Previous experimental and numerical work indicates that an initially symmetric deep-water wave pulse of uniform frequency and moderately small steepness evolves in an asymmetric manner and eventually separates into distinct wave groups, owing to higher-order modulation effects, not accounted for by the nonlinear Schrödinger equation (NLS). Here perturbation methods are used to provide analytical confirmation of this group splitting on the basis of the more accurate envelope equation of Dysthe (1979). It is demonstrated that an initially symmetric multisoliton wave envelope, consisting of N bound NLS solitons, ultimately breaks up into N separate groups; a procedure is devised for determining the relative speed changes of the individual groups. The case of a bi-soliton (N = 2) is discussed in detail, and the analytical predictions are compared to numerical results.

The intermittency of the rate of turbulent energy dissipation ε is investigated experimentally, with special emphasis on its scale-similar facets. This is done using a general formulation in terms of multifractals, and by interpreting measurements in that light. The concept of multiplicative processes in turbulence is (heuristically) shown to lead to multifractal distributions, whose formalism is described in some detail. To prepare proper ground for the interpretation of experimental results, a variety of cascade models is reviewed and their physical contents are analysed qualitatively. Point-probe measurements of ε are made in several laboratory flows and in the atmospheric surface layer, using Taylor's frozen-flow hypothesis. The multifractal spectrum f(α) of ε is measured using different averaging techniques, and the results are shown to be in essential agreement among themselves and with our earlier ones. Also, long data sets obtained in two laboratory flows are used to obtain the latent part of the f(α) curve, confirming Mandelbrot's idea that it can in principle be obtained from linear cuts through a three-dimensional distribution. The tails of distributions of box-averaged dissipation are found to be of the square-root exponential type, and the implications of this finding for the f(α) distribution are discussed. A comparison of the results to a variety of cascade models shows that binomial models give the simplest possible mechanism that reproduces most of the observations. Generalizations to multinomial models are discussed.

Two-dimensional, incompressible flows are discussed by a generalization of the line-vortex model. A large number of structures are randomly distributed initially. Each individual structure is convected by the superposed flow field of all the others. The statistical properties of the resulting space–time varying random flow are studied. Analytical expressions for both Eulerian and Lagrangian correlation functions are obtained for the limit where the density of structures is large. The analytical results compare favourably with numerical simulations. The study serves as a special test on proposed relations between Eulerian and Lagrangian averages which can be generally valid, i.e. also for three-dimensional, turbulent flows.

If a bubble were produced with an initial surface distortion, the energy carried by surface modes could be converted to other modes by nonlinear interaction, a conversion that provides a possible mechanism of second generation by bubbles. Longuet-Higgins (1989a,b) has argued that volume pulsation would be excited at twice the frequency of the distortion mode and that the response to such excitation is ‘surprisingly large’ when its frequency is close to the natural resonance frequency of the volumetrical mode. It is shown in this paper that this is feasible only if the driving system is sufficiently energetic to supply the energy involved in those volume pulsations, and that this is not generally the case. In the absence of external sources, the sum of energies in the interacting modes cannot exceed the initial bubble energy; an increase in one mode is always accompanied by a decrease in another. In contrast to any expectation of significant pulsations near resonance, we find that, once modal coupling is admitted, the volumetrical pulsation has very small amplitude in comparison with that of the initial surface distortion. This is because of the constraint of energy, a constraint that becomes more severe once damping is admitted. Our conclusion therefore is that the distortion modes of a bubble are unlikely to be the origin of an acoustically significant bubble response.

In two recent papers (Longuet-Higgins 1989a,b) the author showed that the shape oscillations of bubbles can emit sound like a monopole source, at second order in the distortion parameter ε. In the second paper (LH2) it was predicted that the emission would be amplified when the second harmonic frequency 2σn of the shape oscillation approaches the frequency ω of the breathing mode. This ‘resonance’ would however be drastically limited by damping due to acoustic radiation and thermal diffusion. The predictions were confirmed by further numerical calculations in Longuet-Higgins (1990a).

Ffowcs Williams & Guo (1991) have questioned the conclusions of LH2 on the grounds that near resonance there is a slow (secular) transfer of energy between the shape oscillation and the volumetric mode which tends to diminish the amplitude of the shape oscillation and hence falsify the perturbation analysis. They have also argued that the volumetric mode never grows sufficiently to produce sound of the stated order of magnitude. In the present paper we show that these assertions are unfounded. Ffowcs Williams & Guo considered only undamped oscillations. Here we show that when the appropriate damping is included in their analysis the secular transfer of energy becomes completely insignificant. The resulting pressure pulse (figure 5 below) is found to be essentially identical to that calculated in LH2, figure 3. Moreover, in the initial-value problem considered in LH2, the excitation of the volumetric mode takes place not by a secular energy transfer but by a resonance during the first few cycles of the shape oscillation. This accounts for the amplification near resonance found in Longuet-Higgins (1990a). Finally, it is pointed out that the initial energy of the shape oscillations is far greater than is required to produce the O(ε2) volume pulsations that were studied in LH2, and which were used for a comparison with field data. This acoustic radiation was not calculated by Ffowcs Williams & Guo.

We consider the effects of a nonlinear–non-equilibrium–viscous critical layer on the spatial evolution of subsonic and supersonic instability modes on a compressible free shear layer. It is shown that the instability wave amplitude is governed by an integro-differential equation with cubic-type nonlinearity. Numerical and asymptotic solutions to this equation show that the amplitude either ends in a singularity at a finite downstream distance or reaches an equilibrium value, depending on the Prandtl number, viscosity law, viscous parameter and a real parameter which is determined by the linear in viscid stability theory. A necessary condition for the existence of the equilibrium solution is derived, and whether or not this condition is met is determined numerically for a wide range of physical parameters including both subsonic and supersonic disturbances. It is found that no equilibrium solution exists for the subsonic modes unless the temperature ratio of the low-to high-speed streams exceeds a critical value, while equilibrium solutions for the most rapidly growing supersonic mode exist over most of the parameter range examined.

Near-wall flow structures in turbulent shear flows are analysed, with particular emphasis on the study of their space–time evolution and connection to turbulence production. The results are obtained from investigation of a database generated from direct numerical simulation of turbulent channel flow at a Reynolds number of 180 based on half-channel width and friction velocity. New light is shed on problems associated with conditional sampling techniques, together with methods to improve these techniques, for use both in physical and numerical experiments. The results clearly indicate that earlier conceptual models of the processes associated with near-wall turbulence production, based on flow visualization and probe measurements need to be modified. For instance, the development of asymmetry in the spanwise direction seems to be an important element in the evolution of near-wall structures in general, and for shear layers in particular. The inhibition of spanwise motion of the near-wall streaky pattern may be the primary reason for the ability of small longitudinal riblets to reduce turbulent skin friction below the value for a flat surface.

An experimental study of the microwave backscatter and acoustic radiation from breaking waves is reported. It is found that the averaged microwave and acoustic measurements correlate with the dynamics of wave breaking. Both the mean-square acoustic pressure and the backscattered microwave power correlate with the wave slope and dissipation, for waves of moderate slope (S < 0.28). The backscattered power and the mean-square pressure are also found to correlate strongly with each other. As the slope and wavelength of the breaking wave packet is increased, both the backscattered power and the mean-square pressure increase. It is found that a large portion of the backscattered microwave power precedes the onset of sound production and visible breaking. This indicates that the unsteadiness of the breaking process is important and that the geometry of the wave prior to breaking may dominate the backscattering. It is observed that the amount of acoustic energy radiated by an individual breaking wave scaled with the amount of mechanical energy dissipated during breaking. These laboratory results are compared to the field experiments of Farmer & Vagle (1988), Crowther (1989) and Jessup et al. (1990).

The linear theory for water waves impinging obliquely on a vertically sided porous structure is examined. For normal wave incidence, the reflection and transmission from a porous breakwater has been studied many times using eigenfunction expansions in the water region in front of the structure, within the porous medium, and behind the structure in the down-wave water region. For oblique wave incidence, the reflection and transmission coefficients are significantly altered and they are calculated here.

Using a plane-wave assumption, which involves neglecting the evanescent eigenmodes that exist near the structure boundaries (to satisfy matching conditions), the problem can be reduced from a matrix problem to one which is analytic. The plane-wave approximation provides an adequate solution for the case where the damping within the structure is not too great.

An important parameter in this problem is Γ2 = ω2h(s - if)/g, where ω is the wave angular frequency, h the constant water depth, g the acceleration due to gravity, and s and f are parameters describing the porous medium. As the friction in the porous medium, f, becomes non-zero, the eigenfunctions differ from those in the fluid regions, largely owing to the change in the modal wavenumbers, which depend on Γ2.

For an infinite number of values of ΓF2, there are no eigenfunction expansions in the porous medium, owing to the coalescence of two of the wavenumbers. These cases are shown to result in a non-separable mathematical problem and the appropriate wave modes are determined. As the two wavenumbers approach the critical value of Γ2, it is shown that the wave modes can swap their identity.

The hydrodynamic problem of a submerged horizontal cylinder advancing in regular water waves of finite depth at constant forward speed is analysed by the linearized velocity potential theory. The Green function is first derived. Far-field equations for calculating damping coefficients and exciting forces are obtained. The numerical method used combines a finite-element approximation of the potential in a region surrounding the cylinder with a boundary-integral-equation representation of the outer region. Numerical results for the hydrodynamic forces on submerged circular cylinders and elliptical cylinders are provided.