This paper studies several geometric aspects of the Poisson and Gaussian random fields approximating Burgers k−2 and Kolmogorov $k^{-\frac{5}{3}}$ homogeneous turbulence. In particular, simulated sample scalar iso-surfaces (e.g. surfaces of constant temperature or concentration) are exhibited, and their relative degrees of wiggliness are shown to be best characterized by saying that the corresponding fractal dimensions are respectively equal to 3−½ and $3-\frac{1}{3}$.

For incompressible three-dimensional (two-dimensional) turbulence of finite energy, bounds are obtained on energy (enstrophy) flux. To estimate the nonlinear terms, we use a decomposition of the Fourier space into shells of exponentially increasing radii and the property of boundedness in position space of square-integrable functions with Fourier transforms of compact support. In the limit of zero viscosity, it is shown that the three-dimensional (two-dimensional) energy (enstrophy) inertial range, if it exists, cannot have an energy spectrum steeper than $k^{-\frac{8}{3}} (k^{-4})$. Similar results are obtained for the advection of a passive scalar. The connexion with the problem of homogeneous turbulence and intermittency is briefly discussed.

Secular instability of unsteady flow of a horizontal layer of viscoelastic liquid set in motion by simple harmonic motion of the lower boundary in its own plane is investigated. Using an extension of Floquet's theory for ordinary differential equations, the stability of long waves is studied by a regular perturbation method. The elastic parameter of the fluid is found to be destabilizing and stabilizing in different ranges of frequency.

The paper studies convection in a horizontal layer of fluid rotating about a vertical axis. The flows at large Rayleigh number R, with a single horizontal wave-number, are investigated using the mean-field approximation of Herring (1963). The flow that maximizes the heat flux is the same as that which gives an upper bound to the heat flux in the limit of infinite Prandtl number as calculated by the methods of Howard (1963) and Chan (1971, 1974).

Rotation is not significant until the Taylor number Ta exceeds O(R). For $O(R) \ll Ta \ll O[(R\log R)^{\frac{4}{3}}]$, it can increase the rate of heat transfer, a phenomenon noted experimentally by Rossby (1969). It does so because an Ekman layer is formed outside the thermal boundary layer, causing a thinning of the thermal layer. The maximum value of the Nusselt number N is approximately $0.177R^{\frac{1}{5}} Ta^{\frac{1}{10}}[\log Ta]^{\frac{1}{5}}$. As the Taylor number increases further into the region $O[(R\log R)^{\frac{4}{3}}] \ll Ta \ll O(R^{\frac{3}{2}})$, the maximum value of N drops sharply, and becomes approximately $0.029 R^{\frac{3}{2}} Ta^{-1} \log(R^{\frac{3}{2}}/Ta)$. Hence, N now decreases with a further increase of Ta and eventually becomes O(1) as $Ta\rightarrow O(R^{\frac{3}{2}})$ and the layer becomes stable.

Measurements of velocity fluctuations u (axial) and v (radial) and temperature fluctuations θ averaged over the turbulent zone have been made in a turbulent heated jet with a co-flowing stream and compared with the conventionally averaged results. The zone-averaged mean temperature and temperature fluctuation intensity appear to be nearly homogeneously distributed in the outer, intermittent region of the jet. This homogeneity does not apply to the u and v fluctuations. The flatness factor of the temperature within the turbulent part of the flow is remarkably constant throughout the intermittent region. Although the skewness of the turbulent θ fluctuations is non-zero, it is smaller than the skewness of the turbulent u and v fluctuations. The average $\overline{\theta v}$ of the heat flux over the turbulent zone increases in the intermittent region whereas the zone-averaged momentum flux $\overline{uv}$ and zone-averaged heat flux $\overline{\theta u}$ continuously decrease. This leads to the Prandtl number of the turbulent fluid being smaller than the conventional Prandtl number in the outer part of the flow. A budget for the square of the temperature fluctuations within the turbulent part of the flow indicates a constant distribution of temperature dissipation. The transport of heat by the large-scale structure of the flow is briefly discussed in the light of available experimental information on other turbulent shear flows.

A flow of an electrolyte in a seventy-diameter length of round pipe is subjected to a two-dimensional electric current and magnetic field which give a controllable streamwise electromagnetic body force. As the body-force distribution is axisymmetric and the effects of induced currents are negligible the fully developed pipe flow is axisymmetric and longitudinally homogeneous, but it can have severely distorted mean velocity and turbulence profiles. Measurements of the mean velocity and turbulence intensity are presented for different levels of distortion and the results are discussed with reference to classical turbulence theories. The inadequacy of these theories is thus demonstrated. The extra degree of freedom provided by the body force combines with the relative simplicity of the fully developed flow to give a useful tool for investigating the nature of shear-flow turbulence and for studying the assumptions involved in analytical approaches. The technique also produces distorted laminar pipe flows with inflexion-point velocity profiles, which are of interest in stability studies.

Brownian motion of particles suspended in a fluid is studied, and expressions derived for the particle diffusivity and velocity autocorrelation function. The theory of thermal noise in a general linear system is applied to both the particles and the fluid in a novel formulation. This enables the recent modification of the Langevin equation to include the effect of fluid inertia to be seen as just a necessary but simple reinterpretation of the original analysis, without introducing the theory of non-Markovian processes.

A series of experiments designed to measure the wave resistance of an accelerating two-dimensional air-cushion vehicle is described. A model was towed at a constant acceleration from rest over water of various depths. In addition, the effects of different levels of acceleration and different cushion pressures were examined. The results are compared with linearized potential-flow theory and show particularly encouraging agreement. The predicted humps and hollows in the curve of wave resistance vs. time are verified, but with a small shift with respect to time. Also, the theoretical region of negative wave resistance in water of finite depth is demonstrated.

Normal and tangential resistance coefficients are calculated for a rigid slender body close to a planar no-slip boundary or midway between and close to two such boundaries. The important length scale is found to be the separation distance from the boundaries, and the forces per unit length acting on the slender body are approximately constant along most of its length. Owing to the presence of the walls, the ratio of the normal and tangential resistance coefficients can be greater than 2, its maximum limiting value in the infinite-fluid case. Applications to the movements of flagellated micro-organisms are discussed.

A description is given of the high Reynolds number (R [Gt ] 1) laminar fluid motion in the neighbourhood of the trailing edge of a flat plate undergoing small amplitude sinusoidal oscillations in a uniform supersonic stream. It is shown that for oscillations of frequency ω* = O(R¼) and amplitude h* = O(R−½) a rational description of the flow at the trailing edge is based on a ‘triple-deck’ structure, which is a familiar feature of steady trailing-edge flows. The theory may be extended in a straightforward manner to include slow oscillations of the plate, and it is shown in general that the occurrence of separation at the trailing edge is dependent upon the magnitude of the product of the frequency and amplitude of oscillation, and that if ω* [les ] O(R½) then the flow is maintained right up to the trailing edge provided that h*ω* [Lt ] R−¼. The precise condition for the occurrence of separation is found for frequencies in the range ω* R−¼.

Experiments with a rotating source-sink annulus have shown that hot-wire probe supports can give rise to low-wavenumber, azimuthally propagating disturbances. These have been observed by a number of workers, and interpreted as Ekman boundary-layer instabilities and inertial eigenmodes of the annulus. The waves are associated with the wake downstream from the probe support; and a simplified model of the wake instability in cylindrical coordinates is presented. This model has a number of features in common with the observed disturbances. Extensive data have been obtained on wave frequencies and magnitudes, wavenumbers and phase relationships, and on wake structure and onset of the disturbances. The results of hot-wire anemometry experiments in an annulus are discussed in light of the present findings. It is concluded that the wave motions interpreted as type-II (class-A) Ekman instabilities and inertial eigenmodes by Tatro & Mollo-Christensen (1967) were probe-associated disturbances, while the boundary-layer waves observed by Caldwell & Van Atta (1970) were type-II disturbances, similar to those observed by Faller & Kaylor (1966a) using dye techniques.