The frequency and amplification rates for a disturbance growing with respect to time are compared with those of a spatially-growing wave having the same wave-number. For small rates of amplification it is shown that the frequencies are equal to a high order of approximation, and that the spatial growth is related to the time growth by the group velocity.

Coherent axisymmetric structures in a turbulent jet are modelled as linear instability modes of the mean velocity profile, regarded as the profile of a, fictitious laminar inviscid flow. The usual multiple-scales expansion method is used in conjunction with a family of profiles consistent with similarity laws for the initial mixing region and approximating the profiles measured by Crow & Champagne (1971), Moore (1977) and other investigators, to deal with the effects of flow divergence. The downstream growth and approach to peak amplitude of axisymmetric wave modes with prescribed real frequency is calculated numerically, and comparisons are made with various sets of experimental data. Excellent agreement is found with the wavelength measurements of Crow & Champagne. Quantities such as the amplitude gain which depend on cumulative effects are less well predicted, though the agreement is still quite tolerable in view of the facts that this simple linear model of slowly diverging flow is being applied far outside its range of strict validity and that many of the published measurements are significantly contaminated by nonlinear effects. The predictions show that substantial variations are to be expected in such quantities as the phase speed and growth rate, according to the flow signal (velocity, pressure, etc.) measured, and that these variations depend not only on the axial measurement location but also on the cross-stream position. Trends of this kind help to explain differences in, for example, the preferred Strouhal number found by investigators using hot wires or pressure probes on the centre-line, in the mixing layer or in the near field.

The large-scale structures that occur in a forced turbulent mixing layer at moderately high Reynolds numbers have been modelled by linear inviscid stability theory incorporating first-order corrections for slow spatial variations of the mean flow. The perturbation stream function for a spatially growing time-periodic travelling wave has been numerically evaluated for the measured linearly diverging mean flow. In an accompanying experiment periodic oscillations were imposed on the turbulent mixing layer by the motion of a small flap at the trailing edge of the splitter plate that separated the two uniform streams of different velocity. The results of the numerical computations are compared with experimental measurements.When the comparison between experimental data and the computational model was made on a purely local basis, agreement in both the amplitude and phase distribution across the mixing layer was excellent. Comparisons on a global scale revealed, not unexpectedly, less good accuracy in predicting the overall amplification.

The stability of small travelling-wave disturbances in the flow over a flat plate is discussed. An iterative method is used to generate an asymptotic series solution in inverse powers of the Reynolds number Rx = Ux/v to the power one half. The neutral-stability boundaries given by the first two terms of this series are obtained and compared with experimental data. It is shown that the parallel flow approximation leads to a valid solution at very large Reynolds numbers.

Water-tunnel experiments on two cones of taper ratio 36:1 and 18:1 have shown that the frequency of vortex shedding is controlled by the local diameter and has a value which is slightly lower than that on a parallel cylinder of the same size. The shedding process is modulated by a low-frequency oscillation which has a frequency dependent only on U2/v and is independent of any physical dimension of the model. A mathematical analogue of the wake, which helps to explain these features of the flow, has been constructed. The pattern of vortices in the wake of a cone suggested by this model is in reasonable agreement with the photographic evidence.

No abstract

Betchov and Criminale found certain singularities in the eigenvalue relations for the combined stability problem in space and time. It is shown why these singularities must occur, and how they influence the perturbation generated by a pulse.

Experiments on slightly tapered models of circular cross-section have shown that the vortex wake structure exists in a number of discrete cells having different shedding frequencies. Within each cell shedding is regular and periodic, the frequency being somewhat lower than that from a parallel cylinder of the same diameter. A similar type of wake behaviour has also been observed on a parallel model in a non-uniform mean flow. These results suggest that the discontinuities in the shedding law observed by Tritton could arise through non-uniformities in the flow.