dynamics of the vortical structures in the mid-plane of turbulent Rayleigh–Bénard convection in SF6 via experiments. For this, a Rayleigh–Bénard cell of aspect ratio 10 is placed inside a pressure vessel and pressurized up to 1, 1.5, and 2.5 bar in order to reach Rayleigh numbers of Ra = 9.4×105,2.0×106, and 5.5×106, respectively. For all three cases, the Prandtl number is Pr =0.79 and ΔT≈7 K. Then, stereoscopic particle image velocimetry is conducted to measure the three velocity components in the horizontal-mid-plane for 5.78×103 free fall times. For the given aspect ratio, the flow is no longer dominated by the side walls of the cell and turbulent superstructures that show a two-dimensional repetitive organization form. These superstructures show diverse shapes with faster dissipation rates as Ra increases. Out-of-plane vortices are the main feature of the flow. As Ra increases, the number of these vortices also increases, and their size shrinks. However, their total number is almost constant for each Ra through the measurement period. Furthermore, their occurrence is random and does not depend on whether the flow is upward-heated, downward-cooled, or horizontally directed. Vortex tracking was applied to measure lifetime, displacement, and traveled distance of these structures. The relation between lifetime and traveled distance is rather linear. Interestingly, in the vortex centers, the out-of-plane momentum transport is larger in comparison to the bulk flow. Therefore, these vortices will play a major role in the heat transport in such flows.

The large-scale circulation and temperature oscillation in turbulent thermal convection in a flattened cylindrical cell of aspect ratio 2

We present an experimental study on the large-scale circulation (LSC) and temperature oscillation in the flattened cylindrical turbulent Rayleigh–Bénard Convection cell with aspect ratio Γ = 2. The Prandtl number is maintained at Pr = 5.7, and the Rayleigh number Ra ranges from 8.0×107 to 6.5×108. The strength and the orientation of the LSC are measured through the multi-point temperature signal at the mid-height of the convection cell. Our findings reveal that the single roll form of the LSC consistently dominates the flow, with its orientation confined to a narrower azimuthal range compared to the slender cell (e.g., Γ = 1 cell). Differing from the diffusion process observed in the Γ = 1 cell, the azimuthal motion of the LSC in the Γ = 2 cell exhibits a superdiffusion process. The mean square change of the strength of the LSC displays multiple regimes, with the scaling exponent of the first regime being 2, indicating ballistic motion within the short time interval. The scaling exponent of the second regime is 0.5 (0.2) for a leveled (tilted) cell, signifying a subdiffusion motion. Moreover, the temperature oscillations in the Γ = 2 cell differ significantly from those reported in a Γ = 1 cell, and it is found that the temperature oscillation exits everywhere at the mid-height of the cell. Furthermore, at the mid-height of the cell, the orientation and strength of the LSC exhibit prominent oscillations with characteristic frequencies of f0 and 2f0, respectively, which are absent in Γ = 1 and 1/2 cells. These behaviors can be well-explained by the motion of the vortex center.

Turbulence causes kinematic and behavioural adjustments in a flapping flier.

Turbulence is a widespread phenomenon in the natural world, but its influence on flapping fliers remains little studied. We assessed how freestream turbulence affected the kinematics, flight effort and track properties of homing pigeons (Columba livia), using the fine-scale variations in flight height as a proxy for turbulence levels. Birds showed a small increase in their wingbeat amplitude with increasing turbulence (similar to laboratory studies), but this was accompanied by a reduction in mean wingbeat frequency, such that their flapping wing speed remained the same. Mean kinematic responses to turbulence may therefore enable birds to increase their stability without a reduction in propulsive efficiency. Nonetheless, the most marked response to turbulence was an increase in the variability of wingbeat frequency and amplitude. These stroke-to-stroke changes in kinematics provide instantaneous compensation for turbulence. They will also increase flight costs. Yet pigeons only made small adjustments to their flight altitude, likely resulting in little change in exposure to strong convective turbulence. Responses to turbulence were therefore distinct from responses to wind, with the costs of high turbulence being levied through an increase in the variability of their kinematics and airspeed. This highlights the value of investigating the variability in flight parameters in free-living animals.

Transition to fully developed turbulence in liquid-metal convection facilitated by spatial confinement

Using thermal convection in liquid metal, we show that strong spatial confinement not only delays the onset Rayleigh number $Ra_c$ of Rayleigh–Bénard instability but also postpones the various flow-state transitions. The $Ra_c$ and the transition to fully developed turbulence Rayleigh number $Ra_f$ depend on the aspect ratio $\varGamma$ with $Ra_c\sim \varGamma ^{-4.05}$ and $Ra_f\sim \varGamma ^{-3.01}$ , implying that the stabilization effects caused by the strong spatial confinement are weaker on the transition to fully developed turbulence when compared with that on the onset. When the flow state is characterized by the supercritical Rayleigh number $Ra/Ra_{c}$ ( $Ra$ is the Rayleigh number), our study shows that the transition to fully developed turbulence in strongly confined geometries is advanced. For example, while the flow becomes fully developed turbulence at $Ra\approx 200Ra_c$ in a $\varGamma =1$ cell, the same transition in a $\varGamma =1/20$ cell only requires $Ra\approx 3Ra_c$ . Direct numerical simulation and linear stability analysis show that in the strongly confined regime, multiple vertically stacked roll structures appear just above the onset of convection. With an increase of the driving strength, the flow switches between different-roll states stochastically, resulting in no well-defined large-scale coherent flow. Owing to this new mechanism that only exists in systems with $\varGamma <1$ , the flow becomes turbulent in a much earlier stage. These findings shed new light on how turbulence is generated in strongly confined geometries.