Arguments are presented to show that the concept of gradient diffusion is inapplicable to mixing in turbulent shear layers. A new model is proposed for treating molecular mixing and chemical reaction in such flows at high Reynolds number. It is based upon the experimental observations that revealed the presence of coherent structures and that showed that fluid elements from the two streams are distributed unmixed throughout the layer by large-scale inviscid motions. The model incorporates features of the strained flame model and makes use of the Kolmogorov cascade in scales. Several model predictions differ markedly from those of diffusion models and suggest experiments for testing the two approaches.

The stability to three-dimensional disturbances of three classical steady vortex configurations in an incompressible inviscid fluid is studied in the limit of small vortex cross-sectional area and long axial disturbance wavelength. The configurations examined are the single infinite vortex row, the Karman vortex street of staggered vortices and the symmetric vortex street. It is shown that the single row is most unstable to a two-dimensional disturbance, while the Karman vortex street is most unstable to a three-dimensional disturbance over a significant range of street spacing ratios. The symmetric vortex street is found to be most unstable to three-dimensional or two-dimensional symmetric disturbances depending on the spacing ratio of the street. Short remarks are made concerning the relevance of the calculations to the observed instabilities in free shear layer, wake and boundary-layer type flows.

Free convective;flow was investigated experimentally in a variety of slender vertical gaps of large horizontal extent. Temperature fields were visualized by holographic real-time interferometry, and local temperatures measured by thermocouples at the lower and upper boundaries of the gap as well as in the fluid. The critical Rayleigh number at the onset of convection was determined for different gap geometries (aspect ratios) and different thermal properties of the sidewalls and the fluid. For supercritical Rayleigh numbers, bounds of stability of steady-state two-dimensional convection were determined for transient and oscillatory states of the flow. The oscillatory flow is caused by an instability of the thermal boundary layers at the lower and upper boundaries, as evidenced by direct interferometric observation and by the measured period of oscillation depending on the Rayleigh number. The oscillations of the flow exhibit a periodic behaviour at the threshold from steady to unsteady flow. However, the periodic character of the oscillations is superseded by stochastic features im- mediately beyond the threshold Rayleigh number.

Experimental studies of the effect of a transverse velocity gradient on the mass transfer between a fixed solid spherical particle and liquid and of the mass-transfer intensity between solid sphere and liquid in a uniform flow have been carried out. Both types of flow were formed between two rotating circular cylinders parallel to each other and separated by a distance of 10mm. The following experimental procedures were applied : a method of stroboscopic visualization to measure velocity profiles, and an electrochemical method to measure the mass-transfer intensity between sphere and liquid. Results were obtained for a wide range of the relevant dimensionless parameters, viz the Reynolds and PBclet numbers specified for each case appropriately. In the case of simple shear flow these ranges are: 0.03 < Re* < 1, 150 < Pe* < 13000, and for the mass-transfer intensity 5 < Nu < 24. It is shown that the experimental data agree fairly well with the approximation formula $Nu = 1.134 Pe^{*\frac{1}{3}}$ obtained theoretically by Batchelor (1979) for an ambient pure straining motion with the assumptions that Re* [Lt ] 1 and Pe* [Gt ] 1. In the case of a uniform flow the ranges of the dimensionless parameters are 0.4 < Re < 20, 3000 < Pe < 40000; and 13 < Nu < 35. The experimental data are here in good agreement with theoretical dependences of the type Nu ∝ Pe1/3 obtained by Aksel'rud (1953) and Acrivos & Taylor (1962).

Energy stability theory has been used to study BBnard convection in one- and two-component horizontal fluid layers heated from below or above when there is a deformable upper surface. To a first approximation in the crispation number, we provide sufficient conditions for stability of the motionless state of the layer, and delineate regions of possible subcritical instability.

High-frequency fluctuations of temperature and of longitudinal and vertical velocity components have been measured with high-resolution probes in order to test the local-isotropy assumption. The simultaneous measurements of u’, w’, θ’ and the measurements in two space points with various separations in either the longitudinal or transverse directions were made in the large boundary layer (Rλ = 616) of the I.M.S.T. Air-Sea Interaction Simulation Tunnel. There is consistent evidence that the local-isotropy assumption is satisfied by the velocity field at all scales smaller than twenty times the Kolmogorov microscale (η ≈ 0.27 × 10−3 m), i.e. in the dissipative range of scales but not in the expected inertial subrange. The direct comparisons of the lateral and longitudinal temperature autocorrelation and structure functions show that the temperature field does not verify the isotropy assumption at all scales greater thanor equal to 37 and presumably at even smaller scales. This is confirmed by the study of the temperature-increment skewness and flatness factors. The spectral distribution -of the non-zero derivative skewness (S(θ) = +0.9) shows that it is essentially contributed by those scales for which the dynamic field satisfies isotropy.

A turbulent field is produced with an oscillating grid in a deep, rotating tank. Near the grid, the Rossby number is kept large, 0(3-33), and the turbulence is locally unaffected by rotation. Away from the grid, the scale of the turbulence increases, the r.m.s. turbulent velocity decreases, and rotation becomes increasingly important. The flow field changes dramatically at a local Rossby number of about 0.20, and thereafter remains independent of depth. The flow consists of concentrated vortices having axes approximately parallel to the rotation axis, and extending throughout the depth of the fluid above the turbulent Ekman layer. The number of vortices per unit area is a function of the grid Rossby number. The local vorticity within cores can be a factor of 50 larger than the tank vorticity 2Ω. The total relative circulation contained in the vortices remains, however, a small fraction of the tank circulation.

The concentrated vortex cores support waves consisting of helical distortions, which travel along the axes of individual vortices. Isolated, travelling waves seem well-described by the vortex-soliton theory of Hasimoto (1972). The nonlinear waves transport mass, momentum and energy from the vigorously turbulent region near the grid to the rotation-dominated flow above. Interactions between waves, which are frequent occurrences, almost always result in a local breakdown of the vortex core, and small-scale turbulence production. Usually the portions of broken core reform within ½−1 rotation periods, but occasionally cores are destroyed and reformed on a much longer timescale.