Large amplitude short waves confined near the crests of a swell have been observed when a stiff breeze was blowing against the swell. This would seem to imply the existence of both a wavelength-selective generating mechanism and a trapping mechanism, neither of which is to be expected of surface gravity waves of the observed length. It is suggested that there are significant changes in the dynamics of such waves if allowance is made for the dynamic coupling between wind and waves. For a Kelvin-Helmholtz model it is shown that energy transfer rates from the turbulent pressure fluctuations are greatly enhanced for subcritical conditions by the inclusion of the dynamic coupling. The group velocity of subcritical waves is profoundly affected, becoming infinite at the stability boundary. Thus subcritical waves could be trapped on a swell. An examination of the effects of wind shear suggest that Kelvin-Helmholtz type instability could still be present, although for stronger winds, particularly for rather longer waves.

The energy and momentum fed from the mean wind, being trapped at crests of the swell, may contribute significantly to the attenuation of the swell. The profound wave dynamic effects of the coupling between the wind and the swell for short gravity waves may be of significance in other oceanic phenomena, even when the Kelvin-Helmholtz type of instability is not present.

When we look at photographs of real transonic flows which are predicted to be shockless, we find a very large number of weak shocks almost perpendicular to the streamlines. These are no more than almost-trapped upstream-propagating nonlinear waves. In this paper we try to obtain a simple approximate equation which gives their complete history and takes into account both their turning effect, owing to a non-zero gradient of the fluid velocity in a direction normal to the streamlines, and also the finite radius of curvature of the wave front. We first give a brief discussion of a few results which can be easily obtained from the solution of the approximate equation and then compute the history of two nonlinear pulses by numerically integrating the equation.

Measurements of the shear-stress variation along and the velocity profiles above a solid wavy wall bounding a turbulent flow are presented for waves with height-to-length ratios of 2a/λ = 0·0312 and 0·05. These are compared with previous measurements of the wall shear stress reported by Thorsness (1975) and by Morrisroe (1970) for 2a/λ = 0·012. The investigation covered a range of conditions from those for which a linear behaviour is observed to those for which a separated flow is just being initiated.

Pressure measurements indicate a linear response in that the spatial variation is described quite well by a single harmonic with a wavelength equal to that of the surface. However, the variation of τw for waves with 2a/λ = 0·0312 and 0·05 can be more rapid on the leeward side of the wave. The degree of departure from a sinusoidal variation increases with increasing wave height and fluid velocity and, from the results reported in this paper, it is suggested that nonlinear behaviour will become evident when au*/v [ges ] 27.

Many aspects of the flow for all three waves are described by a solution of the linear momentum equations previously presented by Thorsness (1975) and by Thorsness & Hanratty (1977). These include the phase and amplitude of the pressure profile and the first harmonic of the shear-stress profile and the velocity field outside the viscous wall region.

These results suggest that up to separation the flow is approximated quite well by linear theory. Nonlinearities affect the flow only in a region very close to the wave surface and are manifested by the appearance of higher harmonics in the variation of τw.

A series of experiments has been conducted in a low-speed wind tunnel in which measurements were performed in a two-dimensional turbulent shear layer experiencing the mixing of both a passive and a chemically reacting species. The low-temperature air in the jet's primary flow was seeded with dilute concentrations of N2O4 so that the dissociation reaction N2 + N2O4 [harr ] 2NO2 + N2 occurred in a near-equilibrium manner within the mixing layer owing to the turbulent mixing properties and the imposed temperature gradient. Mean and fluctuating values of velocity, temperature and NO2 concentration were measured up to axial distances of 25 in. for jet velocities of 23 and 50ft/s (Rex [les ] 7 × 105) and for three primary temperatures (252, 273 and 305°K). Velocity and temperature measurements were performed with hot-wire probes, whereas a fibre optics light sensor probe was used to measure NO2 concentrations. Local correlations between species and other fluid properties were obtained by positioning a hot-wire sensor within the light gap of the fibre optics probe and simultaneously recording output signals from both probes. A relatively complete set of turbulent statistics was measured for the non-reacting shear layer, including such results as temperature/species correlations, probability densities, filtered and unfiltered moving-frame velocities, skewness and flatness factors, spectra, velocity and temperature integral scales, intermittency factors for velocity, temperature and passive species, and conventional intensities. Some typical results from the investigation are as follows: the turbulent Schmidt and Lewis numbers were 0·5 and 1·0 respectively; the correlation between passive NO2 concentration and temperature was approximately 0·95; dramatic changes consistent with equilibrium chemistry occurred in NO2 concentration profiles with chemical reaction; velocity, temperature and concentration spectra were comparable over a 2½-decade range in wavenumber (k−2); spectra, probability densities, time-trace data and smoke-seeded shear-layer photographs indicate that, for axial locations x = x0 [ges ] 18·5 in. and for speeds u1 [ges ] 23ft/s, undisturbed edge fluid rarely penetrates completely across the mixing region. Although not specifically addressed during the current study, measured results herein suggest that the turbulent motion for the present shear layer is characterized more by random and/or three-dimensionality effects than by large-scale two-dimensional coherent structures, as has been observed recently in other shear-layer investigations.

The problem of Rayleigh-Bénard convection at low Prandtl number σ is investigated in a circular geometry. Jones, Moore & Weiss (1976) have formulated, but not solved analytically, an asymptotic nonlinear problem in the limit σ → 0 at small velocities. It is shown that the problem they posed can be solved exactly in this geometry. The solutions are extended by means of expansions in the amplitude ε and the reciprocal of the Reynolds number σε−1, both assumed small. The problem is related to one that occurs in nonlinear mean-field dynamo theory (Malkus & Proctor 1975) and it is surmised that similar problems may be expected to appear in a variety of physical situations.

Following weak plane shock diffraction at a knife-edge situated in a duct, a two-dimensional vortex sheet springs from the salient edge. The method of ‘vortex discretization’ is used, in conjunction with a Schwarz-Christoffel transformation, to develop a two-dimensional potential model for this constrained form of vortex generation. The analysis is independent of empirical parameters and describes, qualitatively, the pattern of streamlines through the orifice.

Flow-visualization photographs are presented which illustrate the spiral shape of the starting vortex. Although of a limited nature, quantitative experimental vortex growth rates have been obtained and are compared with initial growth rates predicted theoretically. The results are discussed together with other aspects of the problem, including the limitations of the theory.

An extension of vortex discretization is developed whereby the pressure distribution remote from the vortex sheet can be calculated. The combination of flow separation and the associated static wall pressure distribution gives theoretical insight into the mechanism of flow through an orifice.

It is shown that the use of axes moving with the tide (Shinohara et al. 1969) simplifies the analysis of contaminant dispersion in estuaries. Attention is restricted to estuaries which are small in the sense that cross-sectional mixing is rapid and that the tidal elevation can be taken to be constant along the estuary. In agreement with the work of Fischer (1972a, b) it is found that the dominant mechanism for dispersion is the transverse shear and not the vertical shear. Results are presented to illustrate the dependence of the upstream penetration of salt upon the estuary geometry as well as upon the fresh-water discharge rate.

This paper describes an experimental study of a stratified fluid which is flowing over a smooth two-dimensional obstacle which induces no flow separation and in which effects of viscosity and diffusion are not important. The results are restricted to fluid of finite depth. Various properties of the flow field, in particular the criterion for the onset of gravitational instability in the lee-wave field, are measured and compared with the theoretical predictions of Long's model. The agreement is found to be generally poor, and the consequent inapplicability of Long's model is explained by the failure of Long's hypothesis of no upstream influence, which is demonstrably invalid when stationary lee waves are possible. The obstacle generates upstream motions with fluid velocities which appear to be of first order in the obstacle height. These motions have some of the character of shear fronts or columnar disturbance modes and have the same vertical structure as the corresponding lee-wave modes generated downstream. They result in a reduced fluid velocity upstream below the level of the top of the obstacle, together with a jet of increased fluid velocity above this level which pours down the lee side of the obstacle. This phenomenon becomes more pronounced as the number of modes is increased.

The return to isotropy of homogeneous turbulence without mean velocity gradients is attacked by considering changes to be slow relative to turbulence time scales. This single assumption permits the problem to be cast as one of finding the form of three invariant functions. Examination of limiting behaviour for large Reynolds number and small anisotropy, as well as small Reynolds number and arbitrary anisotropy, places restrictions on the form of the functions. Realizability conditions (requiring that energies be non-negative) reduce the problem to two functions subject to further restrictions. A convenient interpolation form is found for the functions, satisfying all the restrictions, and it is shown that predictions based on this are in excellent agreement with all available data.

The purpose of the present study is to assess the possibility of the so-called choking flutter in a transonic cascade operating under choking conditions. In the experiment, measurements of the unsteady aerodynamic moment acting on an aerofoil which is oscillating in pitch about the midchord in a transonic channel flow are performed for channel height-to-chord ratios H/c = 0·5−3 and oscillation frequencies up to 120 Hz. For a large channel height such as H/c = 3, the unsteady aerodynamic behaviour is similar to that of an isolated aerofoil, and the system will be aeroelastically stable in the transonic region as well as in the subsonic one. For smaller channel heights such as H/c = 0·5, however, the flow chokes and the aerodynamic behaviour becomes significantly different from that at large channel heights. As soon as a shock appears, i.e. in the incipient transonic region, the aerodynamic derivatives change discontinuously, so that the subsonic and transonic regions can be clearly separated. In this case, the aerodynamic damping becomes negative in the transonic region.

In order to understand the transonic features, a one-dimensional unsteady analysis is undertaken for small channel heights H/c [les ] 0·5. The numerical results show good qualitative agreement with the experimental ones, predicting in the incipient transonic region a discontinuous variation of the aerodynamic moment which results in system instability.

It is concluded that choking flutter may occur in transonic channel flow with a moderately small channel height when the passage is choked.

From Whitham's ray-shock theory and the Brinkley-Kirkwood theory of shock propagation, a general theory for the propagation of asymmetrical blast waves of arbitrary shapes and strengths is developed in this paper. The general theory requires the simultaneous numerical solution of a set of partial differential equations and a pair of ordinary differential equations. If the shock shape is assumed to be known and remains invariant with time then the geometrical and the dynamical relationships in the theory can be decoupled. In this case the solution simply requires the integration of the ordinary differential equations governing the dynamics of the blast motion since the geometry is already known. As a specific example the asymmetrical blast waves generated by the rupture of a pressurized ellipsoid are studied. The peak pressure is calculated by assuming that the shock surface remains ellipsoidal for all times and that the peak overpressure decay rate of the blast depends on the local curvature. For weak shocks, it is found that the degree of directionality is more pronounced than for stronger shocks. For weak blasts the present theory agrees with the solution based on acoustic theory. Experimental results on the shock trajectories for asymmetrical blast waves generated by exploding wires are found to agree with the present theory.