A theoretical and experimental investigation of oscillatory flow in curved pipes is presented. The equations for fully developed laminar flow are found to depend on an amplitude parameter G and a frequency parameter α. Initially the Navier–Stokes equations are expanded in terms of G and the resulting linearized equations are solved numerically using finite Hankel integral transforms. A further expansion is used for the case α → 0 and closed-form solutions are presented.

Laser-Doppler anemometry has been used to obtain velocity information in oscillatory air flow in small-diameter curved glass tubes. Using this technique, low-Reynolds-number experiments were carried out and comparison between theory and experiments is presented.

For α [les ] 1 the velocity distributions found are essentially those for steady flow, while for α [ges ] 11·0 the results are not at variance with earlier work. It is for the transition stage between these two regimes that unexpected behaviour is recorded, but a satisfactory explanation is found in terms of general trends within the flow.

The development of a three-dimensional water boundary layer along a heated longitudinal horizontal cylinder is studied by a finite-difference method. The secondary flow is induced in an otherwise axially symmetric laminar boundary layer by the buoyancy force. The development of the boundary layer is studied under two heating conditions: constant wall heat flux and constant wall temperature. In general, close to the leading edge, the magnitude of the secondary flow is small and the boundary-layer flow is forced-convection dominant. The secondary flow grows downstream, and the interaction of the free and forced convection becomes important. The flow becomes free-convection dominant further downstream. The temperature-dependent viscosity of water has the effect of thinning the heated boundary layer. The buoyancy effect and the variable viscosity effect enhance each other over the lower part of the cylinder and compete with each other over the upper part of the cylinder. The numerical results compare with the forced convection dominant asymptotic solution and indicate that the asymptotic solution is only valid when x < 0·1a/ε½. Since the boundary layer is thin compared with the radius of the cylinder, the transverse curvature effect is small and can be neglected. Therefore, the solution can be applied to the entrance region of heated straight pipes as the zeroth-order boundary-layer flow.

Harris, Graham & Corrsin (1977) have measured the properties of the quasi-homo-geneous turbulence field induced by a large mean shear, and in analysing their measurements they neglect the diagonal components of the mean-field contribution to the pressure–strain correlation. Their measurements are re-analysed using the recommendations of Gibson & Launder (1978) for modelling this correlation, the imbalance between production and dissipation being allowed for by the algebraic modelling technique of Rodi (1976): the experimental data give strong support to Rodi's basic assumption.

The data suggest that the only substantial defect in the Gibson–Launder model is its failure to predict the anisotropy measured in the 23 plane normal to the mean flow. The longitudinal predictions are good, and those for the shear (12) component are much improved when measured values of the anisotropy are substituted into the calculation. This analysis does not suggest any clear need for a nonlinear representation of the pressure–strain correlation. However, the most general linear representation of the mean-field term is even more complex than the analysis of Launder, Reece & Rodi (1975) would suggest: their model is disproved by an example.

Attempts to deduce the dissipation directly from the experiments, rather than by energy balance, are not very successful.