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Tandem cylinder flow comprises several different flow regimes. Within the reattachment regime, the development of the gap shear layers is of utmost importance to the flow, but has received little attention so far. Through direct numerical simulations at $Re = 10^{4}$ , for a gap ratio of 3.0, we have discovered that the shear layers are significantly altered with respect to a single cylinder. These differences include early onset of separation, crossflow stabilising, delayed transition to turbulence and little meandering of the transition region. Vortex pairing in the gap shear layers is reported for the first time. The interaction between the recirculating gap flow and the shear layers was investigated. Asymmetrical, large-scale gap vortices influence the position of transition to turbulence through direct contact and through secondary flows. The occurrence of transition in the gap shear layers has consequences for both the reattachment mechanism and the development of the downstream cylinder wake. The reattachment points are unsteady with large amplitude fluctuations on a fine time scale. Reattachment is seen to be a combination of impingement and modification of the upstream shear layers, which causes a double shear layer in the downstream cylinder near-wake. Buffeting by and interaction with the gap shear layers likely cause transition to turbulence in the downstream cylinder boundary layer. This leads to significant changes in the wake topology, compared with a single-cylinder wake.

The structure of free-surface flows in a straight compound channel was investigated in a laboratory flume, consisting of a central smooth-bed main channel (MC) and two adjacent rough-surface floodplains (FPs). The experiments covered both uniform and non-uniform flow conditions, with the latter generated by imposing an imbalance in the discharge distribution between MC and FPs at the flume entrance. The non-uniform cases involved transverse currents directed from MC to FPs and vice versa . The focus of the study was on assessing the effects of transverse currents on: (i) transverse shear layer and horizontal Kelvin–Helmholtz-type coherent structures (KHCSs) forming at the interfaces between MC and FPs; (ii) helical secondary currents (SCs) developing across the channel due to topography-induced flow heterogeneity; and (iii) turbulent large- and very-large-scale motions (VLSMs). Transverse currents can entirely displace the shear layer over FP or in MC, but they do not alter the KHCSs to the same degree, resulting in a mismatch between shear layer extent and KHCS length scales. KHCSs emerge once dimensionless velocity shear exceeds a critical value above which KHCS length scales increase with the shear. Three well-established SC cells, which are induced by turbulence anisotropy, are observed in uniform flow and non-uniform flow with transverse currents towards FP. They are replaced by a single cell in the presence of a transverse mean flow towards MC. The spectral signatures of VLSMs are visible at the upstream section of the flume but they quickly disappear along the flow, being suppressed by simultaneous development of KHCSs and SCs.

A study of the physics of separating and reattaching flows around bodies with sharp edges is reported. Data from direct numerical simulations of the flow around a rectangular cylinder with aspect ratio 5 at different Reynolds numbers are used. The flow is decomposed into multiple interacting flow phenomena such as the laminar boundary layer in the front face, the separated shear layer, the flow impingement at reattachment, the reverse boundary layer within the recirculating bubble and the near- and far-wake flow. A detailed analysis of the physics of these phenomena is provided, including the slow modulation induced by large-scale instabilities related with vortex shedding. The entrainment phenomena acting along the separated shear layer and their unbalance between its inner and outer sides are recognised as fundamental mechanisms determining the tendency of the flow to reattach and the overall fluxes of momentum and heat. The behaviour of entrainment is found to be strictly related with the shear-layer velocity difference that in turn is determined by the behaviour of the reverse boundary layer and by its strength in counteract adverse pressure gradients. The physical understanding of the compound role played by these and all the other mechanisms composing the flow, poses the basis for the formulation of theoretical frameworks able to unify all these interacting phenomena. Finally, the present work provides access to high-fidelity flow statistics of relevance for benchmark activities on bluff bodies with sharp edges.

The perturbation response of small-scale shear layers in turbulence is investigated with direct numerical simulations (DNS). The analysis of shear layers in isotropic turbulence suggests that the typical layer thickness is about four times the Kolmogorov scale $\\eta$. Response for sinusoidal perturbations is investigated for an isolated shear layer, which models a mean flow around the shear layers in turbulence. The vortex formation in the shear layer is optimally promoted by the perturbation whose wavelength divided by the layer thickness is about 7. These results indicate that the small-scale shear instability in turbulence is efficiently promoted by velocity fluctuations with a wavelength of about $30\\eta$. Furthermore, DNS are carried out for decaying turbulence initialised by the artificially modified velocity field of isotropic turbulence. The vortex formation from shear layers is accelerated under the influence of external perturbations with the efficient wavelength to promote the instability. When velocity fluctuations with this wavelength are eliminated by a band-cut filter, the shear layers tend to persist for a long time without producing vortices. These behaviours affect the number of vortices in turbulence, which increases and decreases when velocity perturbations with the unstable wavelength of the instability are artificially amplified and damped, respectively. The increase in the number of vortices results in the enhancement of kinetic energy dissipation, enstrophy production and strain self-amplification. These results indicate that the perturbation response of shear layers is important in the small-scale dynamics of turbulence as well as the modulation of small-scale turbulent motions by external disturbance.

The influence of the nozzle-exit boundary-layer profile on high-subsonic jets is investigated by performing compressible large-eddy simulations (LES) for three isothermal jets at a Mach number of 0.9 and a diameter-based Reynolds number of $5\\times 10^{4}$ , and by conducting linear stability analyses from the mean-flow fields. At the exit section of a pipe nozzle, the jets exhibit boundary layers of momentum thickness of approximately 2.8 % of the nozzle radius and a peak value of turbulence intensity of 6 %. The boundary-layer shape factors, however, vary and are equal to 2.29, 1.96 and 1.71. The LES flow and sound fields differ significantly between the first jet with a laminar mean exit velocity profile and the two others with transitional profiles. They are close to each other in these two cases, suggesting that similar results would also be obtained for a jet with a turbulent profile. For the two jets with non-laminar profiles, the instability waves in the near-nozzle region emerge at higher frequencies, the mixing layers spread more slowly and contain weaker low-frequency velocity fluctuations and the noise levels in the acoustic field are lower by 2–3 dB compared to the laminar case. These trends can be explained by the linear stability analyses. For the laminar boundary-layer profile, the initial shear-layer instability waves are most strongly amplified at a momentum-thickness-based Strouhal number $St_{\\unicode[STIX]{x1D703}}=0.018$ , which is very similar to the value obtained downstream in the mixing-layer velocity profiles. For the transitional profiles, on the contrary, they predominantly grow at higher Strouhal numbers, around $St_{\\unicode[STIX]{x1D703}}=0.026$ and 0.032, respectively. As a consequence, the instability waves rapidly vanish during the boundary-layer/shear-layer transition in the latter cases, but continue to grow over a large distance from the nozzle in the former case, leading to persistent large-scale coherent structures in the mixing layers for the jet with a laminar exit velocity profile.

Studies of Kelvin–Helmholtz (KH) instability have typically modelled the initial flow as an isolated shear layer. In geophysical cases, however, the instability often occurs near boundaries and may therefore be influenced by boundary proximity effects. Ensembles of direct numerical simulations are conducted to understand the effect of boundary proximity on the evolution of the instability and the resulting turbulence. Ensemble averages are used to reduce sensitivity to small variations in initial conditions. Both the transition to turbulence and the resulting turbulent mixing are modified when the shear layer is near a boundary: the time scales for the onset of instability and turbulence are longer, and the height of the KH billow is reduced. Subharmonic instability is suppressed by the boundary because phase lock is prevented due to the diverging phase speeds of the KH and subharmonic modes. In addition, the disruptive influence of three-dimensional secondary instabilities on pairing is more profound as the two events coincide more closely. When the shear layer is far from the boundary, the shear-aligned convective instability is dominant; however, secondary central-core instability takes over when the shear layer is close to the boundary, providing an alternate route for the transition to turbulence. Both the efficiency of the resulting mixing and the turbulent diffusivity are dramatically reduced by boundary proximity effects.

The present paper uses the detailed flow data produced by direct numerical simulation (DNS) of a three-dimensional, spatially developing plane free shear layer to assess several commonly used turbulence models in compressible flows. The free shear layer is generated by two parallel streams separated by a splitter plate, with a naturally developing inflow condition. The DNS is conducted using a high-order discontinuous spectral element method (DSEM) for various convective Mach numbers. The DNS results are employed to provide insights into turbulence modelling. The analyses show that with the knowledge of the Reynolds velocity fluctuations and averages, the considered strong Reynolds analogy models can accurately predict temperature fluctuations and Favre velocity averages, while the extended strong Reynolds analogy models can correctly estimate the Favre velocity fluctuations and the Favre shear stress. The pressure–dilatation correlation and dilatational dissipation models overestimate the corresponding DNS results, especially with high compressibility. The pressure–strain correlation models perform excellently for most pressure–strain correlation components, while the compressibility modification model gives poor predictions. The results of an a priori test for subgrid-scale (SGS) models are also reported. The scale similarity and gradient models, which are non-eddy viscosity models, can accurately reproduce SGS stresses in terms of structure and magnitude. The dynamic Smagorinsky model, an eddy viscosity model but based on the scale similarity concept, shows acceptable correlation coefficients between the DNS and modelled SGS stresses. Finally, the Smagorinsky model, a purely dissipative model, yields low correlation coefficients and unacceptable accumulated errors.

We perform a computational study on the effects of localized arc filament plasma actuator based control on the flow field and acoustics of a supersonic 2:1 aspect ratio rectangular jet. Post validation of the baseline jet, effects of control in the context of noise reduction are studied at experimentally guided forcing parameters, including frequencies $St=0.3, 1.0$ and $St=2.0$ with duty cycles of $20\\,\\%$ and $50\\,\\%$. In general, high-frequency forcing reduces noise in the downstream direction, with the actuator signature appearing mostly in the sideline direction. Here $St=1$, ${\\rm DC}=50\\,\\%$ yields an optimum balance between peak noise reduction (of ${\\sim }1.5$ dB) and actuator tones, with control being most effective on the major axis plane that bisects the shorter edges of the nozzle. Shear layer response to the most effective forcing includes generation of successive arrays of mutually interacting staggered lambda vortices, which eventually energize streamwise vortical elements. Causal mechanisms of noise mitigation are further elucidated as follows. First, the control reduces the energy within the supersonic phase speed regime of peak radiating frequencies by redistributing a part of it into a high-frequency band. Second, it enhances azimuthal percolation of energy into the first and second helical modes at frequencies where noise reduction is seen, thus weakening the radiatively efficient axisymmetric mode. Finally, sound-producing intermittent events in the jet are significantly reduced, thereby minimizing the high-intensity acoustic emissions. This small-perturbation-based control strategy results in only minor variations in the mean flow properties. However, reduced production and enhanced convection attenuate turbulent kinetic energy within the spreading shear layer in the controlled jet.

Shallow mixing layers (SMLs) behind a splitter plate were studied in a tilted rectangular open-channel flume for a range of flow depths and the initial shear parameter ${\\lambda = (U_{2}-U_{1})/(U_{2}+U_{1})}$, where $U_1$ and $U_2$ are streamwise velocities of the slow and fast streams, respectively. The main focus of the study is on (i) key parameters controlling the time-averaged SMLs; and (ii) the emergence and spatial development of Kelvin–Helmholtz coherent structures (KHCSs) and large- and very-large-scale motions (LSMs and VLSMs) and associated turbulence statistics. The time-averaged flow features of the SMLs are mostly controlled by bed-friction length scale $h/c_f$ and shear parameter $\\lambda$ as well as by time-averaged spanwise velocities $V$ and momentum fluxes $UV$, where $h$ and $c_f$ are flow depth and bed-friction coefficient, respectively. For all studied cases, the effect of shear layer turbulence on the SML growth is comparatively weak, as the fluxes $UV$ dominate over the spanwise turbulent fluxes. Initially, the emergence of KHCSs and their length scales largely depend on $\\lambda$. The KHCSs cannot form if ${\\lambda \\lessapprox 0.3}$ and the turbulence behind the splitter plate resembles that of free mixing layers. Further downstream, shear layer turbulence becomes dependent on the bed-friction number $S = c_f \\delta _v /(4 h \\lambda )$, where $\\delta _v$ is vorticity thickness. When $S \\gtrapprox 0.01$, the KHCSs are longitudinally stretched and the scaled transverse turbulent fluxes decrease with increasing $S$. The presence and streamwise development of LSMs/VLSMs away from the splitter plate depends on the $\\lambda$-value, particularly when $\\lambda > 0.3$, resembling LSMs/VLSMs in conventional open-channel flows when $\\lambda$ is small.

Unsteadiness in separated shock–boundary layer interactions have been previously analysed in order to propose a scenario of entrainment–discharge as the origin of unsteadiness. It was assumed that the fluid in the separated zone is entrained by the free shear layer formed at its edge, and that this layer follows the properties of the canonical mixing layer. This last point is addressed by reanalysing the velocity measurements in an oblique shock reflection at a nominal Mach number of 2.3 and for two cases of flow deviation ( $8^{\\circ }$ and $9.5^{\\circ }$ ). The rate of spatial growth of this layer is evaluated from the spatial growth of the turbulent stress profiles. Moreover, the entrainment velocity at the edge of the layer is determined from the mean velocity profiles. It is shown that the values of turbulent shear stress, spreading rate and entrainment velocity are consistent, and that they follow the classical laws for turbulent transport in compressible shear layers. Moreover, the measurements suggest that the vertical normal stress is sensitive to compressibility, so that the anisotropy of turbulence is affected by high Mach numbers. Dimensional considerations proposed by Brown & Roshko (J. Fluid Mech., vol. 64, 1974, 775–781) are reformulated to explain this observed trend.