## Publications

74 results found

Buxton O, Chen J, 2023, The relative eﬃciencies of the entrainment of mass, momentum, and kinetic energy from a turbulent background, *Journal of Fluid Mechanics*, ISSN: 0022-1120

Caros L, Buxton O, Vincent P, 2023, Optimization of triangular airfoils for Martian helicopters using direct numerical simulations, *AIAA Journal: devoted to aerospace research and development*, Vol: 61, Pages: 4935-4945, ISSN: 0001-1452

Mars has a lower atmospheric density than Earth, and the speed of sound is lower due to its atmospheric composition and lower surface temperature. Consequently, Martian rotor blades operate in a low-Reynolds-number compressible regime that is atypical for terrestrial helicopters. Nonconventional airfoils with sharp edges and flat surfaces have shown improved performance under such conditions, and second-order-accurate Reynolds-averaged Navier–Stokes (RANS) and unsteady RANS (URANS) solvers have been combined with genetic algorithms to optimize them. However, flow over such airfoils is characterized by unsteady roll-up of coherent vortices that subsequently break down/transition. Accordingly, RANS/URANS solvers have limited predictive capability, especially at higher angles of attack where the aforementioned physics are more acute. To overcome this limitation, we undertake optimization using high-order direct numerical simulations (DNSs). Specifically, a triangular airfoil is optimized using DNSs. Multi-objective optimization is performed to maximize lift and minimize drag, yielding a Pareto front. Various quantities, including lift spectra and pressure distributions, are analyzed for airfoils on the Pareto front to elucidate flow physics that yield optimal performance. The optimized airfoils that form the Pareto front achieve up to a 48% increase in lift or a 28% reduction in drag compared to a reference triangular airfoil studied in the Mars Wind Tunnel at Tohoku University. The work constitutes the first use of DNSs for aerodynamic shape optimization.

Chen J, Buxton O, 2023, Spatial evolution of the turbulent/turbulent interface geometry in a cylinder wake, *Journal of Fluid Mechanics*, Vol: 969, Pages: 1-23, ISSN: 0022-1120

This study aims to examine the spatial evolution of the geometrical features of the turbulent/turbulent interface (TTI) in a cylinder wake. The wake is exposed to various turbulent backgrounds in which the turbulence intensity and the integral length scale are varied independently, and comparisons to a turbulent/non-turbulent interface (TNTI) are drawn. The turbulent wake was marked with a high Schmidt number ( Sc ) scalar, and a planar laser induced fluorescence experiment was carried out to capture the interface between the wake and the ambient flow from x/d=5 to 40, where x is the streamwise coordinate from the centre of the cylinder, and d is the cylinder's diameter. It is found that the TTI generally spreads faster towards the ambient flow than the TNTI. A transition region of the interfaces’ spreading is found at x/d≈15 , after which the interfaces propagate at a slower rate than previously (upstream), and the mean interface positions of both the TNTI and TTI scale with the local wake half-width. The locations of both the TNTI and TTI have non-Gaussian probability density functions (PDFs) in the near wake because of the influence of the large-scale coherent motions present within the flow. Further downstream, after the large-scale coherent motions have dissipated, the TNTI position PDF does become Gaussian. For the first time, we explore the spatial variation of the ‘roughness’ of the TTI, quantified via the fractal dimension, from near field to far field. The length scale in the background flow has a profound effect on the TTI fractal dimension in the near wake, whilst the turbulence intensity becomes important only for the fractal dimension farther downstream.

Cicolin M, Bearman P, Assi G,
et al., 2023, Bistability in the wake of a circular cylinder with passive control using two leeward rods, *Journal of Fluids and Structures*, Vol: 120, Pages: 1-14, ISSN: 0889-9746

This paper presents an experimental investigation on the flow around a circular cylindercontrolled by a pair of rods placed close to the separated shear layers from the leewardface of the cylinder. Past research of Cicolin et al. (2021) has shown that one control rod,placed at specific positions, induces a late flow separation on the main cylinder’s surfacein a typical occurrence of the Coandă effect. As a result the control rod reduced the meandrag acting on the cylinder but also produced a net mean lift force. We now presentan extension of the aforementioned study to consideration of a pair of symmetricallyarranged control rods, aimed at eliminating the mean lift force whilst maintaining a dragreduction. The experiments were carried out at a Reynolds number Re = 20, 000 basedon the diameter of the main cylinder D, with the diameter of the control rods being tentimes smaller than that of the cylinder. The centre-to-centre distances between eachcontrol rod and the cylinder was 0.7D, and the angular position of the rods varied fromθ = 120◦to 125◦, where θ is measured from the front stagnation point. Time-resolvedPIV velocity fields and hydrodynamic forces were measured for the different setups.Results show that the mean flow is asymmetric in spite of the symmetry of the geometricmodel and position of the rods. The pair of control rods induces a bistable flow, inducedby the imbalance of two colliding jets in the near wake. The dynamics were found tobe random, with the average switching time between stable states depending on theposition of the rods. The mean drag force was reduced by up to 15%, and the mean liftforce was reduced by 80% compared to the cases with a single control rod. It was alsoobserved that the control rod can induce two different types of flow separation fromthe main cylinder, one in which the flow separates from the main cylinder only onceand one in which a small separation bubble forms in proximity to the control rod beforereatta

Buxton O, Lingkan E, 2023, An assessment of the scalings for the streamwise evolution of turbulent quantities in wakes produced by porous objects, *Renewable Energy*, Vol: 209, Pages: 1-9, ISSN: 0960-1481

Experimental results are presented for the evolution of three turbulent quantities in the wake of a porous object, analogous to a wind-turbine wake. These are the mean velocity deficit, the turbulence intensity, and the characteristic wake width. It is noted that characteristic wake widths can be defined both in terms of the mean velocity deficit profile and the profile of turbulence intensity. Both definitions of wake width are observed to grow linearly, although not at the same rate, with that defined by turbulence intensity growing more rapidly than velocity deficit. The streamwise scaling of both wake width, and velocity deficit is found to conform to a non-equilibrium dissipation scaling in which the dissipation rate within the wake is out of equilibrium with the inter-scale energy flux within the mean cascade of turbulent kinetic energy. The cumulative effect of turbulence intensity produced by Ν upstream porous objects is also considered. It is shown that when the object spacing is sufficiently large that the wake-added turbulence decays substantially only consideration of the most immediately upstream wake is important. Contrastingly, when the spacing between adjacent objects is small then summing the contributions from all upstream wakes in the array is necessary.

Kankanwadi K, Buxton O, 2023, Influence of freestream turbulence on the near-field growth of a turbulent cylinder wake: Turbulent entrainment and wake meandering, *Physical Review Fluids*, Vol: 8, Pages: 28-28, ISSN: 2469-990X

he effect of freestream turbulence on the spreading of the near wake of a circular cylinder (<11 cylinder diameters from the rear face of the cylinder) is investigated through particle image velocimetry data. Different “flavors” of freestream turbulence, in which the turbulence intensity and integral length scale are independently varied, are subjected to the cylinder. The time-averaged spreading of the near wake is decoupled into the growth through entrainment of background fluid and the envelope of the spatial extent of the instantaneous wake due to wake “meandering,” induced by the presence of large-scale vortical coherent structures, i.e., the von Kármán vortex street. Unlike for the far-field of a turbulent wake, examined by Kankanwadi and Buxton [J. Fluid Mech. 905, A35 (2020)], it is shown that freestream turbulence enhances the entrainment rate into the wake in comparison to a nonturbulent background. Furthermore, both the turbulence intensity and the integral length scale of the background turbulence are important in this regard, further contrasting to the far wake where only the turbulence intensity is important. Additionally, wake meandering is enhanced by the presence of background turbulence, and here the integral length scale is the dominant parameter. Combining these findings yields the oft-reported result that background turbulence enhances the time-averaged near-wake growth rate. The influence of wake meandering is isolated by conducting similar experiments in which a splitter plate is mounted to the rear face of the cylinder, thereby eliminating the von Kármán vortex street. These results show that when large-scale vortices are not present within the turbulent wake then freestream turbulence actually suppresses the entrainment rate, relative to a nonturbulent background, in results that mirror Kankanwadi and Buxton [J. Fluid Mech. 905, A35 (2020)]. We therefore postulate that freestream turbule

Kankanwadi K, Buxton O, 2022, On the physical nature of the turbulent/turbulent interface, *Journal of Fluid Mechanics*, Vol: 942, ISSN: 0022-1120

The existence of a turbulent/turbulent interface (TTI) has recently been verified in the far wake of a circular cylinder exposed to free-stream turbulence (Kankanwadi & Buxton, J. Fluid Mech., vol. 905, 2020, p. A35). This study aims to understand the physics within the TTI. The wake boundary, approximately 40 diameters downstream of a circular cylinder subjected to grid-generated turbulence, was investigated through simultaneous cinematographic, stereoscopic particle image velocimetry and planar laser induced fluorescence experiments. With no grid placed upstream of the cylinder, the behaviour of the resultant interface, our closest approximation to a turbulent/non-turbulent interface, exactly matched what is observed in existing literature. When background turbulence is present, viscous action is no longer the only method by which enstrophy is transported to the background fluid, unlike for turbulent/non-turbulent interfaces. The presence of rotational fluid on both sides of the TTI allows the vorticity stretching term of the enstrophy budget equation to be the dominant actor in this process. The role of viscosity within a TTI is greatly diminished as the vorticity stretching term takes over responsibilities for enstrophy production. The turbulent strain rate normal to the TTI was found to be enhanced in the interfacial region. Decomposing the vorticity stretching term into components aligned with the three principal strain-rate directions, it was found that the term most aligned with the interface-normal direction contributed to the largest share of enstrophy production. This indicates that better ‘organised’ vorticity on the wake side of the interface yields the enstrophy amplification leading to the previously discovered enstrophy jump across the TTI by Kankanwadi & Buxton (J. Fluid Mech., vol. 905, 2020, p. A35).

Biswas N, Marangon Cicolin M, Buxton O, 2022, Energy exchanges in the flow past a cylinder with a leeward control rod, *Journal of Fluid Mechanics*, Vol: 941, ISSN: 0022-1120

We study the energy exchanges between coherent structures and the mean flow in the wake of a cylinder in the presence of a leeward control rod using Particle Image Velocimetry (PIV) data at Reynolds number (Re) 20 × 103. The shedding of the control rod depends on the oncoming shear layer and hence the downstream interaction of the main cylinder’s and control rod’s wake strongly depends on the control rod’s setting angle (θ). In this work we study this interaction between the shedding modes from the cylinder and control rod at different θ. New secondary coherent motions with distinct characteristic frequencies appear in the flow field aside from the frequencies associated with the sheddings of the control rod, the main cylinder and its harmonics. A multiscale triple decomposition method is applied to extract the coherent modes associated with each of these frequencies and the dynamics of the modes are studied using kinetic energy budget equations. The primary shedding modes of the control rod and main cylinder, as well as the harmonics of the main cylinder’s shedding modes, are found to be primarily energised by the mean flow at this Re, while the secondary modes are almost entirely energised by the primary modes, similar to the findings of Baj and Buxton (2017) for a different multiscale flow configuration. The remarkable similarity in the energy exchange process forming the secondary coherent modes, observed in two different studies, hints at a possible universality in the formation process of these secondary structures in amultiscale flow.

Caros Roca L, Buxton O, Shigeta T,
et al., 2022, Direct numerical simulation of flow over a triangular airfoil under martian atmospheric conditions, *AIAA Journal: devoted to aerospace research and development*, Vol: 60, Pages: 3961-3972, ISSN: 0001-1452

Martian conditions present various challenges when designing rotorcraft. Specifically, the thin atmosphere and low sound speed require Martian rotor blades to operate in a low Reynolds number (1,000 to 10,000) compressible regime, for which conventional airfoils are not designed. Here we utilize PyFR to undertake high-order Direct Numerical Simulations (DNS) of flow over a triangular airfoil at a Mach number of 0.15 and Reynolds number of 3,000. Initially, span-wise periodic DNS are undertaken. Extending the domain-span-to-chord ratio from 0.3 to 0.6 leads to better agreement with wind tunnel data at higher angles of attack, when the flow is separated. This is because smaller domain spans artificially suppress three-dimensional breakdown of coherent structures above the suction surface of the airfoil. Subsequently, full-span DNS in a virtual wind tunnel are undertaken, including all wind tunnel walls. These capture blockage and wall boundary layer effects, leading to better agreement with wind tunnel data for all angles of attack compared to span-wise periodic DNS. The results are important in terms of understanding discrepancies between previous span-wise periodic DNS and wind tunnel data. They also demonstrate the utility of high-order DNS as a tool for accurately resolving flow over triangular airfoils under Martian conditions.

Caros L, Blank J, Buxton O, et al., 2022, Comparing Strategies for DNS Based Optimization of Airfoils for Martian Rotorcraft

Martian atmospheric conditions present various challenges when designing rotorcraft. Specifically, the thin atmosphere and lower speed of sound compared to Earth requires Martian rotor blades to operate in a low-Reynolds-number (≈ 103 to 104) compressible regime, for which conventional airfoils have not been designed. Airfoils with sharp leading edges and flat surfaces have been shown to perform better than conventional airfoils under these conditions. In order to find the optimal airfoils, several studies have explored optimizing non-conventional airfoils with evolutionary techniques. These algorithms usually require many cost function evaluations, and hence, they typically employ Reynolds-Averaged Navier Stokes (RANS) solvers because of their low computational cost. However, RANS solvers have limited predictive capability when the flow becomes unsteady and separated at moderate angles of attack. Enabled by recent advances in solver technology and GPU hardware, we are able to overcome this limitation by undertaking optimization using high-fidelity Direct Numerical Simulations (DNS), able to capture the flow physics, via the compressible flow solver in PyFR (www.pyfr.org). In order to reduce the cost of the optimization, given that it involves expensive cost function evaluations, the current study compares two multi-objective optimization strategies using pymoo (www.pymoo.org) as the optimizer. Specifically, the study compares the cost of Genetic Algorithm (GA) optimization with two-dimensional DNS used to evaluate the cost function, with the cost of surrogate-assisted GA optimization where the model is generated and updated with two-dimensional DNS. Results help elucidate efficient strategies for high-fidelity two- and three-dimensional DNS optimization for aerospace applications, specifically rotorcraft airfoils in Martian atmospheric conditions.

Buxton ORH, Kankanwadi KS, 2022, ON THE NATURE OF THE TURBULENT/TURBULENT INTERFACE

We perform combined PIV and PLIF experiments to investigate the nature of the interface between two adjacent streams of fully-developed turbulence; the turbulent/turbulent interface (TTI). For the first time we definitively prove the existence of the TTI, something that had been previously questioned for cases where the intensity of the turbulence in both streams is comparable. We then examine the dominant physics in the TTI. Unlike for turbulent/non-turbulent interfaces viscosity does not play an important role and the inertial vortex stretching term is dominant in producing the discontinuity in enstrophy that is characteristic of the TTI. We show that the particular organisation of the small-scale turbulent strain rate and vorticity in the TTI is responsible for driving this vortex stretching and show that freestream turbulence diminishes the rate of entrainment into the primary flow relative to a non-turbulent freestream.

Biswas N, Buxton ORH, 2022, ENERGY EXCHANGES IN THE WAKE OF A MULTISCALE SYSTEM

In this study, we investigate the energy exchanges between coherent structures in the wake of a model multiscale geometry consisting of a cylinder and a leeward control rod using Particle Image Velocimetry (PIV) data. For certain control rod positions, we observe new secondary coherent motions with distinct characteristic frequencies in the flow field aside from the frequencies associated with the sheddings of the control rod, the main cylinder and its harmonics. We employ the multiscale triple-decomposition technique proposed by Baj et al. (2015), to extract the spatio-temporal structure of the coherent modes associated with each of the frequencies and also study the energy exchanges to/from the coherent motions using the triple decomposed kinetic energy budget equations derived by Baj & Buxton (2017). We find almost the same sequence of energy transfers between the primary and secondary modes as reported by Baj & Buxton (2017) for a different multiscale geometry, hinting at a possible universality of these structures in any multiscale flow. We perform a series of PIV experiments to look for similar energy exchanges in the wake of a representative rotor which is also a multiscale system due to the presence of multiple length (and time) scales simultaneously introduced in the flow from the nacelle, tower and rotor blades. If the universality in energy exchanges is upheld even for a multiscale system with rotation, it would prove to be a powerful tool for the near wake-modeling of wind turbines.

Rodriguez-López E, Alonso-Rodríguez D, Rueda-Guglieri F, et al., 2022, Advances on the telescope structure conceptual design of the European Solar Telescope, ISSN: 0277-786X

The works described in the current paper correspond to some exploratory advances that were performed by ESTEYCO in close collaboration with IAC on the European Solar Telescope (EST) main structure beyond the conceptual design activities conducted up to 2011, which were taken as the starting point. The works to develop this advanced conceptual design of the EST telescope structure were conducted within a collaboration agreement between ESTEYCO and IAC. The paper presents a brief summary of the main design modification activities that are proposed for the telescope structure, the different methodologies involved including structural, mechanical and aerodynamic performance, the rationale behind the different design change proposals and, finally, a quantitative assessment of the effectiveness of the different design alternatives and modifications in order to provide a consistent methodology to judge the improvement between the different alternatives. In order to have a clear and consistent comparison, it was decided to generate independent Finite Element models from the reference conceptual design. After this assessment, the elevation structure is proposed to undergo several modifications (mainly oriented at the suppression of the rocking-chair like wheels) to improve its structural and mechanical performance. The load transfer path is also changed by modifying the azimuthal radial guides radii in order to have a more direct transfer from the elevation structure to the ground. Some of these modifications are conducted by means of a newly developed in-house program that enables automatizing a series of constrained numerical optimization to improve the structural response.

Kankanwadi K, Buxton O, 2021, Turbulent/Turbulent Entrainment, Progress in Turbulence IX Proceedings of the iTi Conference in Turbulence 2021, Editors: Orlu, Talamelli, Peinke, Oberlack, Publisher: Springer, Pages: 13-19, ISBN: 9783030807153

This volume collects the edited and reviewed contribution presented in the 9th iTi Conference that took place virtually, covering fundamental and applied aspects in turbulence.

Cicolin M, Buxton O, Assi G,
et al., 2021, The role of separation on the forces acting on a circular cylinder with a control rod, *Journal of Fluid Mechanics*, Vol: 915, Pages: 1-29, ISSN: 0022-1120

The development of the flow around a circular cylinder with a smaller diameter control rod in close proximity is the subject of this paper. It has long been known that this is an effective way to attenuate regular vortex shedding leading to reductions in its adverse effects on bluff body flow. The aim of this study is to improve understanding of the ways the control rod affects the near wake flow including how it influences the positions of boundary layer separation. Experiments were carried out in a water channel to measure lift and drag forces and PIV was employed to obtain detailed information on flow structure. The values of important properties were fixed as follows: Reynolds number20,000; ratio of cylinder and control rod diameters 10:1; centre to centre distance between main cylinder and control rod 0.7D, where Dis main cylinder diameter. The adjustable parameter was the angular position of the rod,θ, which was varied between 90◦and 180◦from the front stagnation line. Lift and drag forces were measured separately for the main cylinder and the control rod. A new method for identifying flow states is introduced using PIV to interrogate the instantaneous flow velocity in the gap between the main cylinder and the control rod. Similarly to previous studies, three stable flow states were observed together with a bi-stable state. The bi-stable state is very sensitive to the control rod angle with a small change of±1◦being sufficient to change the flow state.

Lasagna D, Buxton O, Fiscaletti D, 2021, Near-field coherent structures in circular and fractal orifice jets, *Physical Review Fluids*, Vol: 6, Pages: 1-27, ISSN: 2469-990X

To investigate the influence of the orifice geometry on near-field coherent structures in a jet, Fourier proper orthogonal decomposition (Fourier-POD) is applied. Velocity and vorticity snapshots obtained from tomographic particle image velocimetry at the downstream distance of two equivalent orifice diameters are analyzed. Jets issuing from a circular orifice and from a fractal orifice are examined, where the fractal geometry is obtained from a repeating fractal pattern applied to a base square shape. While in the round jet energy is mostly contained at wave number m=0, associated to the characteristic Kelvin-Helmholtz vortex rings, in the fractal jet modal structures at the fundamental azimuthal wave number m=4 capture the largest amount of energy. In addition, energy is scattered across a wider range of wave numbers than in the round jet. The radial Fourier-POD profiles, however, are nearly insensitive to the orifice geometry, and collapse to a universal distribution when scaled with a characteristic radial length. A similar collapse was recently observed in POD analysis of turbulent structures in pipe flow. However, unlike in pipe flow, the azimuthal-to-radial aspect ratio of the Fourier-POD structures is not constant and varies greatly with the wave number. The second part of the paper focuses on the relationship between streamwise vorticity and streamwise velocity, to characterize the role of the orifice geometry on the lift-up mechanism recently found to be active in turbulent jets [P. Nogueira, A. Cavalieri, P. Jordan, and V. Jaunet, Large-scale streaky structures in turbulent jets, J. Fluid Mech. 873, 211 (2019)]. The averaging of the streamwise vorticity conditioned on intense positive fluctuations of streamwise velocity reveals a pair of vorticity structures of opposite sign flanking the conditioning point, inducing a radial flow towards the jet periphery. This pair of structures is observed in both jets, even if the azimuthal extent of this pattern is 30

Fiscaletti D, Buxton O, Attili A, 2021, Internal layers in turbulent free-shear flows, *Physical Review Fluids*, Vol: 6, Pages: 1-33, ISSN: 2469-990X

The characteristics of the internal layers of intense shear are examined in a mixing layer and in a jet, in the range of Reynolds numbers 134<Reλ<275. Conditionally averaged profiles of streamwise velocity conditioned on the identified internal layers present strong velocity jumps, which account for approximately 10% of the characteristic large-scale velocity of the flow. The thickness ⟨δw⟩ of the internal layers from the combined analysis of both the mixing layer and the jet scales with ⟨δw⟩/λ∼Re−1/2λ, which suggests a scaling with the Kolmogorov length scale (η), analogous to recent observations on the turbulent/nonturbulent interface (TNTI). The thickness of the internal shear layers within the mixing layer is found to be between 9η and 11η. The concentration of a passive scalar across the internal layers is also examined, at the Schmidt number Sc=1.4. The scalar concentration does not show any jumps across the internal layers, which is an important difference between the internal layers and the TNTI. This can be explained from the analysis of the internal layers of intense scalar gradient, where the flow topology node/saddle/saddle dominates, associated with strain, whereas the internal layers of intense shear are characterized by a prevalence of focus/stretching. A topological content analogous to that obtained in layers of intense scalar gradient is found in proximity to the TNTI, at the boundary between the viscous superlayer and the turbulent sublayer. These observations evidence that the TNTI and the internal layers of intense scalar gradient are similar in several respects.

Kankanwadi K, Buxton O, 2020, Turbulent entrainment into a cylinder wake from a turbulent background, *Journal of Fluid Mechanics*, Vol: 905, ISSN: 0022-1120

The effects of background turbulence on the entrainment process, as well as the nature of the interfacial region between two bodies of turbulent fluid, was examined through an investigation of the far-wake of a circular cylinder that is subjected to free-stream turbulence. Simultaneous particle image velocimetry and planar laser induced fluorescence measurements were conducted 40 diameters downstream of the cylinder. Despite the availability of turbulent, rotational fluid in the background, the outer interface between the wake and the ambient fluid exhibits an enstrophy jump akin to the classical result of a turbulent/non-turbulent interface. This jump at the wake boundary persists even when the intensity of the background turbulence is greater than the turbulence intensity of the wake itself. Analysis on the structure of the wake boundary reveals that an increase in background turbulence intensity, results in an increased interfacial surface area relative to the non-turbulent case. However, instead of the intuitive result of increased entrainment as a result of increased surface area, a reduction in mean entrainment mass flux is observed with increased background turbulence intensity. Through the analysis of the flux probability density functions, the reduction in mean entrainment can be attributed to a tip in balance of extreme entrainment and detrainment events to the detrainment side in the presence of background turbulence. Lastly, a scale by scale analysis of entrainmentbehaviour revealed that free-stream turbulence affects entrainment behaviour across all length scales and isn’t just limited to the energy containing scales.

Es-Sahli O, Sescu A, Afsar M,
et al., 2020, Investigation of wakes generated by fractal plates in the compressible flow regime using large-eddy simulations, *Physics of Fluids*, Vol: 32, ISSN: 1070-6631

We investigate flows interacting with square and fractal shape multi-scale structures in the compressible regime for Mach numbers under subsonic and supersonic upstream conditions using large-eddy simulations. We also aim at identifying similarities and differences that these interactions have with the corresponding interactions in the canonical incompressible flow problem. To account for the geometrical complexity associated with the fractal structures, we apply an immersed boundary method to model the no-slip boundary condition at the solid surfaces, with adequate mesh resolution in the vicinity of the small fractal features. We validate the numerical results through extensive comparisons with experimental wind tunnel measurements at a low Mach number. Similar to the incompressible flow case results, we find a breakup of the flow structures by the fractal plate and an increase in turbulent mixing in the downstream direction. As the Mach number increases, we observe noticeable wake meandering and higher spread rate of the wake in the lateral direction perpendicular to the streamwise–spanwise plane. Although not significant, we quantify the difference between the square and the fractal plates using two-point velocity correlations across the Mach number range. The wakes generated by the fractal plate in the compressible regime showed lower turbulent kinetic energy and energy spectra levels compared to those of the square case. Moreover, results in terms of the near-field pressure spectra seem to indicate that the fractal plate has the potential to reduce the aerodynamic noise.

Breda M, Buxton ORH, 2019, Behaviour of small-scale turbulence in the turbulent/non-turbulent interface region of developing turbulent jets, *Journal of Fluid Mechanics*, Vol: 879, Pages: 187-216, ISSN: 0022-1120

Tomographic particle image velocimetry experiments were conducted in the near and intermediate fields of two different types of jet, one fitted with a circular orifice and another fitted with a repeating-fractal-pattern orifice. Breda & Buxton (J. Vis., vol. 21 (4), 2018, pp. 525–532; Phys. Fluids, vol. 30, 2018, 035109) showed that this fractal geometry suppressed the large-scale coherent structures present in the near field and affected the rate of entrainment of background fluid into, and subsequent development of, the fractal jet, relative to the round jet. In light of these findings we now examine the modification of the turbulent/non-turbulent interface (TNTI) and spatial evolution of the small-scale behaviour of these different jets, which are both important factors behind determining the entrainment rate. This evolution is examined in both the streamwise direction and within the TNTI itself where the fluid adapts from a non-turbulent state, initially through the direct action of viscosity and then through nonlinear inertial processes, to the state of the turbulence within the bulk of the flow over a short distance. We show that the suppression of the coherent structures in the fractal jet leads to a less contorted interface, with large-scale excursions of the inner TNTI (that between the jet’s azimuthal shear layer and the potential core) being suppressed. Further downstream, the behaviour of the TNTI is shown to be comparable for both jets. The velocity gradients develop into a canonical state with streamwise distance, manifested as the development of the classical tear-drop shaped contours of the statistical distribution of the velocity-gradient-tensor invariants and . The velocity gradients also develop spatially through the TNTI from the irrotational boundary to the bulk flow; in particular, there is a strong small-scale anisotropy in this region. This strong inhomogeneity of the velocity gradients in the TNTI region has strong conseque

Beaumard P, Buxton O, Keylock CJ, 2019, The importance of non-normal contributions to velocity gradient tensor dynamics for spatially developing, inhomogeneous, turbulent flows, *Journal of Turbulence*, Vol: 20, Pages: 577-598, ISSN: 1468-5248

We investigate the properties of the velocity gradient tensor for spatially evolving turbulent flows (a near-wake, two axisymmetric jets and a planar mixing layer). Emphasis is placed on the study of the normal and non-normal parts of the tensor. Non-normality plays a greater role in the dynamics than is observed for HIT and does so for all spatial locations examined. This implies a greater role for the deviatoric part of the pressure Hessian. Results for the wake flow, where we isolate the coherent part of the dynamics using a modal decomposition, clarify how these competing effects operate. Previous studies have shown the shape of the Q–R diagram (formed by the second and third invariants of the characteristic equation for the tensor) is approximately universal at small-scales for different flows. The non-normal dynamics are neglected in the Q–R approach but appear to differ significantly between flows.

Buxton O, Baj P, 2019, Inter-scale energy transfer in a multi-scale flow, Progress in Turbulence VIII Proceedings of the iTi Conference on Turbulence 2018, Editors: Orlu, Talamelli, Peinke, Oberlack, Publisher: Springer, Pages: 3-8, ISBN: 9783030221959

This volume collects the edited and reviewed contributions presented in the 8th iTi Conference on Turbulence, held in Bertinoro, Italy, in September 2018.

Buxton O, Baj P, 2019, Scalar dispersion in a multi-scale generated turbulent flow, Eleventh International Symposium on Turbulence and Shear Flow Phenomena

Combined PLIF and PIV experiments were performedin the near-wake region of a multi-scale array of three dif-ferent length scales. We document, and measured terms ofthe multi-scale triple-decomposed energy budget and showthe importance of non-linear interactions between the pri-mary shedding structures in multi-scale generated turbu-lence. We subsequently observe a cascade of scalar burstingevents, in which the scalar is transported a large distance inthe transverse direction over a short period of time. Thesebursts unfolded spatially, such that they were observed be-tween the small and medium wakes and the medium andlarge wakes. These bursts were also observed in the wakeof a single-scale array of objects of comparable blockageto the multi-sale array, but there was no cascade of burstsidentified and they all occurred in the same spatial location.Combined, these findings verify the space-scale unfolding(SSU) mechanism originally postulated in Laizet & Vassil-icos (2012). By performing the multi-scale triple decompo-sition of Bajet al.(2015) we show that the dominant modein the scalar transport is that associated to the fundamentalshedding of the larger of the two intersecting wakes. Wethus conclude that the SSU mechanism is subtly differentto that originally postulated by Laizet & Vassilicos (2012).Those authors originally attributed the SSU mechanism tothe coherence of the overall, Reynolds-decomposed veloc-ity fluctuationu′. Here we show that the dominant effect isin fact the coherent part of the fluctuating velocity concor-dant with the fundamental shedding frequency of the largerof the two interacting wakes. Downstream of the wake in-tersection point this particular coherent scalar flux compo-nent is the major contributor to the overall scalar flux.

Kankanwadi K, Buxton O, 2019, Turbulent entrainment from a turbulent background, Eleventh International Symposium on Turbulence and Shear Flow Phenomena

Simultaneous particle image velocimetry (PIV) andplanar laser induced fluorescence (PLIF) measurementswere conducted in order to investigate the effects of back-ground turbulence on the entrainment process as well ason the behaviour of the wake interface. Previous studieshave highlighted the importance of length scale as well asturbulence intensity in the background flow. This paperreports on a parametric study examining entrainment intothe wake of a circular cylinder by independently varyingbackground turbulence parameters through the use of tur-bulence generating grids. Despite the availability of tur-bulent rotational fluid on both sides of the interface, theclassical turbulent/non-turbulent interface result of an en-strophy jump is reproduced, even in the harshest incomingfree-stream turbulence conditions. Examining the tortuos-ity, reveals that both length scale and turbulence intensityin the background turbulence act to increase the interfacesurface area. Furthermore, the entrainment process is foundto be greatly sensitive to the turbulence intensity of the sub-jected free-stream turbulence. However, despite an increasein surface area, a net reduction in mean entrainment massflux is observed with increased intensity in the backgroundturbulence. Examining the mass flux PDFs, reveals that thisbehaviour is a result of substantial, yet infrequent detrain-ment events.

Baj P, Buxton ORH, 2019, Passive scalar dispersion in the near wake of a multi-scale array of rectangular cylinders, *Journal of Fluid Mechanics*, Vol: 864, Pages: 181-220, ISSN: 0022-1120

The near wakes of flows past single- and multi-scale arrays of bars are studied by means of planar laser induced fluorescence (PLIF) and particle image velocimetry (PIV). The aim of this research is to better understand dispersion of passive scalar downstream of the multi-scale turbulence generator. In particular, the focus is on plausible manifestations of the space-scale unfolding (SSU) mechanism, which is often considered in the literature as the reason for the enhancement of the turbulent scalar flux in flows past fractal grids (i.e. specific multi-scale turbulence generators). The analysis of qualitative and quantitative PLIF results, as well as the simultaneously acquired PIV results, confirms the appearance of a physical scenario resembling the SSU mechanism. Unlike the anticipation of the literature, however, this scenario applies to some extent also to the flow past the single-scale obstacle. Application of a triple decomposition technique (which splits the acquired fields into their means, a number of coherent fluctuations and their stochastic parts) and a conditional-averaging technique reveals that the SSU mechanism is active in the vicinity of an intersection point between two adjacent wakes and is driven almost exclusively by coherent fluctuations associated with the larger of the intersecting wakes. This suggests that the SSU mechanism is related to the coherent fluctuations embedded in the flow rather than to the fine-scale turbulence and its underlying integral length scale, as proposed in previous works.

Buxton O, Breda M, Dhall K, 2019, Importance of small-scale anisotropy in the turbulent/nonturbulent interface region of turbulent free shear flows, *Physical Review Fluids*, Vol: 4, Pages: 034603:1-034603:17, ISSN: 2469-990X

There has been much debate over the past decade or so over the scaling of the thickness of the turbulent/nonturbulent (TNT) interface for turbulent shear flows. It is generally considered to consist of the outer viscous superlayer, in which viscous processes are significant, and an inner turbulent sublayer which is dominated by inertial processes. Various authors have stated that the interface thickness scales with the Taylor length scale λ while others state that it scales with the Kolmogorov length scale η [Buxton et al., Phys. Fluids 23, 061704 (2011)]. Frequently, only self-similar turbulent flows are considered in which a single value of either λ or η is sufficient to scale various phenomena, including the thickness of the TNT interface. In this paper we show that for flows which are not self-similar the local Kolmogorov length scale increases quite significantly as one moves closer to the boundary between the turbulent and nonturbulent fluid. We find that the variation of this local Kolmogorov length scale with normal distance from the TNT boundary may be collapsed by the local Kolmogorov length scale computed from the TNT boundary itself. We subsequently show that this variation in local Kolmogorov length scale occurs concurrently with an increase in the small-scale anisotropy in the TNT interface. This anisotropy peaks at the boundary between the viscous superlayer and the turbulent sublayer, suggesting that these two sublayers are in fact quite distinct from one another. We show that these results hold for a number of different TNT interfaces from various flows and with the bulk turbulence being in a variety of states of development. The local viscous scaling that we obtain, along with an increase in anisotropy primarily driven by an increased magnitude of velocity gradients in the TNT-boundary-normal direction, leads us to draw an analogy between TNT interfaces and the wall in wall-bounded turbulence.

Buxton ORH, Baj P, 2019, Scalar dispersion in a multi-scale generated turbulent flow

Combined PLIF and PIV experiments were performed in the near-wake region of a multi-scale array of three different length scales. We document, and measured terms of the multi-scale triple-decomposed energy budget and show the importance of non-linear interactions between the primary shedding structures in multi-scale generated turbulence. We subsequently observe a cascade of scalar bursting events, in which the scalar is transported a large distance in the transverse direction over a short period of time. These bursts unfolded spatially, such that they were observed between the small and medium wakes and the medium and large wakes. These bursts were also observed in the wake of a single-scale array of objects of comparable blockage to the multi-sale array, but there was no cascade of bursts identified and they all occurred in the same spatial location. Combined, these findings verify the space-scale unfolding (SSU) mechanism originally postulated in Laizet & Vassilicos (2012). By performing the multi-scale triple decomposition of Baj et al. (2015) we show that the dominant mode in the scalar transport is that associated to the fundamental shedding of the larger of the two intersecting wakes. We thus conclude that the SSU mechanism is subtly different to that originally postulated by Laizet & Vassilicos (2012). Those authors originally attributed the SSU mechanism to the coherence of the overall, Reynolds-decomposed velocity fluctuation u′. Here we show that the dominant effect is in fact the coherent part of the fluctuating velocity concordant with the fundamental shedding frequency of the larger of the two interacting wakes. Downstream of the wake intersection point this particular coherent scalar flux component is the major contributor to the overall scalar flux.

Kankanwadi KS, Buxton ORH, 2019, Turbulent entrainment from a turbulent background

Simultaneous particle image velocimetry (PIV) and planar laser induced fluorescence (PLIF) measurements were conducted in order to investigate the effects of background turbulence on the entrainment process as well as on the behaviour of the wake interface. Previous studies have highlighted the importance of length scale as well as turbulence intensity in the background flow. This paper reports on a parametric study examining entrainment into the wake of a circular cylinder by independently varying background turbulence parameters through the use of turbulence generating grids. Despite the availability of turbulent rotational fluid on both sides of the interface, the classical turbulent/non-turbulent interface result of an enstrophy jump is reproduced, even in the harshest incoming free-stream turbulence conditions. Examining the tortuosity, reveals that both length scale and turbulence intensity in the background turbulence act to increase the interface surface area. Furthermore, the entrainment process is found to be greatly sensitive to the turbulence intensity of the subjected free-stream turbulence. However, despite an increase in surface area, a net reduction in mean entrainment mass flux is observed with increased intensity in the background turbulence. Examining the mass flux PDFs, reveals that this behaviour is a result of substantial, yet infrequent detrainment events.

Breda M, Buxton O, 2018, Effects of multiscale geometry on the large-scale coherent structures of an axisymmetric turbulent jet, *Journal of Visualization*, Vol: 21, Pages: 525-532, ISSN: 1343-8875

In this study, the effect of multiscale geometry on the near-field structure of an axisymmetric turbulent jet is examined at a global Reynolds number of ReG=10,000. With the aid of tomographic particle image velocimetry, the suppression of the coherent structures due to this fractal geometry is analysed and the changes to the near-field vorticity are evaluated. This particular geometry leads to the breakup of the azimuthal vortex rings present for round jets and to the formation of radial and streamwise opposite-signed patches of vorticity. The latter are found to be responsible for the axis switching of the jet, a phenomenon observed for some noncircular jets where the major axis shrinks and the minor one expands in the near field, effectively switching the two axes of the jet. This was the first time, to the knowledge of the authors, that axis switching has been observed for a jet where the coherent structures have been suppressed. Following the significant differences found in the near field, the far field is examined. There, the integral lengthscale of the large scale eddies Lur and the size of the jet evaluated in terms of the jet half-width r1/2 are found to evolve in a similar fashion, whilst the ratio Lur/r1/2 is found to be higher for the fractal jet than for the round jet, for which the near-field structures have not been suppressed.

Breda M, Buxton O, 2018, Influence of coherent structures on the evolution of an axisymmetric turbulent jet, *Physics of Fluids*, Vol: 30, Pages: 035109-1-035109-24, ISSN: 1070-6631

The role of initial conditions in affecting the evolution toward self-similarity of an axisymmetric turbulent jet is examined. The jet’s near-field coherence was manipulated by non-circular exit geometries of identical open area, D2e, including a square and a fractal exit, for comparison with a classical round orifice jet. Hot-wire anemometry and 2D-planar particle image velocimetry experiments were performed between the exit and a location 26De downstream, where the Reynolds stress profiles are self-similar. This study shows that a fractal geometry significantly changes the near-field structure of the jet, breaking up the large-scale coherent structures, thereby affecting the entrainment rate of the background fluid into the jet stream. It is found that many of the jet’s turbulent characteristics scale with the number of eddy turnover times rather than simply the streamwise coordinate, with the entrainment rate (amongst others) found to be comparable across the different jets after approximately 3-4 eddies have been overturned. The study is concluded by investigating the jet’s evolution toward a self-similar state. No differences are found for the large-scale spreading rate of the jets in the weakly self-similar region, so defined as the region for which some, but not all of the terms of the mean turbulent kinetic energy equation are self-similar. However, the dissipation rate of the turbulent kinetic energy was found to vary more gradually in x than predicted according to the classical equilibrium theories of Kolmogorov. Instead, the dissipation was found to vary in a non-equilibrium fashion for all three jets tested.

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