The decay of two-dimensional, homogeneous, isotropic, incompressible turbulence is investigated both by means of numerical simulation (in spectral as well as in grid-point form), and theoretically by use of the direct-interaction approximation and the test-field model. The calculations cover the range of Reynolds numbers 50 ≤ RL ≤ 100. Comparison of spectral methods with finite-difference methods shows that one of the former with a given resolution is equivalent in accuracy to one of the latter with twice the resolution. The numerical simulations at the larger Reynolds numbers suggest that earlier reported simulations cannot be used in testing inertial-range theories. However, the large-scale features of the flow field appear to be remarkably independent of Reynolds number.

The direct-interaction approximation is in satisfactory agreement with simulations in the energy-containing range, but grossly underestimates enstrophy transfer at high wavenumbers. The latter failing is traced to an inability to distinguish between convection and intrinsic distortion of small parcels of fluid. The test-field model on the other hand appears to be in excellent agreement with simulations at all wavenumbers, and for all Reynolds numbers investigated.

Using the framework of Lighthill's acoustic analogy, a theory has been developed for combustion-generated noise. The theory is used to derive the scaling laws for combustion-generated noise in open turbulent flames. It is shown that the scaling laws for both power and frequency are in good agreement with experiment.

We obtain the solutions, under the Oseen and Boussinesq approximations, for the flow field disturbance due to a line singularity in an otherwise uniform, horizontal, inviscid, incompressible flow of a vertically stratified fluid. The results obtained show no upstream influence for those singularities across which [xdtri ]2ψ + (N/U)2ψ is continuous. Doublet and vortex singularities are examples of these. Uniform flows past doublets and vortices are considered for a range of internal Froude numbers, including the calculation of the pressure distributions and drag for the doublet. An application of the vortex solution to flows in the β-plane is discussed.

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.

This paper deals with a survey of mean flow and fluctuating quantities in a turbulent boundary layer developing on a smooth wall in a pressure domain P(x), where both dP/dx and d2P/dx2 are positive (increasingly adverse). The two-dimensional nature of the flow field was checked by momentum balance, as well as velocity traverses either side of the working section centre-line. Using the integrated form of the momentum integral equation, it was found that the skinfriction term and the summed momentum and pressure terms differed by at most 19%; but for the majority of measuring points they differed by less than 14%. The off-centre-line velocity profiles were indistinguishable from those taken on the centre-line. The flow field was also surveyed for fluctuating components $(\overline{u^2_1})^{\frac{1}{2}}, (\overline{u^2_2})^{\frac{1}{2}}, (\overline{u^2_3})^{\frac{1}{2}}$, and $\overline{u_1u_2}$, as well as for u1 spectra. Wherever possible, the results were compared with existing models of boundary-layer development. These comparisons indicated that the only all-embracing model for boundary-layer development is the law of the wall.

Experimental results are presented for two turbulent boundary-layer experiments conducted at a free-stream Mach number of 4 with wall cooling. The first experiment examines a constant-temperature cold-wall boundary layer subjected to adverse and favourable pressure gradients. It is shown that the boundary-layer data display good agreement with Coles’ general composite boundary-layer profile using Van Driest's transformation. Further, the pressuregradient parameter βK found in previous studies to correlate adiabatic highspeed data with low-speed data also correlates the present cooled-wall high-speed data. The second experiment treats the response of a constant-pressure highspeed boundary layer to a near step change in wall temperature. It is found that the growth rate of the thermal boundary layer within the existing turbulent boundary layer varies considerably depending upon the direction of the wall temperature change. For the case of an initially cooled boundary layer flowing onto a wall near the recovery temperature, it is found that δT ∼ x whereas the case of an adiabatic boundary layer flowing onto a cooled wall gives δT ∼ x½. The apparent origin of the thermal boundary layer also changes considerably, which is accounted for by the variation in sublayer thicknesses and growth rates within the sublayer.

A model is developed for the phenomenon of non-Newtonian secretion in tubes. The motivation for this study is the problem of glandular secretion, particularly in the pancreas. Power-law fluids are considered in some detail, as being biologically appropriate. It is found that for a power-law fluid whose exponent is less than unity (the biological case) two types of flow occur. For a sufficiently high secretion pressure, all of the tube is used for secretion, and a nonlinear pressure profile results. Numerical solutions are obtained for the pressure and rate of efflux. When the secretion pressure parameter falls below a certain critical value, the upper end of the tube begins to be choked off, only part of the tube being used for secretion. This phenomenon does not occur for exponents greater than or equal to unity. Physiological implications are considered, and a qualitative discussion given for the case of non-power-law fluids.

An analysis of two-dimensional steady flow of an incompressible, viscous, electrically conducting fluid past an infinite vertical porous plate is carried out under the following assumptions: (i) that the suction velocity normal to the plate is constant, (ii) that the plate temperature is constant, (iii) that the difference between the temperatures of the plate and the free stream is moderately large, causing free convection currents, (iv) that the transversely applied magnetic field and magnetic Reynolds number are very small and hence the induced magnetic field is negligible.

Approximate solutions to the coupled nonlinear equations governing the steady velocity and temperature are derived. They are shown graphically. During the course of discussion, the effects of positive and negative G (the Grashof number: G > 0 implies cooling of the plate, G < 0 heating of the plate), of P (the Prandtl number), of positive and negative E (the Eckert number) and of M (the magnetic field parameter) are presented quantitatively.

The strength (initial circulation) and spacing of vortices in the wake of a circular cylinder have been obtained for conditions under which the body undergoes lateral vibrations. The vibrations of the cylinder were at all times synchronized with those in the wake, thereby suppressing the natural Strouhal frequency in favour of a common synchronized or ‘locked-in’ frequency for the body-wake system. All experiments were performed at a Reynolds number of 144 or 190. An inverse relation between the initial circulation K and the length lF of the vortex formation region was obtained for cylinder oscillations of up to 50% of a diameter, at vibration frequencies both above and below the Strouhal shedding frequency. The initial circulation K of the vortices was increased by as much as 65%, at lF = 1·6 diameters, from the stationary-cylinder value of K corresponding to lF = 3·2d. An increase in the rate A of vorticity generation of 80% from the stationary-cylinder wake value was obtained with the cylinder vibrating at 30% of a diameter and 110% of the Strouhal frequency. Both flow-visualization and hot-wire results show that the lateral spacing of the vortex street decreases as the vibration amplitude of the cylinder is increased, but that the longitudinal vortex spacing is independent of changes in amplitude. The longitudinal spacing, however, varies inversely with the vibration frequency. The street approaches a single line of vortices of alternating sign as the amplitude of vibration approaches values near a full cylinder diameter, and secondary vortex formation at these large amplitudes is associated with the vanishing lateral spacing of the street. Observation of the wake has elucidated the mechanism of vortex formation; the entrainment processes in the formation region have been observed at small intervals over a cycle of the cylinder's motion.

In this paper an exact formulation of the strength of the disturbance overtaking a shock is presented. The similarity solution is used to find the five interaction terms at all points of the flow. This work confirms that when the strength of the overtaking disturbance is known the CCW approximation may be modified to become an exact theory.

An experimental and theoretical investigation has been carried out to determine the effect of a stable ambient thermal stratification on the developing buoyancyinduced flow adjacent to a flat vertical surface dissipating a uniform heat flux. The nature of the resulting base flow and its instability characteristics, linearized for two-dimensional disturbances, were analysed for Prandtl numbers Pr of 6·7 and 0·733, for several levels of ambient stratification. Stratification was found to cause initial stabilization of the flow but later destabilization downstream. Disturbance growth rates, frequency filtering and amplitude distributions across the boundary region were calculated. These aspects of the disturbance field were measured in a flow generated by an electrically heated metal foil, with artificially introduced two-dimensional disturbances, in water (Pr = 6–7). The experimental results are in very good agreement with the calculations. Measurements of natural transition indicate that a stable ambient stratification delays the onset of transition. A tentative transition-correlating parameter is generalized to include the effect of stratification.

Isothermal Newtonian film flow is put forward as a simple model of the film casting process. Methods of linear hydrodynamic stability theory are applied to study the stability of the film flow. The relevant eigenvalue problems are formulated and solved numerically. Results are presented in the form of neutral-stability curves in the appropriate parameter space. For the case of two-dimensional disturbances stability results obtained here are compared with those of Pearson & Matovich (1969) and Gelder (1971) for the stability of isothermal Newtonian threadline flow.