The average wave drag in unsteady motion is studied experimentally with force measurements. Towing hulls of size $L$ at sinusoidal speed, the mean drag is measured for different amplitudes and frequencies of the fluctuating velocity, as well as different Froude numbers $\mathcal {F}_0$ associated with the mean velocity $V_0$ ($\mathcal {F}_0 = V_0/\sqrt {gL}$). The wave drag is reported to be either increased or decreased by velocity fluctuations depending on $\mathcal {F}_0$. For small fluctuation amplitudes, this drag change is proportional to the square of the amplitude. The effect is maximized for a resonance frequency identified as the Wehausen frequency, which scales as $\sqrt {g/L}$ times the inverse of the Froude number. All these results are rationalized by developing an extension to Havelock's theory.

An asymmetric body with a sharp leading edge and a rounded trailing edge produces a smaller wave disturbance moving forwards than backwards, and this is reflected in the wave drag coefficient. This experimental fact is not captured by Michell’s theory for wave drag (Michell Lond. Edinb. Dubl. Phil. Mag. J. Sci., vol. 45 (272), 1898, pp. 106–123). In this study, we use a tow-tank experiment to investigate the effects of asymmetry on wave drag, and show that these effects can be replicated by modifying Michell’s theory to include the growth of a symmetry-breaking boundary layer. We show that asymmetry can have either a positive or a negative effect on drag, depending on the depth of motion and the Froude number.

When a wave breaks, the tip forms a liquid sheet which impinges the base and creates an air cavity which breaks into bubbles. Gomez-Ledesma, Kiger & Duncan (J. Fluid Mech., this issue, vol. 680, 2011, pp. 5–30) have conducted a nice experiment on this problem, enabling them to discuss both the inclination of the jet and the effect of its translation. This work has interesting links with other transient cavities.

We study the collapse of a transient cavity of air in water created by the impact of a solid body. Experimentally, we characterize the dynamics of the cavity from its creation (t = 0) until it collapses (t = τ) in the limit where inertia dominates viscous and capillary effects. Theoretically, we find in this regime an approximate analytical solution which describes the time evolution of the shape of the cavity. This theoretical solution predicts the existence of two different types of cavities that we also observe experimentally.

The fragmentation of a laminar undulating liquid sheet flowing in quiescent air is investigated. Combining various observations and measurements we propose a sequential atomization scenario describing the overall sheet–drop transition in this configuration. The undulation results from a controlled primary Kelvin–Helmholtz instability. As the liquid travels through the undulating pattern, it experiences transient accelerations perpendicular to the sheet. These accelerations trigger a secondary instability responsible for the amplification of spanwise thickness modulations of the sheet. This mechanism, called the ‘wavy corridor’, is responsible for the sheet free edge indentations from which liquid ligaments emerge and break, forming drops. The final drop size distribution is of a Gamma type characterized by a unique parameter independent of the operating conditions once drop sizes are normalized by their mean.

Superhydrophobic surfaces generate very high contact angles as a result of their microstructure. The impact of a water drop on such a surface shows unusual features, such as total rebound at low impact speed. We report experimental and numerical investigations of the impact of approximately spherical water drops. The axisymmetric free surface problem, governed by the Navier–Stokes equations, is solved numerically with a front-tracking marker-chain method on a square grid. Experimental observations at moderate velocities and capillary wavelength much less than the initial drop radius show that the drop evolves to a staircase pyramid and eventually to a torus. Our numerical simulations reproduce this effect. The maximal radius obtained in numerical simulations precisely matches the experimental value. However, the large velocity limit has not been reached experimentally or numerically. We discuss several complications that arise at large velocity: swirling motions observed in the cross-section of the toroidal drop and the appearance of a thin film in the centre of the toroidal drop. The numerical results predict the dry-out of this film for sufficiently high Reynolds and Weber numbers. When the drop rebounds, it has a top-heavy shape. In this final stage, the kinetic energy is a small fraction of its initial value.

A round liquid jet with density ρ, surface tension σ and diameter D0 impacting a solid circular surface at normal incidence with velocity U0 takes the form of a radially expanding sheet whose thickness decreases with distance from the impact point. When the sheet develops in a still environment with density ρa = αρ, it destabilizes, provided the impacting Weber number We = ρU20D0/σ is larger than about 40α−1/2, as a result of a shear instability with the surrounding medium, in a sinuous, flag-like motion. We show how the instability properties set both the radial extent of the liquid sheet and the drop formation process at its rim. The shear instability gives the liquid a flag-like motion, ultimately triggering a Rayleigh–Taylor instability at the rim of the sheet which disintegrates, at the radial location R, into disjointed droplets of size d such that

R/D0 ∼ α−2/3We−1/3 and d/D0 ∼ α−2/3We−1.

The features of the sheet instability, its radius and the droplet sizes are determined experimentally for a broad range of control parameters, using different liquids and ambient-medium densities.

We consider the critical Weber number (Wec≡ ρV20D/σ) at which the transition from dripping to jetting occurs when a Newtonian liquid of density ρ and surface tension σ is injected with a velocity V0 through a tube of diameter D downward into stagnant air, under gravity g. We extend Taylor's (1959) model for the recession speed of a free edge, and obtain in the inviscid limit an exact solution which includes gravity and inertia effects. This solution provides a criterion for the transition which is shown to occur at a critical Weber number

formula here

where Bo and Boo are the Bond numbers (Bo≡[ρgD2/(2σ)]1/2), respectively based on the inside and outside diameter of the tube, and K is a constant equal to 0.37 for the case of water injected in air. This critical Weber number is shown to be in good agreement with existing experimental values as well as with new measurements performed over a wide range of Bond numbers.