We consider the radially expanding sheet formed upon impact of a drop on a surface of comparable size to that of the drop. A unified self-similar solution for the unsteady radial thickness profile of the expanding sheet is derived from first principles in the inviscid limit. This unified functional form reconciles two conflicting theoretical profiles of sheet thickness proposed in the literature and allows for the collapse on a single curve direct measurements of sheet thickness profiles reported in the literature and the detailed measurements conducted herein. We show good agreement between our proposed unified thickness profile and data from our experiments for a range of surface-to-drop size ratios. We show that there is an optimal range of surface-to-drop size ratio for which the hypothesis of inviscid thin sheet expansion in the air holds. Outside of this optimal range, either insufficient vertical momentum is transferred to horizontal momentum to form an expanding sheet or viscous effects become too important to neglect. In this latter regime, the dominant effect of surface friction is to modify the velocity profile. We elucidate this effect using a Blasius-type boundary layer model. Finally, we relate the geometry of the drop in its early phase of impact to the sheet thickness profile in the air. We show that the coefficients of the proposed unified similarity thickness profile can directly be linked to volume flux conservation at early times, and to the maximum sheet thickness at the edge of the surface. Our results thus quantitatively link the fluid history on the surface to the thickness and velocity profiles of the freely expanding sheet in the air.

A plate placed above a porous substrate through which air is blown can levitate if the airflow is strong enough. We first model the flow needed for taking off, and then examine how an asymmetric texture etched on the porous surface induces directional motion of the hovercraft. We discuss how the texture design impacts the propelling efficiency, and how it can be used to manipulate these frictionless objects both in translation and in rotation.

The vortex–body interaction problem, which characterizes the flow field of a rudder placed downstream of a single-blade marine rotor, is investigated by numerical simulations. The particular topology of the propeller wake, consisting of a helicoidal vortex detached from the blade tips (tip vortex) and a longitudinal, streamwise oriented vortex originating at the hub (hub vortex), embraces two representative mechanisms of vortex–body collisions: the tip vortices impact almost orthogonally to the mean plane, whereas the hub vortex travels in the mean plane of the wing (rudder), perpendicularly to its leading edge. The two vortices evolve independently only during the approaching and collision phases. The passage along the body is instead characterized by strong interaction with the boundary layer on the rudder and is followed by reconnection and merging in the middle and far wake. The features of the wake were investigated by the $\unicode[STIX]{x1D706}_{2}$ -criterion (Jeong & Hussain, J. Fluid Mech., vol. 285, 1995, pp. 69–94) and typical flow variables (pressure, velocity and vorticity) of the instantaneous flow field; wall pressure spectra were analysed and related to the tip and hub vortices evolution, revealing a non-obvious behaviour of the loading on the rudder that can be related to undesired unsteady loads.

A theory is presented where the weakly nonlinear analysis of laminar globally unstable flows in the presence of external forcing is extended to the turbulent regime. The analysis is demonstrated and validated using experimental results of an axisymmetric bluff-body wake at high Reynolds numbers, $Re_{D}\sim 1.88\times 10^{5}$, where forcing is applied using a zero-net-mass-flux actuator located at the base of the blunt body. In this study we focus on the response of antisymmetric coherent structures with azimuthal wavenumbers $m=\pm 1$ at a frequency $St_{D}=0.2$, responsible for global vortex shedding. We found experimentally that axisymmetric forcing ($m=0$) couples nonlinearly with the global shedding mode when the flow is forced at twice the shedding frequency, resulting in parametric subharmonic resonance through a triadic interaction between forcing and shedding. We derive simple weakly nonlinear models from the phase-averaged Navier–Stokes equations and show that they capture accurately the observed behaviour for this type of forcing. The unknown model coefficients are obtained experimentally by producing harmonic transients. This approach should be applicable in a variety of turbulent flows to describe the response of global modes to forcing.

We report on optical field measurements of snow settling in atmospheric turbulence at $Re_{\unicode[STIX]{x1D706}}=940$. It is found that the snowflakes exhibit hallmark features of inertial particles in turbulence. The snow motion is analysed in both Eulerian and Lagrangian frameworks by large-scale particle imaging, while sonic anemometry is used to characterize the flow field. Additionally, the snowflake size and morphology are assessed by digital in-line holography. The low volume fraction and mass loading imply a one-way interaction with the turbulent air. Acceleration probability density functions show wide exponential tails consistent with laboratory and numerical studies of homogeneous isotropic turbulence. Invoking the assumption that the particle acceleration has a stronger dependence on the Stokes number than on the specific features of the turbulence (e.g. precise Reynolds number and large-scale anisotropy), we make inferences on the snowflakes’ aerodynamic response time. In particular, we observe that their acceleration distribution is consistent with that of particles of Stokes number in the range $St=0.1{-}0.4$ based on the Kolmogorov time scale. The still-air terminal velocities estimated for the resulting range of aerodynamic response times are significantly smaller than the measured snow particle fall speed. This is interpreted as a manifestation of settling enhancement by turbulence, which is observed here for the first time in a natural setting.

In this experimental study, we investigate the interaction of gravity–capillary solitary waves generated by two surface pressure sources moving side by side at constant speed. The nonlinear response of a water surface to a single source moving at a speed just below the minimum phase speed of linear gravity–capillary waves in deep water ($c_{min}\approx 23~\text{cm}~\text{s}^{-1}$) consists of periodic generation of pairs of three-dimensional solitary waves (or lumps) in a V-shaped pattern downstream of the source. In the reference frame of the laboratory, these unsteady lumps propagate in a direction oblique to the motion of the source. In the present experiments, the strengths of the two sources are adjusted to produce nearly identical responses and the free-surface deformations are visualized using photography-based techniques. The first lumps generated by the two sources move in intersecting directions that make a half-angle of approximately $15^{\circ }$ and collide in the centreplane between the sources. A steep depression is formed during the collision, but this depression quickly decreases in amplitude while radiating small-amplitude radial waves. After the collision, a quasi-stable pattern is formed with several rows of localized depressions that are qualitatively similar to lumps but exhibit periodic amplitude oscillations, similar to a breather. The shape of the wave pattern and the period of oscillations depend strongly on the distance between the sources.

The modified Townsend–Perry attached-eddy model of Vassilicos et al. (J. Fluid Mech., vol. 774, 2015, pp. 324–341) combines the outer peak/plateau behaviour of root-mean-square streamwise turbulence velocity profiles and the Townsend–Perry log decay of these profiles at higher distances from the wall. This model was validated by these authors for high-Reynolds-number turbulent pipe flow data and is shown here to describe equally well, and with approximately the same parameter values, turbulent boundary layer flow data from four different facilities and a wide range of Reynolds numbers. The model has predictive value as, when extrapolated to the extremely high Reynolds numbers of the SLTEST data obtained at the Great Salt Lake Desert atmospheric test facility, it matches these data quite well.