Material lines and surfaces transported in a random velocity field undergo bending and stretching. In this paper we investigate the time evolution of curvature in line and surface elements both analytically and by numerical simulation for a simple model turbulence. Our analysis is close to that of Pope (1988) for the evolution of curvature in surface elements. We show that the equation governing the evolution of curvature in a line element is very similar to that governing the evolution of the principal curvature in a surface patch. We investigate the circumstances in which the effect of straining fluctuations is to cause the exponential rate of growth of curvature discovered by Pope et al. (1989). Our simulation confirms that the presence of helicity in the turbulent flow results in the development of a non-vanishing mean torsion in a line element. The results of the simulation also suggest that the generation of curvature tends to occur in regions different from those associated with rapid stretching. The generation of torsion, however, is found not to be correlated with either bending or stretching.

Turbulent boundary-layer fluctuations in the incompressive domain are expressed in terms of fluctuating velocity-product 'sources’ in order to elucidate relative characteristics of fluctuating wall-shear stress and pressure in the subconvective range of streamwise wavenumbers. Appropriate viscous wall conditions are applied, and results are obtained to lowest order in this Strouhal-scaled wavenumber which serves as the expansion parameter. The spectral amplitudes of pressure and of the shear stress component directed along the wavevector both contain additive terms proportional to source integrals with exponential wall-distance weighting characteristic respectively of the irrotational and the rotational fields. At low wavenumbers, barring unexpected relative smallness of the pertinent boundary-layer source term, the rotational terms become dominant. There the wall pressure and shear-stress component have spectra that approach the same non-vanishing, wavevector-white but generally viscous-scale-dependent level and are totally coherent with phase difference ½π. The other, irrotational contributions to the shear-stress and pressure amplitudes likewise bear a simple and previously known, generally wavevector– and frequency-dependent, ratio to one another. In an inviscid limit this contribution to the pressure amplitude reduces to the one obtained previously from inviscid treatments. A representative class of models is introduced for the source spectrum, and the resulting rotational contribution to the spectral density of wall pressure and K-aligned shear stress at low (but incompressive) wavenumbers is estimated. It is suggested that this contribution may predominate and account for measured low-wavenumber levels of wall pressure.

A detailed numerical study of two-dimensional flow past a circular cylinder at moderately low Reynolds numbers has been conducted using three different numerical algorithms for solving the time-dependent compressible Navier–Stokes equations. It was found that if the algorithm and associated boundary conditions were consistent and stable, then the major features of the unsteady wake were well predicted. However, it was also found that even stable and consistent boundary conditions could introduce additional periodic phenomena reminiscent of the type seen in previous wind-tunnel experiments. However, these additional frequencies were eliminated by formulating the boundary conditions in terms of the characteristic variables. An analysis based on a simplified model provides an explanation for this behaviour.

The transition process of a small-amplitude wave packet, generated by a controlled short-duration air pulse, to the formation of a turbulent spot is traced experimentally in a laminar boundary layer. The vertical and spanwise structures of the flow field are mapped at several downstream locations. The measurements, which include all three velocity components, show three stages of transition. In the first stage, the wave packet can be treated as a superposition of two- and three-dimensional waves according to linear stability theory, and most of the energy is centred around a mode corresponding to the most amplified wave. In the second stage, most of the energy is transferred to oblique waves which are centred around a wave having half the frequency of the most amplified linear mode. During this stage, the amplitude of the wave packet increases from 0.5 % to 5 % of the free-stream velocity. In the final stage, a turbulent spot develops and the amplitude of the disturbance increases to 27 % of the free-stream velocity.

Theoretical aspects of the various stages are considered. The amplitude and phase distributions of various modes of all three velocity components are compared with the solutions provided by linear stability theory. The agreement between the theoretical and measured distributions is very good during the first two stages of transition. Based on linear stability theory, it is shown that the two-dimensional mode of the streamwise velocity component is not necessarily the most energetic wave. While linear stability theory fails to predict the generation of the oblique waves in the second stage of transition, it is demonstrated that this stage appears to be governed by Craik-type subharmonic resonances.

The starting flows past a two-dimensional NACA 0012 airfoil translating and oscillating at large incidences are investigated by visualization experiments and numerical calculations. The airfoil model is set in motion impulsively and subjected simultaneously to a constant translation and harmonic oscillation in pitch. The evolution of the vortex wake is followed in a sequence of streamline visualizations and the wake pattern generated is analysed. The parameters varied in the visualization experiment are the Reynolds number ranging from 1500 to 10000, the reduced frequency from 0.1 to 1.0, the mean incidence 30° or 15° and the angular amplitude 15° or 7°. There are also two additional parameters of special interest: the airfoil cross-section and the pitching axis. The effects of these parameters are discussed in relation to the resultant wake patterns. Some comparison is made with the results of earlier experiments.

This paper deals with initial-value problems for the Burgers equation with the inclusion of a hereditary integral known as the fractional derivative of order ½. Emphasis is placed on the difference between the local and global dissipation due to the second-order and the half-order derivatives, respectively. Exploiting the smallness of the coefficient of the second-order derivative, an asymptotic analysis is first developed. When a discontinuity appears, the matched-asymptotic expansion method is employed to derive a uniformly valid solution. If the coefficient of the half-order derivative is also small, as is usually the case, the evolution comprises three stages, namely a lossless near field, an intermediate Burgers region, and a hereditary far field. In view of these results, the equation is then solved numerically, under various initial conditions, by finite-difference and spectral methods. It is revealed that the effect of the fractional derivative accumulates slowly to give rise to a significant dissipation and distortion of the waveform globally, which is to be contrasted with the effect of the second-order derivative, significant only locally, in a thin 'shock layer’.

Numerical solutions are presented for steady two-dimensional incompressible flow past an infinite row of cylinders (of unit radii, with distances W between their centres). The calculations cover R [les ] 700 for 5 [les ] W [les ] ∞ and also R = 800 for 5 [les ] W [les ] 100 (where R denotes the Reynolds number based on the cylinder diameters). The recirculation regions (wake bubbles) are found to grow in length approximately linearly with R in all cases. For high values of R, a major change occurs in their character when W is increased past Wcrit ≈ 16. While they have remained slender up to this point (essentially only stretching in length in proportion to R), their centres of circulation have moved towards their ends. As W is further increased, the wake bubbles widen rapidly, beginning from the rear of the wakes. In the limit of W→∞, the present results agree with the previous ones for a single cylinder as reported by Fornberg (1985).

The early motion of a single vortex suddenly placed near a free surface is studied analytically. The general initial/boundary-value problem is solved in terms of a Taylor expansion in time. The vortex position and the surface elevation are determined to third order. We find a precise distinction between subcritical (weak) and supercritical (strong) vortices. All vortices start with retrograde horizontal motion. After a short time, subcritical vortices tend to turn and continue their motion in the prograde direction. Supercritical vortices cannot turn, but will continue their retrograde motion. They will accumulate a surface mound until surface breaking eventually occurs.

This first Euromech Colloquium to be held in Kiev attracted 74 participants including 19 from outside the USSR: from Austria, Bulgaria, France, Germany, Italy, Japan, Norway, Poland, Portugal and the United Kingdom. Despite unexpected absences or delays for some participants due to travel difficulties, a full programme of talks, each followed by a lively discussion, was maintained throughout the entire three and a half days of the Colloquium. In addition considerable space was set aside for posters, which ensured that the discussions were not confined to the lecture theatre. The colloquium was dominated by two major areas of interest: scattering of acoustic waves by elastic shells or bodies, and problems of surface gravity-wave diffraction. Also presented was a selection of widely varying topics within the general area of wave diffraction. A summary of the presented talks is given below.