Large-scale circulation (LSC) dynamics have been studied in thermal convection driven by heat-releasing particles via the four-way coupled Euler–Lagrange approach. We consider a wide range of Rayleigh–Robert number (${\textit{Rr}}=4.97\times 10^{5} - 4.97 \times 10^{8}$) and density ratio ($\hat {\rho }_r=1- 1000$) that characterize the thermal buoyancy and the particle inertia, respectively. An intriguing flow transition has been found as $\hat {\rho }_r$ continuously increases, involving in sequence three typical LSC regimes, i.e. the bulk-flow-up regime, the marginal regime and the bulk-flow-down (BFD) regime. The comprehensive influence of the LSC regime transition is demonstrated by examining the key flow statistics. As integral flow responses, the heat transfer efficiency and flow intensity change substantially when the LSC regime transition happens, and the thermal boundary layer thicknesses at the top and bottom walls exhibit similar alterations. Significant local accumulation of particles occurs as $\hat {\rho }_r$ increases to a sufficiently high value, resulting in a great modification in the flow dynamics. Specifically, particles aggregate near the sidewalls and heat the local surrounding fluid to generate rising warmer plumes that drive the LSC regime transition. Of interest, well-patterned cellular structures of particles take place near the top wall and obtain notable deviation from the thermal convection cells for the BFD regimes. A mechanical interpretation is proposed and substantiated based on a conceptual vortex–particle model, namely, the centrifugal motion of heat-releasing particles that is confirmed to play a driving role for the LSC regime transition.

A series of new laboratory experiments explore the transient flow in an enclosed space of depth $H$, which is subject to an upward displacement ventilation flux, $Q_V$, and which contains a localised heat source of buoyancy flux $F_s$, when the buoyancy of the ventilation air changes by $\Delta g'$. Initially, the plume, produced by the heat source, entrains the ventilation air, leading to a two-layer stratification which depends on the dimensionless strength of convection, $\mu \propto F_s^{1/3}H^{5/3}/Q_V$. When the buoyancy of the ventilation air decreases, $\Delta g' \lt 0$, a new layer of relatively dense fluid grows next to the floor. The fluid entrained by the plume from this new layer causes the plume to intrude between the original upper and lower layers. For a sufficiently large decrease in buoyancy, $|\Delta g' Q_V /F_s| \gt 1$, then as the new lower layer grows, the plume eventually becomes negatively buoyant relative to the original lower layer and intrudes between the new lowest layer and the original lower layer. When the buoyancy of the air supply increases, $\Delta g'\gt 0$, it mixes with the fluid in the original lower layer. If the increase in buoyancy is sufficient, $\Delta g' Q_V/F_s\gt 1$, then the new supply air eventually also mixes with the original upper layer. In each case, a new two-layer stratification becomes re-established. We propose new models for the evolution of the transient flow, assuming that the buoyancy profile can be approximated by a staircase of well-mixed layers. These layers are emptied or filled through the action of the plume and ventilation. We find that the model predictions are consistent with our new experiments in each of the four regimes. We conclude by discussing the implications of these transient flows for thermal comfort and the mixing of contaminants into the occupied lower region of the space.

We consider laminar forced convection in a shrouded longitudinal-fin heat sink (LFHS) with tip clearance, as described by the pioneering study of (Sparrow, Baliga & Patankar 1978 J. Heat Trans. 100). The base of the LFHS is isothermal but the fins, while thin, are not isothermal, i.e. the conjugate heat transfer problem is of interest. Whereas Sparrow et al. numerically solved the fully developed flow and thermal problems for a range of geometries and fin conductivities, we consider the physically realistic asymptotic limit where the fins are closely spaced, i.e. the spacing is small relative to their height and the clearance above them. The flow problem in this limit was considered by (Miyoshi et al. 2024, J. Fluid Mech. 991, A2), and we consider the corresponding thermal problem. Using matched asymptotic expansions, we find explicit solutions for the temperature field (in both the fluid and fins) and conjugate Nusselt numbers (local and average). The structure of the asymptotic solutions provides further insight into the results of Sparrow et al.: the flow is highest in the gap above the fins, hence heat transfer predominantly occurs close to the fin tips. The new formulas are compared with numerical solutions and are found to be accurate for practical LFHSs. Significantly, existing analytical results for ducts are for boundaries that are either wholly isothermal, wholly isoflux or with one of these conditions on each wall. Consequently, this study provides the first analytical results for conjugate Nusselt numbers for flow through ducts.

This paper numerically investigates the heat transport and bifurcation of natural convection in a differentially heated cavity filled with entangled polymer solution combined with the boundary layer and kinetic energy budget analysis. The polymers are described by the Rolie-Poly model, which effectively captures the rheological response of entangled polymers. The results indicate that the competition between its shear-thinning and elasticity dominates the flow structures and heat transfer rate. The addition of polymers tends to enhance the heat transfer as the polymer viscosity ratio ($\beta$) decreases or the relaxation time ratio ($\xi$) increases. The amount of heat transfer enhancement (HTE) behaves non-monotonically, which first increases significantly and then remains almost constant or decreases slightly with the Weissenberg number ($Wi$). The critical $Wi$ gradually increases with the increasing $\xi$, where the maximum HTE reaches approximately $64.9\,\%$ at $\beta = 0.1$. It is interesting that even at low Rayleigh numbers, the flow transitions from laminar to periodic flows in scenarios with strong elasticity. The bifurcation is subcritical and exhibits a typical hysteresis loop. Then, the bifurcation routes driven by inertia and elasticity are examined by direct numerical simulations. These results are illustrated by time histories, Fourier spectra analysis and spatial structures observed at varying time intervals. The kinetic energy budget indicates that the stretch of the polymers leads to great energy exchange between polymers and flow structures, which plays a crucial role in the hysteresis phenomenon. This dynamic behaviour contributes to the strongly self-sustained and self-enhancing processes in the flow.

Phase change materials (PCMs) hold considerable promise for thermal energy storage applications. However, designing a PCM system to meet a specific performance presents a formidable challenge, given the intricate influence of multiple factors on the performance. To address this challenge, we hereby develop a theoretical framework that elucidates the melting process of PCMs. By integrating stability analysis with theoretical modelling, we derive a transition criterion to demarcate different melting regimes, and subsequently formulate the melting curve that uniquely characterises the performance of an exemplary PCM system. This theoretical melting curve captures the key trends observed in experimental and numerical data across a broad parameter space, establishing a convenient and quantitative relationship between design parameters and system performance. Furthermore, we demonstrate the versatility of the theoretical framework across diverse configurations. Overall, our findings deepen the understanding of thermo-hydrodynamics in melting PCMs, thereby facilitating the evaluation, design and enhancement of PCM systems.

The three-dimensional stability of two-dimensional natural convection flows in a heated, square enclosure inclined to the horizontal is investigated numerically. First, the computational procedure is validated by comparison of base flow solutions to results reported in literature across a range of inclinations. A bi-global linear stability analysis is then conducted to investigate the stability of these two-dimensional base flows to infinitesimal three-dimensional perturbations, and the effect that buoyancy forces (defined by a buoyancy number $R_N$) and enclosure inclination $\theta$ have on these stability characteristics. The flow is first observed to become three-dimensionally unstable at buoyancy number $R_N = 213.8$ when $\theta$ is $180^\circ$; this increases to $R_N = 2.54 \times 10^4$ at inclination $\theta =58^\circ$. It is found that the two-dimensional base flow is more unstable to three-dimensional perturbations with the critical $R_N$ corresponding to three-dimensional instability being significantly lower than its two-dimensional counterpart across all considered inclinations except $83^\circ \leq \theta \leq 88^\circ$, where the most unstable mode is a two-dimensional oscillatory mode that develops in the boundary layers along the conducting walls. Eight different leading three-dimensional instability modes are identified, with inclinations $58^\circ \leq \theta < 88^\circ$ transitioning through an oscillatory mode, and inclinations $88^\circ \leq \theta \leq 180^\circ$ transitioning through a stationary mode. The characteristics of the primary instability modes corresponding to inclinations $88^\circ \leq \theta \leq 179^\circ$ indicate the presence of a Taylor–Görtler instability.

The sloping boundaries of stratified aquatic systems, such as lakes, are crucial environmental dynamic zones. While the role of sloping boundaries as energy dissipation hotspots is well established, their contribution to triggering large-scale motions has received less attention. This review delves into the development of thermally driven cross-shore flows on sloping boundaries under weak wind conditions. We specifically examine ‘thermal siphons’ (TS), a dynamical process that occurs when local free convection transforms into a horizontal circulation over sloping boundaries. Thermal siphons result from bathymetrically induced temperature (i.e. density) gradients when a lake experiences a uniform surface buoyancy flux, also known as differential cooling or heating. In the most common case of differential cooling of waters above the temperature of maximum density, TS lead to an overturning circulation characterised by a downslope density current and a surface return flow within a convective environment. Field observations, laboratory experiments and high-fidelity simulations of TS provide insights into their temporal occurrence, formation mechanisms, water transport dynamics and cross-shore pathways, addressing pivotal questions from an aquatic system perspective. Fluid mechanics is a fundamental tool in addressing such environmental questions and thereby serves as the central theme in this review.

We explore the interaction of natural convection and mechanical ventilation in a room where fresh air is supplied at low level and stale air is extracted at high level. Turbulent buoyant plumes rising from heat sources interact with this upward airflow and establish a steady-state stratification with a warm upper layer above a layer of the cold supply air. Adapting the volume balance model used in natural ventilation (Linden et al., J. Fluid Mech., vol. 212, 1990, pp. 309–335) leads to the prediction that the upper layer will vent from the room when the ventilation volume flux exceeds the volume flux in the plumes at the ceiling. However, our new laboratory experiments establish that there is still a stable two-layer stratification beyond this point of critical ventilation. Motivated by our observations, we propose that the kinetic energy flux supplied by the plume leads to turbulent mixing in the upper layer. We propose a new model of this mixing which is consistent with our experiments in both the over- and under-ventilated regimes. This has important implications for air recirculation in buildings with large ventilation flows, particularly hospital operating theatres and clean rooms.

Vertical thermal convection is a non-equilibrium system in which both buoyancy and shear forces play a role in driving the convective flow. Beyond the onset of convection, the driven dissipative system exhibits chaotic dynamics and turbulence. In a three-dimensional domain extended in both the vertical and the transverse dimensions, Gao et al. (Phys. Rev. E, vol. 97, 2018, 053107) have observed a variety of convection patterns which are not described by linear stability analysis. We investigate the fully nonlinear dynamics of vertical convection using a dynamical-systems approach based on the Oberbeck–Boussinesq equations. We compute the invariant solutions of these equations and the bifurcations that are responsible for the creation and termination of various branches. We map out a sequence of local bifurcations from the laminar base state, including simultaneous bifurcations involving patterned steady states with different symmetries. This atypical phenomenon of multiple branches simultaneously bifurcating from a single parent branch is explained by the role of $D_4$ symmetry. In addition, two global bifurcations are identified: first, a homoclinic cycle from modulated transverse rolls and second, a heteroclinic cycle linking two symmetry-related diamond-roll patterns. These are confirmed by phase space projections as well as the functional form of the divergence of the period close to the bifurcation points. The heteroclinic orbit is shown to be robust and to result from a 1:2 mode interaction. The intricacy of this bifurcation diagram highlights the essential role played by dynamical systems theory and computation in hydrodynamic configurations.

Melting and solidification in periodically time-modulated thermal convection are relevant for numerous natural and engineering systems, for example, glacial melting under periodic sun radiation and latent thermal energy storage under periodically pulsating heating. It is highly relevant for the estimation of melt rate and melt efficiency management. However, even the dynamics of a solid–liquid interface shape subjected to a simple sinusoidal heating has not yet been investigated in detail. In this paper, we offer a better understanding of the modulation frequency dependence of the melting and solidification front. We numerically investigate periodic melting and solidification in turbulent convective flow with the solid above and the melted liquid below, and sinusoidal heating at the bottom plate with the mean temperature equal to the melting temperature. We investigate how the periodic heating can prevent the full solidification, and the resulting flow structures and the quasi-equilibrium interface height. We further study the dependence on the heating modulation frequency. As the frequency decreases, we found two distinct regimes, which are ‘partially solid’ and ‘fully solid’. In the fully solid regime, the liquid freezes completely, and the effect of the modulation is limited. In the partially solid regime, the solid partially melts, and a steady or unsteady solid–liquid interface forms depending on the frequency. The interface height can be derived based on the energy balance through the interface. In the partially solid regime, the interface height oscillates periodically, following the frequency of modulation. Here, we propose a perturbation approach that can predict the dependency of the oscillation amplitude on the modulation frequency.

Buoyancy-driven bubbly flows play pivotal roles in various scenarios, such as the oxygenation and mixing in the upper ocean and the reaction kinetics in chemical and bio-reactors. This work focuses on the convective flow induced by the localised release of large air bubbles ($D_b=3.7$ mm, ${Re}_b=950$) in a water tank, exploring the resulting flow and the transition from laminar to disturbed states as a function of the Rayleigh number ranging from $3\times 10^3$ to $2\times 10^5$. At low ${Ra}$ the flow is smooth and laminar with weak temporal oscillations, while a highly disturbed state appears above a critical value ${Ra}_c$. A theoretical analysis is presented that links the mean flow circulation to the Rayleigh number. Through an experimental investigation, utilising three-dimensional particle tracking velocimetry and flow visualisation, we confirm the theory presented, and characterise the laminar to disturbed transition in the system. These findings not only enhance our fundamental understanding of buoyancy-driven convective flows but also hold significant implications for practical applications, particularly in the optimisation of bio-reactor design and other industrial processes reliant on controlled convective dynamics.

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.

Vertical convection is the fluid motion that is induced by the heating and cooling of two opposed vertical boundaries of a rectangular cavity (see e.g. Wang et al., J. Fluid Mech., vol. 917, 2021, A6). We consider the linear stability of the steady two-dimensional flow reached at Rayleigh numbers of O($10^8$). As a function of the Prandtl number, $Pr$, and the height-to-width aspect ratio of the domain, $A$, the base flow of each case is computed numerically and linear simulations are used to obtain the properties of the leading linear instability mode. Flow regimes depend on the presence of a circulation in the entire cavity, detachment of the thermal layer from the boundary or the corner regions and on the oscillation frequency relative to the natural frequency of oscillation in the stably temperature-stratified interior, allowing for the presence of internal waves or not. Accordingly, the regime is called slow or fast, respectively. Either the global circulation or internal waves in the interior may couple the top and bottom buoyancy currents, while their absence implies asymmetry in their perturbation amplitude. Six flow regimes are found in the range of $0.1 \leq Pr \leq 4$ and $0.5 \leq A \leq 2$. For $Pr \lessapprox 0.4$ and $A>1$, the base flow is driven by a large circulation in the entire cavity. For $Pr \gtrapprox 0.7$, the thermal boundary layers are thin and the instability is driven by the motion along the wall and the detached boundary layer. A transition between these regimes is marked by a dramatic change in oscillation frequency at $Pr = 0.55 \pm 0.15$ and $A <2$.

The paper presents the results of an experimental and numerical study of turbulent thermal convection in a rectangular box containing an extended immersed free-floating plate. Varying the values of control parameters, such as Rayleigh number, aspect ratio and vertical position of the plate, provides a wide range of possible modes, from immobile and purely periodic to stochastic. We have shown that stable periodic motions occur when the plate floats close to one of the heat exchangers. An increase in the distance between the plate and the heat exchanger breaks the periodic motion and (at moderate Rayleigh numbers) leads to a pronounced asymmetry, when the plate stays close to one of the walls most of the time, makes rare excursions to the opposite wall and immediately returns. As the Rayleigh number increases, the plate motions from one edge of the box to the other reappear, but always have an irregular character. Regarding the dependence of the system behaviour on the geometry of the box, both lower and upper limits of periodic plate motions were found in the experiments. In the numerical simulations, the upper limit was not achieved – the plate moves quasi-periodically through the chain of vortices of different signs even at the largest aspect ratio being considered. The heat-insulating floating plate provides the spatial and temporal variation of the heat flux and reduces the integral heat flux, but the reduction in heat flux depends significantly on the vertical position of the plate.

We report an experimental investigation of the heat transport and flow field in a rectangular Rayleigh–Bénard convection (RBC) cell with two immiscible fluids: silicone oil and glycerol. The global heat transport of the system is divided into three ranges corresponding to the different flow structures formed in the glycerol layer. In range I, the glycerol layer is dominated by conduction, and no plume is formed over the interface. In range II, cellular rolls are formed in the glycerol layer and the horizontal motion of rolls causes an oscillation of temperature in the interface. In range III, the cellular pattern is time-independent, and the interface forms a group of wavelets with wave numbers consistent with the mode of the cellular pattern. In lower-thin glycerol, the Nusselt (Nu) grows from conduction to convection through an oscillating subcritical bifurcation at critical Rayleigh number $Ra_c$. The value of $Ra_c$ in the present work is smaller than the theoretical prediction of both-rigid boundaries and greater than the prediction of one-rigid and one-free boundaries. In the upper-thick silicone oil layer, $Nu$ increases with increasing $Ra$, but it is smaller than that of traditional RBC. For the silicone oil layer in two-layer RBC, the hot plumes emitting over the liquid–liquid interface showed different shape and different velocity from cold plumes emitting from the top rigid plate. This implies that the velocity boundary condition strongly influences the flow structure in turbulent convection.

This study investigates the effect of vibration on the flow structure transitions in thermal vibrational convection (TVC) systems, which occur when a fluid layer with a temperature gradient is excited by vibration. Direct numerical simulation (DNS) of TVC in a two-dimensional enclosed square box is performed over a range of dimensionless vibration amplitudes $0.001 \le a \le 0.3$ and angular frequencies $10^{2} \le \omega \le 10^{7}$, with a fixed Prandtl number of 4.38. The flow visualisation shows the transition behaviour of flow structure upon the varying frequency, characterising three distinct regimes, which are the periodic-circulation regime, columnar regime and columnar-broken regime. Different statistical properties are distinguished from the temperature and velocity fluctuations at the boundary layer and mid-height. Upon transition into the columnar regime, columnar thermal coherent structures are formed, in contrast to the periodic oscillating circulation. These columns are contributed by the merging of thermal plumes near the boundary layer, and the resultant thermal updrafts remain at almost fixed lateral position, leading to a decrease in fluctuations. We further find that the critical point of this transition can be described nicely by the vibrational Rayleigh number ${{Ra}}_{vib}$. As the frequency continues to increase, entering the so-called columnar-broken regime, the columnar structures are broken, and eventually the flow state becomes a large-scale circulation (LSC), characterised by a sudden increase in fluctuations. Finally, a phase diagram is constructed to summarise the flow structure transition over a wide range of vibration amplitude and frequency parameters.

In this paper, we report on a direct numerical simulation (DNS) study of turbulent thermal convection in mixed porous–pure fluid domains. The computational domain consists of a cavity that contains a porous medium placed right above the bottom wall. The solid matrix is internally heated which, in turn, induces the convective motions of the fluid. The Rayleigh number of the flow in the pure fluid region above the porous medium is of the order of $10^7$. In our study, we consider cases of different sizes of the porous medium, as well as cases with both uniform and non-uniform heat loading of the solid matrix. For each case, we analyse the convective structures in both the porous and the pure fluid domains and investigate the effect of the porous medium on the emerging flow patterns above it. Results for the flow statistics, as well as for the Nusselt number and each of its components, are also presented herein. Further, we make comparisons of the flow properties in this pure fluid region with those in Rayleigh–Bénard convection. Our simulations predict that, depending on the area coverage, the large-scale circulation above the porous medium can be in a single-roll, dual-roll or intermediate state. Also, when the area coverage increases, the temperatures inside it increase due to reduced fluid circulation. Accordingly, when the area coverage increases, then the Nusselt number becomes smaller whereas the Rayleigh number is increased.

This paper revisits the melting process of phase change materials (PCMs) enclosed in a horizontally placed rectangular cavity, with isothermal and adiabatic conditions subjected to the vertical and horizontal walls, respectively. First, numerical simulations based on an improved lattice Boltzmann method are conducted to illustrate and to inform the theoretical modelling. It is shown that, compared with the traditional two-stage conduction–convection melting description, it is more reasonable to include a third stage in terms of the heat transfer behaviour. During the third stage, the remnant solid PCM is located in the corner formed by the cold and bottom walls of the cavity, and an increasing part of the input energy will be transferred directly out of the cavity without compensating for the melting latent heat, thus inducing a continuously decreasing melting rate until the end of the melting process. Then theoretical predictions are derived piecewise for the melted liquid fraction during the entire melting process, and the corresponding transitions between two successive stages are also discussed. The results are validated successfully via the available experimental and numerical data in the literature, and could guide the design and operation of latent heat storage systems.

We investigate the dynamics of a fluid layer subject to a bottom heat flux and a top monotonically increasing temperature profile driving horizontal convection (HC). We use direct numerical simulations and consider a large range of flux-based Rayleigh numbers $10^6 \leq Ra_F \leq 10^9$ and imposed top horizontal to bottom vertical heat flux ratios $0 \leq \varLambda \leq 1$. The fluid domain is a closed two-dimensional box with aspect ratio $4\leq \varGamma \leq 16$ and we consider no-slip boundaries and adiabatic side walls. We demonstrate a regime transition from Rayleigh–Bénard (RB) convection to HC at $\varLambda \approx 10^{-2}$, which is independent of $Ra_F$ and $\varGamma$. At small $\varLambda$, the flow is organised in multiple overturning cells with approximately unit aspect ratio, whereas at large $\varLambda$ a single cell is obtained. The RB-relevant Nusselt number scaling with $Ra_F$ and the HC-relevant Nusselt number scaling with the horizontal Rayleigh number $Ra_L=Ra_F\varLambda \varGamma ^4$ are in good agreement with previous results from classical RB convection and HC studies in the limit $\varLambda \ll 10^{-2}$ and $\varLambda \gg 10^{-2}$, respectively. We demonstrate that the system is multi-stable near the transition $\varLambda \approx 10^{-2}$, i.e. the exact number of cells not only depends on $\varLambda$ but also on the system's history. Our results suggest that subglacial lakes, which motivated this study, are likely to be dominated by RB convection, unless the slope of the ice–water interface, which controls the horizontal temperature gradient via the pressure-dependence of the freezing point, is greater than unity.

A numerical investigation and reduced-order modelling of natural convection in a cavity with differentially heated sidewalls is discussed. The effect of conjugate boundary conditions on the cavity's heat transfer and natural flow circulation with varying aspect ratios and Rayleigh numbers is examined. Validation of the canonical differentially heated cavity reveals that a modification to the definition of the Rayleigh number (Ra) is required to reconcile the $Nu\sim Ra^{1/4}$ scaling (where Nu is the Nusselt number) and validity of previously proposed correlations for the heat transfer in vertical enclosures. Dynamic mode decomposition is used to uncover the underlying time-dependent flow structures and the results are compared with stability bifurcation studies in the literature. A flow mode previously associated with smaller aspect ratio cavities is identified as the unstable mode for a larger aspect ratio of 4. The effect of conjugate boundary conditions is scaled based on the ratio of the internal and external boundary layers, wherein higher external Reynolds numbers aid in the heat transfer as the Nusselt number approaches the isothermal limit. A reduced-order theoretical model is proposed to predict the Nusselt number for the conjugate boundary conditions. The performance of conjugate boundary conditions is connected to the flow stability, with the parallel-flow configuration acting in a destabilizing manner while the counterflow configuration has a stabilizing effect and results in the highest heat transfer. We also found that relatively large heat transfer can be achieved with substantially lower external actuation with intermediate aspect ratios, translating to less power in practice.