We have developed a parameter-free, two-phase, volume-averaged approach to predictively describe the spin-up flow of dilute, cluster-free ferrofluids excited by low-frequency rotating magnetic fields. Predictive validation of the model was performed through a thorough comparison with local velocity profile measurements, and it demonstrated its ability to capture the spin-up flow dynamics without the need for parameter tuning by carefully delineating the validity domain of the ferrofluid dilutedness conditions. To gain insight into the underlying flow mechanisms, we performed a systematic parametric analysis examining the effects of the induced magnetic field, the dipolar interactions between magnetic nanoparticles and the demagnetizing field. How these mechanisms shape the flow of dilute ferrofluids excited by low-frequency rotating fields in a standard spin-up flow geometry has been addressed using probabilistic nanoparticle orientational dynamics, combining Faxén's laws and the Smoluchowski equation to describe the transport of particle magnetic moments. Our findings revealed that the induced magnetic field is the primary driving force of ferrofluid spin-up flow. The dipole interactions and demagnetizing field, on the other hand, contribute only as secondary phenomena to the overall flow behaviour. Furthermore, we have discussed the potential extension of the two-phase approach, in particular with respect to the formation of chain-like aggregates under the influence of strong magnetic fields. Overall, our study provides valuable insights into the complex dynamics of ferrofluid flow and contributes to a comprehensive understanding of the key mechanisms governing the spin-up flow of dilute ferrofluids excited by low-frequency rotating magnetic fields.

The preference for particles to accumulate at specific regions in the near-wall part is a widely observed phenomenon in wall-bounded turbulence. Unlike small particles more frequently found in low-speed streaks, finite-size particles can accumulate in either low-speed or high-speed streaks. However, mechanisms and influencing factors leading to the different preferential concentration locations still need to be clarified. The present study conducts particle-resolved direct numerical simulations of particle-laden turbulent channel flows to provide a better understanding of this seemingly puzzling behaviour of preferential accumulation. These simulations cover different particle-to-fluid density ratios, particle volume fractions, particle sizes and degrees of sedimentation intensity. We find that the large particle size is the crucial factor that results in particles accumulating in high-speed streaks. Large particles not only are difficult to be conveyed by the quasi-streamwise vortices to low-speed streaks but also can escape from the near-wall region before moving spanwisely out from high-speed streaks. The sedimentation effect allows particles to gather closer to the channel wall and stay longer in the near-wall regions, reinforcing the sweeping mechanism of quasi-streamwise vortices that transport particles from high- to low-speed streaks. As a result, sedimenting particles tend to accumulate in the low-speed streaks.

Three different porous substrates (with different pore sizes, $s$, and permeabilities, $K$) are used to examine their effect on the structure of boundary layer flow over them. The flow is characterised with single-point hot-wire measurements as well as planar particle image velocimetry. In order to elucidate differences in shallow and deep flows past porous substrates, foams with two different thicknesses ($h$) are used (for all three substrates). A wide range of friction Reynolds numbers ($2000< Re_\tau <13\,500$) and permeability-based Reynolds numbers ($1< Re_K< 50$) are attained. For substrates with $Re_K \sim 1$, the flow behaviour remains similar to flow over impermeable smooth walls and as such Townsend's hypothesis remains valid. Very large-scale motions are observed over permeable foams even when the $Re_K > 1$. In contrast, a substantial reduction in velocity disturbances and associated length scales is achieved for permeable foams with intermediate values of pore density and relative foam thickness ($h/s$), which affects outer-layer similarity. As permeability is increased by increasing pore size, the foam becomes sparse relative to viscous scales at high Reynolds numbers. For such foams, the flow conforms to outer-layer similarity and is more akin to flow over rough surfaces. Permeability attenuates the wavelengths associated with the outer-layer peak.

The electrohydrodynamic processes taking place in a cone jet cause ohmic and viscous dissipation, and ultimately self-heating of the liquid. Despite this, previous analyses have modelled cone jets as isothermal systems. To investigate the validity of this assumption, this work applies the leaky-dielectric model to cone jets, while also requiring conservation of energy to reproduce the variation of temperature caused by dissipation and temperature-dependent liquid properties. The main goals are to determine whether there exist electrospraying conditions for which the isothermal assumption is inaccurate, and quantify the temperature field under such conditions. The work confirms that self-heating and thermal effects are important in liquids with sufficiently high conductivities, which is a significant limit because these electrical conductivities are needed to produce jets and droplets with radii of tens of nanometres or smaller. The numerical solution provides accurate expressions for evaluating the dissipation and the temperature increase in cone jets, and confirms that thermal effects cause the apparent breakdown of the traditional scaling law for the current of cone jets of highly conducting liquids.

We show that a heating pattern applied to a surface with a corrugation pattern generates a propulsive effect. The same heating pattern applied to a smooth surface creates propulsion through nonlinear thermal streaming associated with pitchfork bifurcation. The combination of groove and heating patterns generates thermal drift, representing a forced response whose magnitude changes with the relative position of both patterns. Thermal drift is always present, while thermal streaming requires sufficiently intense heating. When both effects are active, a change in the relative position of these patterns produces rapid changes in the magnitude of propulsion, resulting in the formation of limit points. The strength of propulsion increases with a decrease in the Prandtl number and with an addition of uniform heating.

Two common definitions of the spatially local rate of kinetic energy cascade at some scale $\ell$ in turbulent flows are (i) the cubic velocity difference term appearing in the ‘scale-integrated local Kolmogorov–Hill’ equation (structure-function approach), and (ii) the subfilter-scale energy flux term in the transport equation for subgrid-scale kinetic energy (filtering approach). We perform a comparative study of both quantities based on direct numerical simulation data of isotropic turbulence at Taylor-scale Reynolds number 1250. While in the past observations of negative subfilter-scale energy flux (backscatter) have led to debates regarding interpretation and relevance of such observations, we argue that the interpretation of the local structure-function-based cascade rate definition is unambiguous since it arises from a divergence term in scale space. Conditional averaging is used to explore the relationship between the local cascade rate and the local filtered viscous dissipation rate as well as filtered velocity gradient tensor properties such as its invariants. We find statistically robust evidence of inverse cascade when both the large-scale rotation rate is strong and the large-scale strain rate is weak. Even stronger net inverse cascading is observed in the ‘vortex compression’ $R>0$, $Q>0$ quadrant, where $R$ and $Q$ are velocity gradient invariants. Qualitatively similar but quantitatively much weaker trends are observed for the conditionally averaged subfilter-scale energy flux. Flow visualizations show consistent trends, namely that spatially, the inverse cascade events appear to be located within large-scale vortices, specifically in subregions when $R$ is large.

Flow through sudden expansion finds its application in several engineering and biological processes. Though the stability of flow through steady sudden expansion has garnered much attention, little to none is given to the pulsatile flow through sudden expansion. Hence, in the present work we study the influence of inflow pulsatility on flow characteristics in a sudden expansion. The inflow velocity is a sinusoidal waveform that is modulated to encompass a wide range of amplitudes, ${{a}}$, and reduced velocities, ${{U_{r}}}$. We report four different modes, namely, synchronized growth of the recirculation region (at high ${{U_{r}}}$), necking and diffusion of the recirculation region (at moderately high ${{U_{r}}}$), splitting and convection of the recirculation region (at moderate ${{U_{r}}}$) and inverse growth of the recirculation region (at low ${{U_{r}}}$). In each mode, the symmetry-breaking critical Reynolds number is obtained through numerical experiments and compared with those of Floquet stability analysis. We found that diffusion and the convection mode of the recirculation region increases the stability of the flow while the inverse growth mode of the recirculation region decreases the same. The effect of the expansion ratio, ${{ER}}$, is also explored, and we found that as ${{ER}}$ increases, the absolute stability of flow decreases, but relative stability between the modes remains similar. Finally, we explain the dynamics of the modes by using terms involving the vorticity transport equation.

This study gives insights into the interfacial instabilities of a ventilation cavity by injecting gas vertically into the horizontal liquid crossflow through both numerical and experimental investigations. We identified four distinct regimes of the ventilation cavity based on their topological characteristics: (I) discrete bubble, (II) continuous cavity, (III) bifurcated cavity, and (IV) bubble plume. The boundaries for these regimes are delineated within the parameter space of crossflow velocity and jet speed. A comprehensive analysis of the flow characteristics associated with each regime is presented, encompassing the phase mixing properties, the dominant frequency of pulsation, and the time-averaged profile of the cavity. This study conducted a detailed investigation of the periodic pulsation at the leading-edge interface of the cavity, also known as the ‘puffing phenomenon’. The results of local spectral analysis and dynamic mode decomposition indicate that the high-frequency instability in the near-field region exhibits the most significant growth rate. In contrast, the low-frequency mode with the largest amplitude spans a broader region from the orifice to the cavity branches. A conceptual model has been proposed to elucidate the mechanism behind the pulsation phenomenon observed along the cavity interface: the pulsation results from the alternate intrusion of the crossflow and the cavity recovery at the leading edge, being governed mainly by the periodic oscillating imbalance between the static pressure of gas near the orifice and the stagnation pressure of crossflow at the leading edge.

We study nonlinear resonant wave–wave interactions which occur when ocean waves propagate into a thin floating ice sheet. Using multiple-scale perturbation analysis, we obtain theoretical predictions of the wave amplitude evolution as a function of distance travelled past the ice edge for a semi-infinite ice sheet. The theoretical predictions are supported by a high-order spectral (HOS) method capable of simulating nonlinear interactions in both open water and the ice sheet. Using the HOS method, the amplitude evolution predictions are extended to multiple (coupled) triad interactions and a single ice sheet of finite length. We relate the amplitude evolution to mechanisms with strong frequency dependence – ice bending strain, related to ice breakup, as well as wave reflection and transmission. We show that, due to sum-frequency interactions, the maximum strain in the ice sheet can be more than twice that predicted by linearised theory. For an ice sheet of finite length, we show that nonlinear wave reflection and transmission coefficients depend on a parameter in terms of wave steepness and ice length, and can have values significantly different than those from linear theory. In particular, we show that nonlinear sum-frequency interactions can appreciably decrease the total wave energy transmitted past the ice sheet. This work has implications for understanding the occurrence of ice breakup, wave attenuation due to scattering in the marginal ice zone and the resulting ice floe size distribution.

Supergranule aggregation, i.e. the gradual aggregation of convection cells to horizontally extended networks of flow structures, is a unique feature of constant heat flux-driven turbulent convection. In the present study, we address the question if this mechanism of self-organisation of the flow is present for any fluid. Therefore, we analyse three-dimensional Rayleigh–Bénard convection at a fixed Rayleigh number ${Ra} \approx 2.0 \times 10^{5}$ across $4$ orders of Prandtl numbers ${Pr} \in [10^{-2}, 10^{2}]$ by means of direct numerical simulations in horizontally extended periodic domains with aspect ratio $\varGamma = 60$. Our study confirms the omnipresence of the mechanism of supergranule aggregation for the entire range of investigated fluids. Moreover, we analyse the effect of ${Pr}$ on the global heat and momentum transport, and clarify the role of a potential stable stratification in the bulk of the fluid layer. The ubiquity of the investigated mechanism of flow self-organisation underlines its relevance for pattern formation in geophysical and astrophysical convection flows, the latter of which are often driven by prescribed heat fluxes.

Adding moving boundaries to convective fluids is known to result in non-trivial and surprising dynamics, leading to spectacular geoformations ranging from kilometre-scale karst terrains to planetary-scale plate tectonics. On the one hand, the moving solid alters the surrounding flow field, but on the other hand, the flow modifies the motion and shape of the solid. This leads to a two-way coupling that is significant in the study of fluid–structure interactions and in the understanding of geomorphologies. In this work, we investigate the coupling between a floating plate and the convective fluid below it. Through numerical experiments, we show that the motion of this plate is driven by the flow beneath. However, the flow structure is also modified by the presence of the plate, leading to the ‘thermal blanket’ effect where the trapped heat beneath the plate results in buoyant and upwelling flows that in turn push the plate away. By analysing this two-way coupling between moving boundary and fluid, we are able to capture the dynamical behaviours of this plate through a low-dimensional stochastic model. Geophysically, the thermal blanket effect is believed to drive the continental drift, therefore understanding this mechanism has significance beyond fluid dynamics.

We propose a linearized deterministic model for predicting coherent structures in the wake of a floating offshore wind turbine subject to platform motions. The model's motion-to-wake predictive capability is achieved through two building blocks: a motion-to-forcing (M2F) part and a forcing-to-wake (F2W) part. The M2F model provides a unified framework to parameterize the effects of arbitrary floating wind turbine motions as unsteady loads of a fixed actuator disk, requiring only the radial distribution of the aerodynamics force coefficient on the blade as input. The F2W model is derived based on a bi-global resolvent model obtained from the linearized Navier–Stokes equations, using the time-averaged wake of a fixed wind turbine as input. In addition to its capability of predicting sensitive frequency ranges, the model excels linear stability analysis by providing spatial modes of the wake response in a motion-specific and phase-resolved manner. The model successfully predicts the wake pulsing mode induced by surge, as well as the similarity and difference of the wake meandering modes caused by sway and yaw. Large-eddy simulations under different inflow turbulence intensities (TIs) and length scales are further conducted to analyse the wake meandering triggered by the simultaneous excitation of free-stream turbulence and sway motion. The results show distinct frequency signatures for the wake dynamics induced by ambient turbulence and sway motion. The inflow TI is found to have a stabilizing effect on the wake, reducing the motion-induced wake responses. Such a stabilizing effect is captured satisfactorily with the proposed model, provided that the effective viscosity is calibrated properly using the data from the fixed turbine wake under the corresponding turbulent inflow.

Superhydrophobic surfaces dramatically reduce skin friction of overlying liquid flows. These surfaces are complex and numerical simulations usually rely on models to reduce this complexity. One of the simplest consists of finding an equivalent boundary condition through a homogenisation procedure, which in the case of channel flow over oriented riblets, leads to the presence of a small spanwise component in the homogenised base flow velocity. This work aims at investigating the influence of such a three-dimensionality of the base flow on stability and transition in a channel with walls covered by oriented riblets. Linear stability for this base flow is investigated: a new instability region, linked to cross-flow effects, is observed. Tollmien–Schlichting waves are also retrieved but the most unstable are three-dimensional. Transient growth is also affected as oblique streaks with non-zero streamwise wavenumber become the most amplified perturbations. When transition is induced by Tollmien–Schlichting waves, after an initial exponential growth regime, streaky structures with large spanwise wavenumber rapidly arise. Modal mechanisms appear to play a leading role in the development of these structures and a secondary stability analysis is performed to retrieve successfully some of their characteristics. The second scenario, initiated with cross-flow vortices, displays a strong influence of nonlinearities. The flow develops into large quasi-spanwise-invariant structures before breaking down to turbulence. Secondary stability on the saturated cross-flow vortices sheds light on this stage of transition. In both cases, cross-flow effects dominate the flow dynamics, suggesting the need to consider the anisotropicity of the wall condition when modelling superhydrophobic surfaces.

Helicity plays a key role in the evolution of vortex structures and turbulent dynamics. The helicity dynamics and vortex structures in streamwise-rotating channel turbulence are discussed in this paper using the helicity budget equation and the differentiated second-order structure function equation of helicity. Generally, rotation and Reynolds numbers exhibit opposing effects on the interscale helicity dynamics and the vortices. Under the buffer layer, the positions of the helicity peaks are proportional to the ratio between the Reynolds and rotation numbers. The mechanism is related to the opposing effects of convection and rotation. Rotation directly affects the helicity balance through the Coriolis term and corresponding pressure term. In the buffer layer, the scale helicity is negative at small scales but positive at large scales, which is mainly induced by the spatial effects (the production and the spatial turbulent convection) but reduced by interscale cascades. Examination of structures reveals the close association between scale helicity and streaks, with streak lift angles exhibiting an increase with rotation and a decrease with Reynolds numbers. In the log-law layer, the Coriolis terms and corresponding pressure terms are proportional to the rotation numbers but remain independent of the Reynolds numbers. The negative scale helicity is forward cascaded towards small scales. Generally, spanwise vortices in the log-law layer are related to sweep events and forward cascades. Our findings indicate that these spanwise vortices are suppressed by rotation but recover with increasing Reynolds numbers, aligning with the effects observed in the scale helicity balance.

To describe the effects of porous roughness on turbulence, we have carried out direct numerical simulations using the lattice Boltzmann method. The simulated flows are fully developed turbulent flows in channels consisting of a solid smooth top wall and a porous bottom wall with transverse porous ribs whose heights are 10 % of the channel height. The considered ratios of the rib spacing to the rib height are $w/k\simeq 1$ and 9. The Kelvin-cell structure is applied to construct faithfully the porous media whose porosities are $\varphi \ge 0.79$. Three kinds of porous media having different permeabilities are considered. The most permeable one has an approximately one order higher permeability than that of the least permeable one. The higher permeability case is designed to have a pore scale that is the same as the rib height so that it is the most permeable case for the rib roughness with the designed porosity. In the simulations, the bulk Reynolds number is set to $Re_b=5500$, and the corresponding permeability Reynolds numbers are $Re_K=2.2\unicode{x2013}7.5$. The simulated field data and the drag coefficient, which includes both the pressure drag by the ribs and the frictional drag over the porous wall, are analysed to understand the characteristics of the permeable roughness in terms of permeability. The decomposition of the drag coefficient into the integrated laminar, rib-drag, dispersion and turbulence parts elucidates the transition mechanism between the typical d-type to k-type roughness depending on $Re_K$. By the double (time and space) averaged budget equations for the dispersion and Reynolds stresses, we explain how the energy generated by the roughness transfers to turbulence through dispersion resulting in the k-type characteristics. The nominal roughness sublayer thickness and the characteristic roughness height are introduced with the parameters obtained by fitting the velocity data to Best's and Nikuradse's logarithmic velocity formulae. Along with data in the literature, it is suggested that the ratio of the characteristic roughness height to the nominal roughness sublayer thickness becomes constant irrespective of the rib spacing in the full permeable-wall turbulence at $Re_K> 7$.

Can-annular combustors feature clusters of thermoacoustic eigenvalues, which originate from the weak acoustic coupling between $N$ identical cans at the downstream end. When instabilities occur, one needs to consider the nonlinear interaction between all $N$ modes in the unstable cluster in order to predict the steady-state behaviour. A nonlinear reduced-order model for the analysis of this phenomenon is developed, based on the balance equations for acoustic mass, momentum and energy. Its linearisation yields explicit expressions for the $N$ complex-valued eigenfrequencies that form a cluster. To treat the nonlinear equations semianalytically, a Galerkin projection is performed, resulting in a nonlinear system of $N$ coupled oscillators. Each oscillator represents the dynamics of a global mode that oscillates in the whole can-annular combustor. The analytical expressions of the equations reveal how the geometrical and thermofluid parameters affect the thermoacoustic response of the system. To gain further insights, the method of averaging is applied to obtain equations for the slow-time dynamics of the amplitude and phase of each mode. The averaged system, whose solutions compare very well with those of the full oscillator equations, is shown to be able to predict complex transient dynamics. A variety of dynamical states are identified in the steady-state oscillatory regime, including push–push (in-phase) and spinning oscillations. Notably, the averaged equations are able to predict the existence of synchronised states. These states occur when the frequencies of two (or more) unstable modes with nominally different frequencies lock onto a common frequency as a result of nonlinear interactions.

The interaction between ingested turbulence and rotating blades is a key source of broadband noise in engineering applications. In this paper, a far-field noise model accounting for source correlation across the span of the blade and between blades is developed and applied to the study of homogeneous isotropic turbulence ingestion by a model cooling fan, wind turbine and aircraft propeller. The widely used theory of Amiet is revisited and it is shown that previous works produce conflicting results when attempting to account for blade-to-blade correlation. Central to the model is the calculation of the time between blade chops of the same turbulent eddy as heard by the observer. In this paper it is shown that, when derived correctly, Amiet's theory accounts for correlated sources between blades and, thus, can predict haystacking tones. Comparisons with the new rotational formulation and with experimental data enable us to show that Amiet's theory can be used to accurately predict turbulence ingestion noise from open rotors. In particular, it is found that the infinite-span assumption in strip theory and the neglect of correlation effects across the span do not undermine the accuracy of this theory. This is of great importance because, unlike Amiet's theory, models which treat rotational effects and source correlation exactly are expensive to evaluate routinely at high frequencies due to the slow convergence of infinite series with Bessel functions.

For dissolving active oil droplets in an ambient liquid, it is generally assumed that the Marangoni effect results in repulsive interactions, while the buoyancy effects caused by the density difference between the droplets, diffusing product and the ambient fluid are usually neglected. However, it has been observed in recent experiments that active droplets can form clusters due to buoyancy-driven convection (Krüger et al., Eur. Phys. J. E, vol. 39, 2016, pp. 1–9). In this study we numerically analyse the buoyancy effect, in addition to the propulsion caused by Marangoni flow (with its strength characterized by the Péclet number $Pe$). The buoyancy effects have their origin in (i) the density difference between the droplet and the ambient liquid, which is characterized by the Galileo number $Ga$; and (ii) the density difference between the diffusing product (i.e. filled micelles) and the ambient liquid, which can be quantified by a solutal Rayleigh number $Ra$. We analyse how the attracting and repulsing behaviour of neighbouring droplets depends on the control parameters $Pe$, $Ga$ and $Ra$. We find that while the Marangoni effect leads to the well-known repulsion between the interacting droplets, the buoyancy effect of the reaction product leads to buoyancy-driven attraction. At sufficiently large $Ra$, even collisions between the droplets can take place. Our study on the effect of $Ga$ further shows that with increasing $Ga$, the collision becomes delayed. Moreover, we derive that the attracting velocity of the droplets, which is characterized by a Reynolds number $Re_d$, is proportional to $Ra^{1/4}/( \ell /R)$, where $\ell /R$ is the distance between the neighbouring droplets normalized by the droplet radius. Finally, we numerically obtain the repulsive velocity of the droplets, characterized by a Reynolds number $Re_{rep}$, which is proportional to $PeRa^{-0.38}$. The balance of attractive and repulsive effect leads to $Pe\sim Ra^{0.63}$, which agrees well with the transition curve between the regimes with and without collision.

We investigate numerically the propulsion characteristics of an oscillating foil undergoing coupled heave and pitch motion in a linearly density-stratified flow. A parameter space defined by the internal Froude number ($1 \le Fr \le 10$) and the maximum angle of attack ($5^\circ \le {\alpha _0} \le 30^\circ$) is considered in our study. The results demonstrate a significant enhancement in both thrust production and propulsive efficiency due to the stratification influence. Notably, the highest efficiency exceeding $80\,\%$ is achieved under moderate stratification conditions, surpassing the performance observed in a homogeneous fluid. We attribute this optimum performance to the proper match between the stratification effect and foil kinematics, which gives rise to intense vortex interactions and sufficient wave–mean flow interactions in the near wake of the oscillating foil. Consequently, the energy is transferred towards wake structures to form a high-intensity momentum jet in close proximity to the foil's trailing edge, indicating efficient propulsion. Furthermore, we find that the stratifications within the moderate-to-strong transitional regime display a reduced dependence of propulsive efficiency on the maximum angle of attack, primarily due to the delaying and alleviating effects on dynamic-stall events. Such a mechanism enables the oscillating foil to maintain a satisfactory performance by sufficiently high angles of attack without the penalty of stall events. Based on our findings, we propose that animals or artificial vehicles utilising oscillatory propulsion can benefit from the presence of density stratification in the surrounding fluid.

In this experimental study, the impact of symmetric local blowing on suppressing the vortex-induced noise of a circular cylinder was investigated. A highly instrumented cylinder with pressure taps and a series of blowing chambers was used to inject air along the span (seven times the cylinder diameter) at circumferential angles $\theta _{b}={\pm }41^{\circ }$, ${\pm }90^{\circ }$ and ${\pm }131^{\circ }$ corresponding to the boundary layer, shear layers on the cylinder and separated shear layers, respectively. The investigation aimed to understand the noise reduction mechanism of local blowing by conducting near-field pressure and far-field noise measurements in synchronisation with flow field velocity measurements. Near-field pressure was measured around the circumference of the cylinder using a remote-sensing technique and planar particle image velocimetry was implemented to measure the velocity of the wake flow field at a diameter-based Reynolds number of $Re=7\times 10^{4}$. The results revealed that the interaction of the rolling up separated shear layers, under the influence of high-momentum fluid travelling from the free stream to the wake, induced significant vertical flow movement in the vortex-formation region. This movement led to strong alternating surface pressure fluctuations at the cylinder's shoulders, contributing to the scattering of noise. It was demonstrated that local blowing delayed vortex shedding for all cases, except at $\theta _{b}={\pm }90^{\circ }$, which elongated the shear layers and pushed the high-momentum transfer area farther downstream. The application of local blowing at $\theta _{b}={\pm }41^{\circ }$ was particularly effective in increasing the vortex formation size due to reduced entrainment of fluid-bearing vorticity.