The disturbance wave pattern produced from a harmonic point source in a compressible flat-plate boundary layer is computed using linear stability theory and the direct numerical integration approach. Receptivity coefficients are computed for a wide band of least-stable spanwise modes generated at the source, which are followed in the streamwise direction in order to study the wave-interference pattern. The effect of boundary-layer growth on the development of linear waves is determined by using the method of multiple scales. Results are presented for Mach numbers of 0, 2 and 7. It is found that disturbances spread in wedge-shaped regions behind the source and the wedge angle decreases with Mach number. The lateral spreading angle for the instability waves turns out to be quite close to the angle found experimentally for lateral contamination of turbulence. It is found that, owing to wave cancellation, the computed maximum disturbance amplitude is significantly lower than that obtained by following the most-amplified single normal mode.

The effect of gravity modulation on long-wavelength disturbances at the free surface of a surfactant-covered thin liquid layer is analysed. The surfactants are assumed to be insoluble so that variations in their concentration along the free surface produce Marangoni flows in the underlying liquid. Lubrication theory is applied to obtain nonlinear partial differential equations that describe the behaviour of the free surface height and surfactant concentration, and the stability of these equations to small-amplitude disturbances is examined by applying Floquet theory. It is found that long-wavelength disturbances are destabilized by gravity modulation when surfactants are present, whereas such disturbances are stable when surfactants are absent. Results from additional calculations indicate that the instability becomes more difficult to excite as the Marangoni forces, body forces, capillary forces and surfactant diffusivity increase, and becomes easier to excite as the van der Waals forces increase.

In this paper we revisit the Landau and Levich analysis of a coating flow in the case where the flow in the thin liquid film is supported by a Rayleigh surface acoustic wave (SAW), propagating in the solid substrate. Our theoretical analysis reveals that the geometry of the film evolves under the action of the propagating SAW in a manner that is similar to the evolution of films that are being deposited using the dip coating technique. We show that in a steady state the thin-film evolution equation reduces to a generalized Landau–Levich equation with the dragging velocity, imposed by the SAW, depending on the local film thickness. We demonstrate that the generalized Landau–Levich equation has a branch of stable steady state solutions and a branch of unstable solutions. The branches meet at a saddle-node bifurcation point corresponding to the threshold value of the SAW intensity. Below the threshold value no steady states were found and our numerical computations suggest a gradual thinning of the liquid film from its initial geometry.

This work aims to study the dynamics of and noise generated by large-scale structures in a Mach 0.9 turbulent jet of Reynolds number $6.2\times 10^{5}$ using plasma-based excitation of shear layer instabilities. The excitation frequency is varied to produce individual or periodic coherent ring vortices in the shear layer. First, two-point cross-correlations are used between the acoustic near field and far field in order to identify the dominant noise source region. The large-scale structure interactions are then investigated by stochastically estimating time-resolved velocity fields using time-resolved near-field pressure traces and non-time-resolved planar velocity snapshots (obtained by particle image velocimetry) by means of an artificial neural network. The estimated time-resolved velocity fields show multiple mergings of large-scale structures in the shear layer, and indicate that disintegration of coherent ring vortices is the dominant aeroacoustic source mechanism for the jet studied here. However, the merging of vortices in the initial shear layer is also identified as a non-trivial noise source mechanism.

In this paper, we analyse by numerical simulations the nonlinear dynamics of the elliptic instability in the configurations of a single strained vortex and a system of two counter-rotating vortices. We show that although a weakly nonlinear regime associated with a limit cycle is possible, the nonlinear evolution far from the instability threshold is, in general, much more catastrophic for the vortex. In both configurations, we put forward some evidence of a universal nonlinear transition involving shear layer formation and vortex loop ejection, leading to a strong alteration and attenuation of the vortex, and a rapid growth of the vortex core size.

We present a generalisation of efficient numerical frameworks for modelling fluid–filament interactions via the discretisation of a recently developed, non-local integral equation formulation to incorporate regularised Stokeslets with half-space boundary conditions, as motivated by the importance of confining geometries in many applications. We proceed to utilise this framework to examine the drag on slender inextensible filaments moving near a boundary, firstly with a relatively simple example, evaluating the accuracy of resistive force theories near boundaries using regularised Stokeslet segments. This highlights that resistive force theories do not accurately quantify filament dynamics in a range of circumstances, even with analytical corrections for the boundary. However, there is the notable and important exception of movement in a plane parallel to the boundary, where accuracy is maintained. In particular, this justifies the judicious use of resistive force theories in examining the mechanics of filaments and monoflagellate microswimmers with planar flagellar patterns moving parallel to boundaries. We proceed to apply the numerical framework developed here to consider how filament elastohydrodynamics can impact drag near a boundary, analysing in detail the complex responses of a passive cantilevered filament to an oscillatory flow. In particular, we document the emergence of an asymmetric periodic beating in passive filaments in particular parameter regimes, which are remarkably similar to the power and reverse strokes exhibited by motile $9+2$ cilia. Furthermore, these changes in the morphology of the filament beating, arising from the fluid–structure interactions, also induce a significant increase in the hydrodynamic drag of the filament.

Only a few fundamental studies on the dynamics and interactions of supersonic streamwise vortices have been conducted so far despite the recognized potential of these structures to enhance supersonic mixing. In an effort to shed light on this largely unexplored field, multiple experimental campaigns were conducted in a Mach 2.5 flow to probe the dynamics of turbulence decay in complex flows originating from selected modes of supersonic streamwise vortex interaction. The first part of the manuscript presents the detailed study of two vortex interaction scenarios: one selected to obtain merging of co-rotating vortices and the other to prevent vorticity amalgamation. In the second part, data from three additional vortex merging cases are used to substantiate the findings of the first part of the study and characterize the decay of turbulence. Stereoscopic particle image velocimetry was employed to probe the resulting flow fields at different downstream stations. It was found that these complex vortex interactions measurably affect both the morphology and the magnitude of the streamwise vorticity and turbulent kinetic energy as well as the associated decays. Particularly, while the turbulent kinetic energy across each vorticity patch undergoes an initial production before decreasing monotonically in both scenarios, its content in the coalesced structure is roughly double that of the isolated vortices. The manuscript also presents the analysis of the turbulence data from 27 supersonic vortical structures differing in shape, strength and modes of interaction, acquired within a range of vortex Reynolds numbers of almost one order of magnitude. Dimensional analysis was then used to correlate the spatial decay of turbulent kinetic energy with the vortex Reynolds number. For all the cases considered here, where the fluctuating Mach number was found to be subsonic, the form of the resulting law was similar to that reported in previous scholarly publications, despite the complexity of the vortex dynamics considered in this work.

Motivated by recent studies that have revealed the existence of trapped acoustic waves in subsonic jets (Towne et al., J. Fluid Mech., vol. 825, 2017, pp. 1113–1152), we undertake a more general exploration of the physics associated with acoustic modes in jets and wakes, using a double vortex-sheet model. These acoustic modes are associated with eigenvalues of the vortex-sheet dispersion relation; they are discrete modes, guided by the vortex sheet; they may be either propagative or evanescent; and under certain conditions they behave in the manner of acoustic-duct modes. By analysing these modes we show how jets and wakes may both behave as waveguides under certain conditions, emulating ducts with soft or hard walls, with the vortex-sheet impedance providing effective ‘wall’ conditions. We consider, in particular, the role that upstream-travelling acoustic modes play in the dispersion-relation saddle points that underpin the onset of absolute instability. The analysis illustrates how departure from duct-like behaviour is a necessary condition for absolute instability, and this provides a new perspective on the stabilising and destabilising effects of reverse flow, temperature ratio and compressibility; it also clarifies the differing symmetries of jet (symmetric) and wake (antisymmetric) instabilities. An energy balance, based on the vortex-sheet impedance, is used to determine stability conditions for the acoustic modes: these may become unstable in supersonic flow due to an energy influx through the shear layers. Finally, we construct the impulse response of flows with zero and finite shear-layer thickness. This allows us to show how the long-time wavepacket behaviour is indeed determined by interaction between Kelvin–Helmholtz and acoustic modes.

In laboratory experiments, horizontal translational motion of columnar vortices formed in rotating Rayleigh–Bénard convection was investigated. Two types of measurements, vertical velocity fields and horizontal temperature fields, were conducted with water as the test fluid. Using particle image velocimetry, the vertical velocity fields determined the parameter range at which the quasi-two-dimensional columnar vortices emerged. Locally, the duration characteristics of the columns, evaluated with their vertical coherence, indicate the minimum time scale of translational motion of the vortices in the horizontal plane. Vortex tracking of the horizontal temperature fields over long observation periods (${>}10^{3}~\text{s}$) was conducted using encapsulated thermochromic liquid crystal visualization. Two cylindrical vessels with different radii showed the emergence of the centrifugal effect in $O({>}10^{2}~\text{s})$ despite the small Froude number ($Fr<0.1$). Further, in the horizontal plane the columnar vortices behaved in a random-walk-like diffusive motion. The statistically calculated mean-squared displacements indicated anomalous diffusive motion of the columns; displacement increasing with time as $t^{\unicode[STIX]{x1D6FE}}$ with $\unicode[STIX]{x1D6FE}\neq 1$. We discuss the causes of this anomaly in both the instantaneous and long-term statistical data gathered from experimental observations over different time scales. The enclosure effect from the repulsion of up-welling and down-welling vortices ensures that vortices diffuse only little, resulting in a sub-diffusive (decelerated) motion $\unicode[STIX]{x1D6FE}<1$ in $O(10^{1}~\text{s})$. With this weak centrifugal contribution, the translational motion of the columns slowly accelerates in the radial direction and thereby yields a super-diffusive (accelerated) motion $\unicode[STIX]{x1D6FE}>1$ in $O(10^{2}~\text{s})$.

Probability distribution functions of fluctuation velocities (P(ux) and P(uy), where ux and uy are the fluctuation velocities in the x- and y-directions, respectively; the gravity is acting along the periodic x-direction and the flow is bounded by two walls parallel to the y-direction) and the density and the spatial velocity correlations are studied using event-driven simulations for an inelastic smooth hard disk system undergoing gravity-driven granular Poiseuille flow (GPF). It is shown that for GPF with smooth and/or perfectly rough walls the Maxwellian/Gaussian is the leading-order distribution over a wide range of densities in the quasi-elastic limit, which is a surprising result, especially for a dilute granular gas for which the Knudsen number belongs to the transitional flow regime. The signature of wall-roughness-induced dissipation mainly shows up in the P(ux) distribution in the form of a sharp peak for negative velocities in the near-wall region. Both P(ux) and P(uy) distributions become asymmetric with increasing dissipation at any density, and the emergence of density waves, which appear in the form of sinuous wave/slug at low-to-moderate values of mean density, makes these asymmetries stronger, especially in the presence of a slug. At high densities, the flow degenerates into a dense plug (where the density approaches its maximum limit and the shear rate is negligibly small) around the channel centreline and two shear layers (where the shear rate is high and the density is low) near the walls. The distribution functions within the shear layer follow the characteristics of those at moderate mean densities. Within the dense plug, the high-velocity tails of both P(ux) and P(uy) appear to undergo a transition from Gaussian in the quasi-elastic limit to power-law distributions at large inelasticity of particle collisions. For dense flows, it is shown that although the density correlations play a significant role in enhancing the velocity correlations when the collisions are sufficiently inelastic, they do not induce velocity correlations when the collisions are quasi-elastic for which the distribution functions are close to Gaussian. The combined effect of enhanced density and velocity correlations around the channel centreline with increasing inelastic dissipation seems to be responsible for the emergence of non-Gaussian high-velocity tails of distribution functions.