The dissemination of scientific results is a vital part of the advancement of knowledge. And disseminate the Journal of Fluid Mechanics certainly has done, in the 25 years of its existence. The first part of volume one of the Journal was published in May 1956, and by the end of April 1981 a total of 4662 papers concerned with fluid mechanics had been published in 105 volumes and distributed to universities, laboratories, institutes and individual subscribers in all countries of the globe. Watching that torrent of information flow past, controlling and regulating it, and at times diverting it, has been an extraordinary experience. It has been a pleasure and privilege to have been involved, even though I have sometimes wished that all research funds would dry up temporarily so as to give editors an interlude in which to reflect on what they are doing.

This is in no way intended as a review of turbulence-the subject is far too big for adequate treatment within a reasonably finite number of pages; the monumental treatise of Monin & Yaglom (1971, 1975) bears witness to this statement. It is rather a discourse on those aspects of the problem of turbulence with which I have myself had contact over the last twenty years or so. My choice of topics therefore has a very personal bias - but that is perhaps consistent with the style and objectives of this rather unusual issue of JFM.

I have approached the dynamical problem of turbulence via two simpler (but nevertheless far from trivial) problems – viz the convection and diffusion of a passive scalar field and of a passive vector field by turbulence of known statistical properties. Particular emphasis is given to the method of successive averaging (a simplified version of the renormalization-group technique) which seems to me to have considerable potential. The difficulty of extending this method to the dynamical problem is discussed.

In a final section (§ 6) I have allowed myself the luxury of discussing a somewhat esoteric topic - the problem of inviscid invariants and their relationship with the topological structure of a complex vorticity field. The helicity invariant is the prototype; it is identifiable with the Hopf invariant (1931) and it may be obtained from appropriate manipulation of Noether's theorem (Moreau 1977). A suggestion is made concerning possible measurement of this fundamental measure of ‘lack of reflexional symmetry’ in a turbulent flow.

Remarks are made about the status of research on the role of vorticity in fluid dynamics and some unsolved problems of current interest are described.

Two topics are discussed in order to illustrate the author's own enjoyment of fluid mechanics. The first and longer discourse is about splashes. It makes no attempt at completeness but includes a little new research. The second part deals briefly with many variations on the theme of flow in pipes.

The first volume of the Journal of Fluid Mechanics contained nine articles (of 39) on shock waves. Some of these pioneered new branches of fluid mechanics. Others dealt with older problem areas. Surprising is one's realization that important elements of all topics are still of current interest. The subjects treated were shock structure, diffraction, refraction, waves in supersonic and hypersonic flows, large-amplitude acoustic and blast waves, and astrophysical processes. The subsequent addition of work on chemically reactive flows, radiating and laser-induced shocks, the effects of electric and magnetic fields on shock propagation in ionized media and the development of computer-based methods of analysis have greatly broadened the scope of shock wave investigations during the ensuing twenty-five years.

The paper traces some of the principal lines of investigation from early motivations to the present state of understanding and application. Motivation is not often consciously expressed in the scientific literature. Usually an external motivation in terms of identifiable needs for better understanding for the solution of practical problems can be identified; though much excellent work must be ascribed to that ubiquitous trait curiosity.

The topics covered in this article were chosen as representative of the basic elements of shock wave interactions and effects. They are: shock structure, refraction, diffraction, shocks in liquid helium, and condensation and liquefaction shocks. The paper closes with an assessment of how approximate and computational methods developed for handling complex flow problems fare when applied to some of the basic shock interactions considered here. Most of the emphasis will be on shock waves in gases, for which knowledge of an equation of state has been key to the significant advances made during the last twenty-five years. For liquids and solids, shock waves have been used the other way around; to study state properties.

The publication of this 25th Anniversary Issue of the Journal of Fluid Nechanics is a fitting moment to consider some of the new ways in which fuid flow has been controlled and exploited and the relationship between these practical developments and the kind of scientific studies reported in this journal. From Leonard0 to Lanchester to Lighthill the application of the understanding of fluid motions to the study and practice of flight, whether man-made or natural, has gone hand-in-hand with the scientific development of the subject. But, although from the earliest times fluid motion has been controlled and exploited for industrial and environmental purposes, the connection between these applications of fluid flow and its scientific study is nothing like as direct or as widespread, perhaps because the costs and dangers of failure in these fields are somewhat less. It is particularly appropriate to discuss these aspects of fluid flow, because one of J F M's most noticeable features has been the publication of papers on new ideas which already have had or may have some interesting non-aeronautical applications.

The Korteweg-de Vries (KdV) equation, usually attributed to Korteweg & de Vries (1895), governs the propagation of weakly dispersive, weakly nonlinear water waves and serves as a model equation for any physical system for which the dispersion relation for frequency vs. wavenumber is approximated by ω/k = c0(1 − βk2) and nonlinearity is weak and quadratic. It first appears explicitly in de Vries's dissertation (1894), although it is implicit in the work of Boussinesq (1872). Its current renaissance stems from the Fermi, Pasta & Ulam (1955) problem for a string of nonlinearly coupled oscillators, which, through the work of Zabusky & Kruskal and their colleagues, led to the discovery of the soliton and the development of inverse-scattering theory by Gardner et al. (1967). Many related evolution equations, each of which represents a balance between some form of dispersion (or variation of dispersion in the case of wave-packet evolution) and weak nonlinearity in an appropriate reference frame, have since been found to have properties analogous to those of the KdV equation - in particular, inverse-scattering solutions that are asymptotically dominated by solitons.

With moderate acoustic stimuli, measurements of basilar-membrane vibration (especially, those using a Mössbauer source attached to the membrane) demonstrate:

1. a high degree of asymmetry, in that the response to a pure tone falls extremely sharply above the characteristic frequency, although much more gradually below it;

2. a substantial phase-lag in that response, and one which increases monotonically up to the characteristic frequency;

3. a response to a ‘click’ in the form of a delayed ‘ringing’ oscillation at the characteristic frequency, which persists for around 20 cycles.

The response (iii) demands a travelling-wave model which incorporates an only lightly damped resonance. Admittedly, waveguide systems including resonance are described in classical applied physics. However, a classical waveguide resonance reflects a travelling wave, thus converting it into a standing wave devoid of the substantial phase-lag (ii); and produces a low-frequency cutoff instead of the high-frequency cutoff (i).

By contrast, another general type of travelling-wave system with resonance has become known more recently; initially, in a quite different context (physics of the atmosphere). This is described as critical-layer resonance, or else (because the resonance absorbs energy) critical-layer absorption. It yields a high-frequency cutoff; but, above all, it is characterized by the properties of the energy flow velocity. This falls to zero very steeply as the point of resonance is approached; so that wave energy flow is retarded drastically, giving any light damping which is present an unlimited time in which to dissipate that energy.

Existing mathematical models of cochlear mechanics, whether using one-, two- or three-dimensional representations of cochlear geometry, are analysed from this standpoint. All are found to have been successful (if only light damping is incorporated, as (iii) requires) when and only when they incorporate critical-layer absorption. This resolves the paradox of why certain grossly unrealistic one-dimensional models can give a good prediction of cochlear response; it is because they incorporate the one essential feature of critical-layer absorption.

At any point in a physical system, the high-frequency limit of energy flow velocity is the slope of the graph of frequency against wavenumberIn any travelling wave, the wavenumber is the rate of change of phase with distance; for example, it is 2π/λ in a sine wave of length λ. at that point. In the cochlea, this is a good approximation at frequencies above about 1 kHz; and, even at much lower frequencies, remains good for wavenumbers above about 0·2 mm−1 (which excludes only a relatively unimportant region near the base).

Frequency of vibration at any point can vary with wavenumber either because stiffness or inertia varies with wavenumber. However, we find that models incorporating a wavenumber-dependent membrane stiffness must be abandoned because they fail to give critical-layer absorption; this is why their predictions (when realistically light damping is used) have been unsuccessful. Similarly, models neglecting the inertia of the cochlear partition must be rejected.

One-dimensional modelling becomes physically unrealistic for wavenumbers above about 0.7 mni-1, and the error increases with wavenumber. The main trouble is that a one-dimensional theory makes the effective inertia ‘flatten out’ to its limiting value (inertia of the cochlear partition alone) too rapidly as wavenumber increases. Fortunately, a two-dimensional, or even a three-dimensional, model can readily be used to calculate a more realistic, and significantly more gradual, ‘flattening out’ of this inertia. All of the models give a fair representation of the experimental data, because they all predict critical-layer absorption. However, the more realistic two- or three-dimensional models must be preferred. These retard the wave energy flow still more, thus facilitating its absorption by even a very modest level of damping. The paper indicates many other features of these models.

The analysis described above is preceded by a discussion of waves generated a t the oval window. They necessarily include:

1. the already-mentioned travelling wave, or ‘slow wave’, in which the speed of energy flow falls from around 100 m s−l at the base to zero at the position of resonance;

2. a pure sound wave, or ‘fast wave’, travelling a t 1400 m s-1, with reflection at the apex which makes i t into a standing wave. Half of the rate of working of the stapes footplate against the oval window is communicated as an energy flow a t this much higher speed down the scala vestibuli, across the cochlear partition and back up the scala tympani to the round window, whence it becomes part of the slow general apical progress of the travelling wave; a progress which, as described above, comes to a halt altogether just in front of the position of resonance.

Mathematical detail is avoided in the discussion of cochlear energy flow in the main part of the paper (§ 1–10), but a variety of relevant mathematical analysis is given in appendices A–E. These include, also, new comments about the functions of the tunnel of Corti (appendix A) and the helicotrema (appendix C).

This essay gives a personal and possibly incomplete history of the way in which the simple idea of weak resonant wave interactions grew to find application to a variety of phenomena in several contexts. The development involved incremental steps by many people in the past twenty years, gaining simplicity with maturity. The final stage seems to be approaching when the limits of usefulness of the idea are beginning to become apparent.

Readers of this Journal do not, in my experience, have a uniform view of what properly constitutes the discipline of Fluid Mechanics; nor would they agree on what the main outstanding problems in the subject are. Many, particularly among those who do not contribute to the Journal, believe – unfortunately – that it has become a branch of applied analysis on the theoretical side, and is dominated by hot-wire and laser anemometry on the experimental side. As an ex-editor, I must hasten to add that this has not been the view of the editors, and that, if such an impression is created by the spectrum of papers published in the Journal, such an imbalance largely reflects the nature of the papers submitted.

Perfect-fluid theory is applied to the description of steady motions that can be generated as the outflow into a horizontal channel from a large reservoir of incompressible heavy fluid whose density is an arbitrary decreasing function of height. A particular aim is to pinpoint the significance of an already known class of flows, called self similar, which satisfy the approximate (shallow-water) equations applicable when the horizontal scale of the motion greatly exceeds its vertical scale, but which have not until now been shown to match the downstream conditions that primarily determine the motion in practice.

New variational principles are introduced characterizing the class of self-similar flows: in §2 there is a characterization in terms of flow force among parallel flows realized asymptotically in a uniform channel, in §3 among a wider range of possibilities including periodic flows, and in §6 among supercritical flows realized in a convergent-divergent channel. Aspects of general flows in channels of gradually varying breadth are treated in §§4 and 5, including the remarkable fact, proven in §5, that every steady flow outside but close to the self-similar class must somewhere undergo a local crisis unaccountable by the shallow-water approximation. Practical interpretations afforded by the theoretical results are noted in §7.

This article gives a review of six areas of current activity and importance in aero-acoustics, including (i) the generation of sound and vorticity by vorticity and sound, respectively, (ii) the basis for, and consequences of, the application of a Kutta condition in unsteady leading- and trailing-edge flows, and (iii) the suppression or amplification of broadband hydrodynamic and acoustic fields in a jet under the influence of weak discrete tone forcing. The intention is also to promote acceptance once again of acoustics as a serious branch of fluid mechanics.

In this paper we present a rather personal view of the important developments in double-diffusive convection, a subject whose evolution has been the result of a close interaction between theoreticians, laboratory experimenters and sea-going oceano-graphers. More recently, applications in astrophysics, engineering and geology have become apparent. In the final section we attempt to draw some general conclusions and suggest that further progress will again depend on a close collaboration between fluid dynamicists and other scientists.

Controversies over ‘the momentum’ of waves have repeatedly wasted the time of physicists for over half a century. The persistence of the controversies is surprising, since regardless of whether classical or quantum dynamics is used the facts of the matter are simple and unequivocal, are well checked by laboratory experiment, are clearly explained in several published papers, and on the theoretical side can easily be verified by straightforward calculations. They are illustrated here by some simple, classical examples involving acoustic and gravity waves.

The success of the Journal since it began in 1956 is impressive; its founders would probably never have believed that some 6 metres of shelf would have been covered in 25 years in spite of adopting a sustained critical and selective approach to the acceptance of papers. Yet modified rapture may be in order. Has the Journal been going wholly in the right direction; are we adjusting to the changing nature of technology; do we know where we are going in the future?