It is shown that the pressure and velocity fluctuations of the unsteady motion on a transversely sheared mean flow can be expressed entirely in terms of the derivatives of two potential functions. One of these is a convected quantity (i.e. it is frozen in the flow) that can be specified as a boundary condition and is related to a transverse component of the upstream velocity field. The other can be determined by solving an inhomogeneous wave equation whose source term is also a convected quantity that can be specified as a boundary condition in any given problem. The latter is related to the curl of the upstream vorticity field. The results are used to obtain an explicit representation of the three-dimensional gust-like or hydrodynamic motion on a transversely sheared mean flow. It is thereby shown that this motion is ‘driven’ entirely by the two convected quantities alluded to above.

The general theory is used to study the interaction of an unsteady flow with a scmi-infinite plate embedded in a shear layer. The acoustic field produced by this interaction is calculated in the limits of low and high frequency. The results are compared with experimental one-third octave sound pressure level radiation patterns. The agreement is found to be excellent, especially in the low frequency range, where the mean-flow and convective effects are shown to have a strong influence on the directivity of the sound.

Mean velocity profiles, turbulence intensity distributions and streamwise energy spectra are presented for turbulent air flow in a smooth-walled, high aspect ratio rectangular duct with small streamwise curvature, and are compared with measurements taken in a similar straight duct.

The results for the present curved flow are found to differ significantly from those for the more highly curved flows reported previously, and suggest the need to distinguish between ‘shear-dominated’ flows with small curvature and ‘inertia-dominated’ flows with high curvature. Velocity defect and angular-momentum defect hypotheses fail to correlate the central-region mean flow data, but the wall-region data are consistent with the conventional straight-wall similarity hypothesis. A secondary flow of Taylor–Goertler vortex pattern is found to occur in the central flow region.

An examination of the flow equations yields a model for the mechanisms by which streamline curvature affects turbulent flow, in which a major effect is a direct change in the turbulent shear stress through a conservative reorientation of the turbulence intensity components. Data for the streamwise and transverse turbulence intensities show behaviour consistent with that expected from the equations, and the distribution of total turbulence energy in the central flow region is found to be nearly invariant with Reynolds number and wall curvature, in agreement with the model.

Energy spectra for the streamwise component are examined in terms of a Townsend-type two-component turbulence model. They indicate that a universal, ‘active’ component exists in all flow regions, with an ‘inactive’ component which affects only the low wavenumber spectra intensities. This is taken to imply that the effects of streamline curvature are determined by the central-region flow structure alone.

Measurements are presented of the fluctuating pressure recorded at a point 90° from the mean position of the forward stagnation point on a circular cylinder oscillating in a water flow. The aspect ratio of the cylinder was 9·5 and the turbulence level in the free-stream was 5·5%. The cylinder Reynolds number was 2·4 × 104 and the cylinder was forced to oscillate transverse to the main flow at amplitudes up to 1·33 cylinder diameters. The reduced velocity was varied over the range 3–18 and the experiments spanned the vortex-shedding lock-in range. Measurements of phase difference between pressure and displacement show that the maximum out-of-phase lift force occurs at an amplitude of about half a diameter. Good agreement is found between measurements on forced and freely oscillating cylinders. A simple potential-flow model gives reasonable predictions of the pressure fluctuations at the body frequency and at twice the body frequency at reduced velocities away from lock-in.

A combined experimental and theoretical investigation was conducted on the shock-tube side-wall ionizing boundary-layer induced by a shock wave moving into argon. The dual-wavelength interferometric boundary-layer data were obtained by using a 23 cm diameter Mach—Zehnder interferometer with the 10 × 18 cm Hypervelocity Shock Tube at initial shock Mach numbers of 13 and 16, an initial pressure of 5 torr and a temperature of 300° K. The plasma density and electron number density in the boundary layer were measured and compared with numerical profiles obtained by using an implicit finite-difference scheme for a two-temperature, chemical non-equilibrium, laminar boundary-layer flow in ionizing argon. The analysis included the variations of transport properties based on elastic-scattering cross-sections, effects of chemical reactions, radiation-energy losses and electron-sheath wall boundary conditions. Considering the difficulties involved in such complex plasma flows, satisfactory agreement was obtained between the analyses and experiments. A comparison was made with the flat-plate case and despite the very different velocity boundary conditions at the wall for the two flows the experimental data appear to be quite similar. The experimental bump in the profile of electron number density which was found in the flat-plate case was not found in the side-wall case. Comparisons and discussions of the results for the different types of boundary layer are presented, including a comparison between experimentally derived and analytical plasma-temperature profiles.

The distribution of vorticity in the wake of a hovering bird or insect is considered. The wake is modelled by a chain of coaxial small-cored circular vortex rings stacked one upon another; each member of the chain is generated by a single wing-stroke. Circulation is determined by the animal's weight and the time for which a single ring must provide lift; ring size is calculated from the circulation distribution on the animal's wing. The theory is equally applicable to birds and insects, although the mechanism of ring formation differs. This approach avoids the use of lift and drag coefficients and is not bound by the constraints of steady-state aerodynamics; it gives a wake configuration in agreement with experimental observations. The classical momentum jet approach has steady momentum flux in the wake, and is difficult to relate to the wing motions of a hovering bird or insect; the vortex wake can be related to the momentum jet, but adjacent vortex elements are disjoint and momentum flux is periodic.

The evolution of the wake starting from rest is considered by releasing vortex rings at appropriate time intervals and allowing them to interact in their own velocity fields. The resulting configuration depends on the feathering parameter f (which depends on the animal's morphology); f increases with body size. At the lower end of the wake rings coalesce to form a single large vortex, which breaks away from the rest of the wake at intervals. Wake contraction depends on f; the minimum areal contraction of one-half (as in momentum-jet theory) occurs only in the limit f → 0, but values calculated for smaller insects of just over one-half suggest that the momentum jet may be a good approximation to the wake when f is small.

Induced power in hovering is calculated as the limit of the mean rate of increase of wake kinetic energy as time progresses. It can be related to the classical momentum-jet induced power by a simple conversion factor. For an insect or hummingbird the usual momentum-jet estimate may be between 10 and 15% too low, but for a bird it may be as much as 50% too low. This suggests that few, if any, birds are able to sustain aerobic hovering, and that as small a value of f as possible would be necessary if the bird were to hover.

Tip losses (energy cost of the vortex-ring wake compared with the equivalent momentum jet) are negligible for insects, but can be in the range 15–20% for birds.

The vortex wake of a bird in steady forward flight is modelled by a chain of elliptical vortex rings, each generated by a single downstroke. The shape and inclination of each ring are determined by the downstroke geometry, and the size of each ring by the wing circulation; the momentum of the ring must overcome parasitic and profile drags and the bird's weight for the duration of a stroke period. From the equation of motion it is possible to determine exactly the kinematics of the wing-stroke for any flight velocity. This approach agrees more readily with the nature of the wing-stroke than the classical actuator disk and momentum-jet theory; it also dispenses with lift and induced drag coefficients and is not bound by the constraints of steady-state aerodynamics. The induced power is calculated as the mean rate of increase of wake kinetic energy. The remaining components of the flight power (parasite and profile) are calculated by traditional methods; there is some consideration of different representations of body parasite drag. The lift coefficient required for flight is also calculated; for virtually all birds the lift coefficient in slow flight and hovering is too large to be consistent with steady-state aerodynamics.

A bird is concerned largely to reduce its power consumption on all but the shortest flights. The model suggests that there are a number of ways in which power reduction can be achieved. These various strategies are in good agreement with observation.

An extension of the model first proposed by Baines & Turner (1969) is derived with careful attention to the conditions required for its application. The most important of these are that the Prandtl number ν/k is of order unity or greater, the ratio of the length L to depth H of the region is greater than about 1·2 for the two-dimensional region considered and R is so large that R [gsim ] L/H and R [Gt ] 1/α. The characteristic group \[ R\equiv \alpha^{\frac{2}{3}}F_0^{\frac{1}{3}}H/\nu. \]R2 is a Grashof number based on the source strength F0 of the buoyant convection which is modelled using turbulent plume theory and the entrainment constant α, the ratio of inflow velocity across the edge of the plume to mean local plume velocity. The conditions on R ensure that the source of buoyant convection is the dominant transportive mechanism in the region and the restrictions on the aspect ratio ensure that there is clear separation between the passive motions in the bulk of the region and the intense highly confined buoyant convection.

The manner in which the convective fluid recirculates to become part of the passive interior is studied and shown to be controlled by the same dynamics as fluid intrusion into a stably stratified environment.

Several new solutions are obtained, including cases of steady conditions involving only one source.