Numerical simulations in two space dimensions are used to examine the dynamics, transport and equilibrium behaviours of a neutrally buoyant circular object immersed in an active suspension within a larger circular container. The continuum model of Gao et al. (Phys. Rev. Fluids, vol. 2, issue 9, 2017, 093302) represents the suspension of non-interacting, immotile, extensor-type microscopic agents that have a direction and strength, and align in response to strain rate. Such a suspension is well known to be unstable above an activity strength threshold, which depends upon the length scale of the confinement. Introducing the object leads to additional phenomenology. It can confine fluid between it and the container wall, which suppresses local suspension activity. However, its motion also correlates strain rates near its surface, which induce a correspondingly correlated active-stress response. Depending on the suspension activity strength, these mechanisms lead to either an attraction toward or a repulsion away from the container wall. In addition, a persistent propagating behaviour is found for modest activity strength, which provides a mechanism for long-range transport. When activity is so weak that the mobility of the object is essential to support suspension instability and sustain flow, all flow terminates when its mobility is diminished as it nears the container wall. If activity strength is scheduled in time, then these mechanisms could be used to perform relatively complex tasks with simple active agents.

A focused laser can cause local optical breakdown of a gas, which leads to rapid deposition of energy into a high-temperature plasma kernel that expands and induces a complex flow. For some conditions, hot gas is rapidly ejected along the laser axis up to distances several times the kernel size, with a particularly curious feature: relatively small changes in, for example, initial pressure can cause the direction of this ejection to reverse. Detailed axisymmetric simulations of a model energy kernel in an inert gas provide a hydrodynamic description of this phenomenon, reproducing key observations in corresponding experiments, including the vortex-ring-like features that constitute the ejection. These simulations are analysed to show how changes in the early-time kernel can lead to ejection or its reversal via alteration in the relative strength and position of the vorticity produced. A corresponding semi-infinite geometry is used to isolate two mechanisms: vorticity production by the generated shock and by baroclinic torque at the kernel boundary. Dependence on the initial kernel asymmetry is quantified, as it ultimately determines whether the vorticity, upon its subsequent evolution, develops into the ring-like structure that ejects. Even simple elongation of the energy kernel alone can reverse the direction.

Jet noise prediction is notoriously challenging because only subtle features of the flow turbulence radiate sound. The article by Brès et al. (J. Fluid Mech., vol. 851, 2018, pp. 83–124) shows that a well-constructed modelling procedure for the nozzle turbulence can provide unprecedented sub-dB prediction accuracy with modest-scale large-eddy simulations, as confirmed by detailed comparison with turbulence and sound-field measurements. This both illuminates the essential mechanisms of the flow and facilitates prediction for engineering design.

Observations in experiments and simulations show that the kinematic behaviour of an elastic capsule, suspended and rotating in shear flow, depends upon the flow strength, the capsule membrane material properties and its at-rest shape. We develop a linear stability description of the periodically rotating base state of this coupled system, as represented by a boundary integral flow formulation with spherical harmonic basis functions describing the elastic capsule geometry. This yields Floquet multipliers that classify the stability of the capsule motion for elastic capillary numbers $Ca$ ranging from $Ca=0.01$ to 5. Viscous dissipation rapidly damps most perturbations. However, for all cases, a single component grows or decays slowly, depending upon $Ca$, over many periods of the rotation. The transitions in this stability behaviour correspond to the different classes of rotating motion observed in previous studies.

Jets with Mach numbers $M\gtrsim 1.5$ are well known to emit an intense, fricative, so-called crackle sound, having steep compressions interspersed with weaker expansions that together yield a positive pressure skewness $S_{k}>0$. Its shock-like features are obvious hallmarks of nonlinearity, although a full explanation of the skewness is lacking, and wave steepening alone is understood to be insufficient to describe its genesis. Direct numerical simulations of high-speed free-shear flows for Mach numbers $M=0.9$, $1.5$, $2.5$ and $3.5$ in the Reynolds number range $60\leqslant Re_{\unicode[STIX]{x1D6FF}_{m}}\leqslant 4200$ are used to examine the mechanisms leading to such pressure signals, especially the pressure skewness. For $M=2.5$ and $3.5$, the pressure immediately adjacent the turbulence already has the large $S_{k}\gtrsim 0.4$ associated with jet crackle. It also has a surprisingly complex three-dimensional structure, with locally high pressures at compression-wave intersections. This structure is transient, and it simplifies as radiating waves subsequently merge through nonlinear mechanisms to form the relatively distinct and approximately two-dimensional Mach-like waves deduced from laboratory visualizations. A transport equation for $S_{k}$ is analysed to quantify factors affecting its development. The viscous dissipation that decreases $S_{k}$ is balanced by a particular nonlinear flux, which is (of course) absent in linear acoustic propagation and confirmed to be independent of the simulated Reynolds numbers. Together these effects maintain an approximately constant $S_{k}$ in the near acoustic field.

The selection and placement of actuators and sensors to control compressible viscous flows is addressed by developing a novel methodology based upon the eigensystem structural sensitivity of the linearized evolution operator appropriate for linear feedback control. Forward and adjoint global modes are used to construct a space of possible perturbations to the linearized operator, which yields a small optimization problem for selecting the parameters that best achieve the control objective, including where they should be placed. The method is demonstrated by informing actuation to suppress amplification of the instabilities in boundary layer separation in a high-subsonic diffuser. Complete stabilization is observed in the separated shear layer for short downstream distances at modest Reynolds number. Higher Reynolds numbers and longer distances are expected to be more challenging to stabilize; here the control informed by the procedure still substantively suppresses amplification of instabilities. It is also demonstrated that more complex actuator–sensor selections may not yield superior controllers.

We consider sound source mechanisms involving the acoustic and instability modes of dual-stream isothermal supersonic jets with the inner nozzle buried within an outer shroud-like nozzle. A particular focus is scattering into radiating sound waves at the shroud lip. For such jets, several families of acoustically coupled instability waves exist, beyond the regular vortical Kelvin–Helmholtz mode, with different shapes and propagation characteristics, which can therefore affect the character of the radiated sound. In our model, the coaxial shear layers are vortex sheets while the incident acoustic disturbances are the propagating shroud modes. The Wiener–Hopf method is used to compute their scattering at the sharp shroud edge to obtain the far-field radiation. The resulting far-field directivity quantifies the acoustic efficiency of different mechanisms, which is particularly important in the upstream direction, where the results show that the scattered sound is more intense than that radiated directly by the shear-layer modes.

One of the principal challenges in the prediction and design of low-noise nozzles is accounting for the near-nozzle turbulent mixing layers at the high Reynolds numbers of engineering conditions. Even large-eddy simulation is a challenge because the locally largest scales are so small relative to the nozzle diameter. Model-scale experiments likewise typically have relatively thick near-nozzle shear layers, which potentially hampers their applicability to high-Reynolds-number design. To quantify the sensitivity of the far-field sound to nozzle turbulent-shear-layer conditions, a family of diameter $D$ nozzles is studied in which the exit turbulent boundary layer momentum thickness is varied from $0.0042D$ up to $0.021D$ for otherwise identical flow conditions. Measurements include particle image velocimetry (PIV) to within $0.04D$ of the exit plane and far-field acoustic spectra. The influence of the initial turbulent-shear-layer thickness is pronounced, though it is less significant than the well-known sensitivity of the far-field sound to laminar versus turbulent shear-layer exit conditions. For thicker shear layers, the nominally missing region, where the corresponding thinner shear layer would develop, leads to the noise difference. The nozzle-exit momentum thickness successfully scales the high-frequency radiated sound for nozzles of different sizes and exhaust conditions. Yet, despite this success, the detailed turbulence statistics show distinct signatures of the different nozzle boundary layers from the different nozzles. Still, the different nozzle shear-layer thicknesses and shapes have a similar downstream development, which is consistent with a linear stability analysis of the measured velocity profiles.

Efforts to reduce the noise from turbulent jets at fixed flow conditions, with aircraft noise as the principal technological motivation, have generally involved some degree of parametric empiricism often based upon a series of trial-and-error testing. As a result, it is unclear if the modest reductions found, in rare cases that do not greatly affect the flow field or incur prohibitive losses, are near the limit of what can be accomplished or if there are undiscovered opportunities for more substantive reductions with better designs or active control. We assess this using an adjoint-based optimization procedure in conjunction with an experimentally validated large-eddy simulation of a Mach 1.3 turbulent jet. The adjoint solution provides a definitive direction in which to adjust a model control actuation in order to reduce noise, providing guidance that seems lacking by any other current means. It is found that three conjugate-gradient iterations in the control space provide ∼3.5 dB of reduction, comparable to other reductions found empirically. The control seems to work by disrupting the coherence of acoustically efficient axisymmetric flow structures. The control and noise-reduction mechanisms are informative, but also suggest that any significantly quieter state would not be a simple perturbation from the uncontrolled jet. Additional iterations might reduce noise more significantly, but there might be only modest opportunities to reduce the sound from simple round turbulent jets without radical changes or relatively sophisticated controls. Though it is difficult to prove any behaviour in a global space of actuations, there does not seem to be a direct route based upon a local sensitivity gradient to substantially quieting a jet, even with an unrealistically flexible actuation. More complex jets or other noisy flows may be more amenable to control, in which case the adjoint-based optimization procedure demonstrated here could provide invaluable engineering guidance.

We propose a generalization of proper orthogonal decomposition (POD) for optimal flow resolution of linearly related observables. This Galerkin expansion, termed ‘observable inferred decomposition’ (OID), addresses a need in aerodynamic and aeroacoustic applications by identifying the modes contributing most to these observables. Thus, OID constitutes a building block for physical understanding, least-biased conditional sampling, state estimation and control design. From a continuum of OID versions, two variants are tailored for purposes of observer and control design, respectively. Firstly, the most probable flow state consistent with the observable is constructed by a ‘least-residual’ variant. This version constitutes a simple, easily generalizable reconstruction of the most probable hydrodynamic state to preprocess efficient observer design. Secondly, the ‘least-energetic’ variant identifies modes with the largest gain for the observable. This version is a building block for Lyapunov control design. The efficient dimension reduction of OID as compared to POD is demonstrated for several shear flows. In particular, three aerodynamic and aeroacoustic goal functionals are studied: (i) lift and drag fluctuation of a two-dimensional cylinder wake flow; (ii) aeroacoustic density fluctuations measured by a sensor array and emitted from a two-dimensional compressible mixing layer; and (iii) aeroacoustic pressure monitored by a sensor array and emitted from a three-dimensional compressible jet. The most ‘drag-related’, ‘lift-related’ and ‘loud’ structures are distilled and interpreted in terms of known physical processes.

In the smallest capillaries, or in tubes with diameter D ≲ 8 μm, flowing red blood cells are well known to organize into single-file trains, with each cell deformed into an approximately static bullet-like shape. Detailed high-fidelity simulations are used to investigate flow in a model blood vessel with diameter slightly larger than this: D = 11.3 μm. In this case, the cells deviate from this single-file arrangement, deforming continuously and significantly. At the higher shear rates simulated (mean velocity divided by diameter U/D ≳ 50s−1), the effective tube viscosity is shear-rate insensitive with μeff/μplasma = 1.21. This matches well with the value μeff/μplasma = 1.19 predicted for the same 30% cell volume fraction by an established empirical fit of high-shear-rate in vitro experimental data. At lower shear rates, the effective viscosity increases, reaching μeff/μplasma ≈ 1.65 at the lowest shear rate simulated (U/D ≈ 3.7s−1). Because of the continuous deformations, the cell-interior viscosity is potentially important for vessels of this size. However, most results for simulations with cell interior viscosity five times that of the plasma (λ = 5), which is thought to be close to physiological conditions, closely match results for cases with λ = 1. The cell-free layer that forms along the vessel walls thickens from 0.3 μm for U/D = 3.7s−1 up to 1.2 μm for U/D ≳ 100s−1, in reasonable agreement with reported experimental results. The thickness of this cell-free layer is the key factor governing the overall flow resistance, and this in turn is shown to follow a trend expected for lubrication lift forces for shear rates between U/D ≈ 8s−1 and U/D ≈ 100s−1. Only in this same range are the cells near the vessel wall on average inclined relative to the wall, as might be expected for a lubrication mechanism. Metrics are developed to quantify the kinematics of this dense cellular flow in terms of the well-known tank-treading and tumbling behaviours often observed for isolated cells in shear flows. One notable effect of λ = 5 versus λ = 1 is that it suppresses treading rotation rates by a factor of about 2. The treading rate is found to scale with the velocity difference across the cell-rich core and is thus significantly slower than the overall shear rate in the flow, which is presumably why the flow is otherwise insensitive to λ. The cells in all cases also have a similarly slow mean tumbling motion, which is insensitive to cell-interior viscosity and decreases monotonically with increasing U/D.

As the vortical disturbances of a shrouded jet pass the sharp edge of the shroud exit some of the energy is scattered into acoustic waves. Scattering into upstream-propagating acoustic modes is a potential mechanism for closing the resonance loop in the ‘howling’ resonances that have been observed in various shrouded jet configurations over the years. A model is developed for this interaction at the shroud exit. The jet is represented as a uniform flow separated by a cylindrical vortex sheet from a concentric co-flow within the cylindrical shroud. A second vortex sheet separates the co-flow from an ambient flow outside the shroud, downstream of its exit. The Wiener–Hopf technique is used to compute reflectivities at the shroud exit. For some conditions it appears that the reflection of finite-wavelength hydrodynamic vorticity modes on the vortex sheet defining the jet could be sufficient to reinforce the shroud acoustic modes to facilitate resonance. The analysis also gives the reflectivities for the shroud acoustic modes, which would also be important in establishing resonance conditions. Interestingly, it is also predicted that the shroud exit can be ‘transparent’ for ranges of Mach numbers, with no reflection into any upstream-propagating acoustic mode. This is phenomenologically consistent with observations that indicate a peculiar sensitivity of resonances of this kind to, say, jet Mach number.

The adjoint of the perturbed and linearized compressible viscous flow equations is formulated in such a way that its solution can be used to optimize control actuation in order to reduce flow-generated sound. We apply it to a direct numerical simulation of a randomly excited two-dimensional mixing layer, with inflow vorticity-thickness Reynolds number 500 and free-stream Mach numbers 0.9 and 0.2. The control actuation is implemented as general source terms in the flow equations (body forces, mass sources, and internal energy sources) with compact support near the inflow boundary. The noise to be reduced is defined by a space-time integral of the mean-square pressure fluctuations on a line parallel to the mixing layer in the acoustic field of the low-speed stream. Both the adjoint and flow equations are solved numerically and without modelling approximations. The objective is to study the mechanics of the noise generation and its control. All controls reduce targeted noise with very little required input power, with the most effective (the internal energy control) reducing the noise intensity by 11 dB. Numerical tests confirm that the control is not by any simple acoustic cancellation mechanism but instead results from a genuine change of the flow as a source of sound. The comparison of otherwise identical flows with and without control applied shows little change of the flow's gross features: the evolution and pairings of the energetic structures, turbulence kinetic energy, spreading rate, and so on are superficially unchanged. However, decomposition of the flow into empirical eigenfunctions, as surrogates for Fourier modes in the non-periodic streamwise direction, shows that the turbulence structures advect downstream more uniformly. This change appears to be the key to reducing their acoustic efficiency, a perspective that is clarified by comparing the randomly excited mixing layer to a harmonically excited mixing layer, which is relatively quiet because it is highly ordered. Unfortunately, from the perspective of any practical implementation with actuators, the optimized control identified has a complex spatial and temporal structure, but it can be simplified. Two empirical eigenmodes were required to represent it sufficiently to reduce the targeted noise intensity by about 50%. Optimization of a simple single-degree-of-freedom control with an ad hoc spatial structure is less effective.

The mechanisms of sound generation in a Mach 0.9, Reynolds number 3600 turbulent jet are investigated by direct numerical simulation. Details of the numerical method are briefly outlined and results are validated against an experiment at the same flow conditions (Stromberg, McLaughlin & Troutt 1980). Lighthill's theory is used to define a nominal acoustic source in the jet, and a numerical solution of Lighthill's equation is compared to the simulation to verify the computational procedures. The acoustic source is Fourier transformed in the axial coordinate and time and then filtered in order to identify and separate components capable of radiating to the far field. This procedure indicates that the peak radiating component of the source is coincident with neither the peak of the full unfiltered source nor that of the turbulent kinetic energy. The phase velocities of significant components range from approximately 5% to 50% of the ambient sound speed which calls into question the commonly made assumption that the noise sources convect at a single velocity. Space–time correlations demonstrate that the sources are not acoustically compact in the streamwise direction and that the portion of the source that radiates at angles greater than 45° is stationary. Filtering non-radiating wavenumber components of the source at single frequencies reveals that a simple modulated wave forms for the source, as might be predicted by linear stability analysis. At small angles from the jet axis the noise from these modes is highly directional, better described by an exponential than a standard Doppler factor.

This work uses direct numerical simulations of time evolving annular mixing layers, which correspond to the early development of round jets, to study compressibility effects on turbulence in free shear flows. Nine cases were considered with convective Mach numbers ranging from Mc = 0.1 to 1.8 and turbulence Mach numbers reaching as high as Mt = 0.8.

Growth rates of the simulated mixing layers are suppressed with increasing Mach number as observed experimentally. Also in accord with experiments, the mean velocity difference across the layer is found to be inadequate for scaling most turbulence statistics. An alternative scaling based on the mean velocity difference across a typical large eddy, whose dimension is determined by two-point spatial correlations, is proposed and validated. Analysis of the budget of the streamwise component of Reynolds stress shows how the new scaling is linked to the observed growth rate suppression. Dilatational contributions to the budget of turbulent kinetic energy are found to increase rapidly with Mach number, but remain small even at Mc = 1.8 despite the fact that shocklets are found at high Mach numbers. Flow visualizations show that at low Mach numbers the mixing region is dominated by large azimuthally correlated rollers whereas at high Mach numbers the flow is dominated by small streamwise oriented structures. An acoustic timescale limitation for supersonically deforming eddies is found to be consistent with the observations and scalings and is offered as a possible explanation for the decrease in transverse lengthscale.

The mixing of fuel and oxidizer in a mixing layer between high-speed streams is important in many applications, especially air-breathing propulsion systems. The details of this process in a turbulent annular mixing layer are studied with direct numerical simulation. Convective Mach numbers of the simulations range from Mc = 0.1 to Mc = 1.8. Visualizations of the scalar field show that at low Mach numbers large intrusions of nearly pure ambient or core fluid span the mixing region, whereas at higher Mach numbers these intrusions are suppressed. Increasing the Mach number is found to change the mixture fraction probability density function from non-marching to marching and the mixing efficiency from 0.5 at Mc = 0.1 to 0.67 at Mc = 1.5. Scalar concentration fluctuations and the axial velocity fluctuations become highly correlated as the Mach number increases and a suppressed role of pressure in the axial momentum equation is found to be responsible for this. Anisotropy of scalar flux increases with Mc, and is explained via the suppression of transverse turbulence lengthscale.