We consider the indirect mechanism for dissipation of short surface waves through their near-resonant interactions with long sub-harmonic waves that are dissipated by the bottom. Using direct perturbation analysis and an energy argument, we obtain analytic predictions of the evolution of the amplitudes of two short primary waves and the long sub-harmonic wave which form a near-resonant triad, elucidating the energy transfer, from the short waves to the long wave, which may be significant over time. We obtain expressions for the rate of total energy loss of the system and show that this rate has an extremum corresponding to a specific value of the (bottom) damping coefficient (for a given pair of short wavelengths relative to water depth). These analytic results agree very well with direct numerical simulations developed for the general nonlinear wave–wave and wave–bottom interaction problem.

Nonlinear travelling waves on a two-dimensional inviscid fluid sheet are investigated when the sheet is bounded above and below by two thin elastic plates. Symmetric and antisymmetric solution branches are identified, together with a pair of bifurcation branches. It is shown that far along the branches the solutions approach limiting configurations that correspond to static solutions valid in the absence of fluid forcing.

Pulsating cone-jets occur in a variety of electrostatic spraying and printing systems. This paper reports an experimental study of the pulsation frequency to reconcile two models based on a choked jet and an oscillating cone, respectively. The two regimes are demarcated by the ratio of the supplied flow rate () to the minimum flow rate () required for a steady Taylor cone-jet. When , the electrohydrodynamic flow is choked at the nozzle because the intermittent jet, when on, emits mass at the minimum flow rate; the pulsation frequency in the choked jet regime is proportional to . When , the Taylor cone anchored at the nozzle experiences a capillary oscillation analogous to the Rayleigh mode of a free drop; the pulsation frequency in the oscillating cone regime plateaus to the capillary oscillation frequency, which is independent of .

Several forms of a theorem providing general expressions for the force and torque acting on a rigid body of arbitrary shape moving in an inhomogeneous incompressible flow at arbitrary Reynolds number are derived. Inhomogeneity arises because of the presence of a wall that partially or entirely bounds the fluid domain and/or a non-uniform carrying flow. This theorem, which stems directly from Navier–Stokes equations and parallels the well-known Lorentz reciprocal theorem extensively employed in low-Reynolds-number hydrodynamics, makes use of auxiliary solenoidal irrotational velocity fields and extends results previously derived by Quartapelle & Napolitano (AIAA J., vol. 21, 1983, pp. 911–913) and Howe (Q. J. Mech. Appl. Maths, vol. 48, 1995, pp. 401–426) in the case of an unbounded flow domain and a fluid at rest at infinity. As the orientation of the auxiliary velocity may be chosen arbitrarily, any component of the force and torque can be evaluated, irrespective of its orientation with respect to the relative velocity between the body and fluid. Three main forms of the theorem are successively derived. The first of these, given in (2.19), is suitable for a body moving in a fluid at rest in the presence of a wall. The most general form (3.6) extends it to the general situation of a body moving in an arbitrary non-uniform flow. Specific attention is then paid to the case of an underlying time-dependent linear flow. Specialized forms of the theorem are provided in this situation for simplified body shapes and flow conditions, in (3.14) and (3.15), making explicit the various couplings between the body’s translation and rotation and the strain rate and vorticity of the carrying flow. The physical meaning of the various contributions to the force and torque and the way in which the present predictions reduce to those provided by available approaches, especially in the inviscid limit, are discussed. Some applications to high-Reynolds-number bubble dynamics, which provide several apparently new predictions, are also presented.

In Magnaudet (2011) an inertial contribution was overlooked during the derivation of (3.6). Indeed, when generalizing (E.5), which is valid for an irrotational velocity field , to (E.6) which holds for any velocity , an extra term arises on the right-hand side of the latter and hence on that of (E.8). Therefore the right-hand side of (3.6) actually involves an additional contribution , where denotes the strain-rate tensor associated with the undisturbed flow field. This contribution to the force and torque results from the distortion by the underlying strain rate of the vortical velocity disturbance generated either by the dynamic boundary condition at the body surface (and possibly on the wall ), or/and by the vorticity of the undisturbed flow within the core of the fluid. This extra term gives in turn rise to an additional contribution on the right-hand side of (3.13)–(3.15). This term was not present in the inviscid expressions established by Miloh (2003) because his derivation was restricted to situations in which the velocity disturbance is irrotational throughout the flow domain. This extra term does not alter the conclusions brought in the present paper for inviscid two-dimensional flows, nor those corresponding to the short-time limit of inviscid three-dimensional flows. In the limit considered in the example of § 4.3, the disturbance is still irrotational outside the boundary layers that develop around the bubble and along the wall, respectively. The leading order in the vortical velocity disturbance is of around the bubble, both in the and directions. Near the wall, it is of (respectively ) in the (respectively ) direction. Since the thickness of both boundary layers is of and grows linearly with the distance to the wall, the extra term yields an net contribution provided by the bubble boundary layer and only an correction provided by the wall boundary layer. Hence the inviscid predictions (4.26) and (4.33) are unchanged and there is an correction to the viscous drag and lift, similar in magnitude to that resulting from the term . Owing to the weak inhomogeneity assumption invoked in §§ 3.2 and 4.3, the dimensionless shear rate must be much smaller than unity for (4.26) and (4.33) to hold. Hence, in this context, the above corrections to the drag are much smaller than the leading, , contribution provided by the surface term . Note that the above prefactor is missing on the right-hand side of (4.16) and (4.19).