Mean velocity and turbulent intensity measurements are reported for five different plane turbulent mixing layers, each with a different velocity ratio. These experiments confirm that increasing free-stream turbulence causes increases in the growth rate and in the Reynolds stresses. Cross-correlation measurements with time delay made in the mixing layer with the lowest free-stream turbulence level show that the large-eddy structure had length scales in the two cross-stream directions which were roughly equal, unlike the results reported by Brown & Roshko (1974) and others. Further measurements showed that a vortex-street wake existed immediately downstream of the splitter plate and that transition occurred in the wake flow rather than in a normal laminar mixing layer. This is thought to have prevented the Brown–Roshko structures from forming. Comparison of the growth rate observed in this case with other measured results suggests that the essential or effective turbulent structure in mixing layers is independent both of velocity ratio and of the degree of two-dimensionality which exists in the largest scales of turbulence.

For a steady plane parallel flow of an inviscid incompressible fluid of variable density under gravity, it is shown that the complex wave velocity for any unstable mode lies in a semi-ellipse whose major axis coincides with the diameter of Howard's semicircle, while its minor axis depends on the stratification.

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.

A general linear theory is presented to describe oscillatory flows of gases and liquids in a tube of circular cross-section, including the effects of radial and tangential pressure gradients as well as the temperature. The basic equations are solved by separation of variables. The resulting eigenvalue equation is extensively discussed whereby the splitting of the eigenvalues into ‘bands’ is obtained in a natural way. A systematic analysis of a number of simplified cases leads to analytic approximations for the eigenvalues over an extended domain of parameter variation (frequency, friction) so that a complete survey of all the eigenvalues is established. Then the problem of satisfying simultaneously arbitrary end-conditions for all flow variables with the obtained bands of eigenfunctions is formulated in a way to allow the application of Galerkin's method. Finally the theory is applied to a few examples of ‘end-layers’ and radial resonance, which cannot be treated by previous theories.

This paper reports the results of an experimental investigation to determine transition mechanisms and limits in gases at high pressure levels. We sought also to refine further the parameters for transition, in particular the role of kinematic viscosity. In flow adjacent to a vertical uniform-flux surface in nitrogen, pressures to 16 atm were used. Both mean and disturbance quantities for the temperature and velocity fields were measured for various values of the heat flux, downstream location and ambient pressure level. Hot-wire and fine thermocouple probes were used. We found that the velocity and thermal fields remain closely coupled. Velocity, or fluid-dynamic, transition is immediately followed by thermal transition. Each was detected as a decrease in the rate of increase of both the maximum velocity and the overall temperature difference, respectively, from the laminar downstream trends. Also, the ends of transition for the velocity and the thermal fields, respectively, signalled by no further appreciable change in the intermittency distributions, were simultaneous. These results re-affirm the finding that the events of transition are not correlated by the Grashof number alone. An additional dependence on both downstream location and pressure level arises. A fixed value of the parameter $Q_{BT} = qB^{\frac{2}{15}}= 290$ characterizes the beginning of transition, where q is the fifth root of the local non-dimensional wall heat flux and B is the unit Grashof number. The end of transition, on the other hand, is best correlated by $Q_{ET} = QB^{\frac{1}{30}} = 11.4$, where Q is the fifth root of the local non-dimensional total heat convected in the boundary region. A re-examination of other transition studies, in both gases and liquids, supports these correlations, although many such data were not determined with fast response to local sensors. There remains a small level of uncertainty in establishing exact limits for transition, since the apparently proper standards for determining them are very difficult to apply precisely in experiments. However, such limits are very important in separating regimes of different transport mechanisms.

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.

Flow-visualization experiments for Stokes flow past thin spherical caps show separation from the rims of the caps in agreement with Dorrepaal, O'Neill & Ranger's (1976) theoretical prediction.

Changes in dune properties due to a sudden change in the water discharge are analysed. The transport of sediment is assumed to occur mainly as bed load and the square of the Froude number must be much smaller than unity. The theory is based on similarity in the bed-shear distribution close to the dune top just before and just after the change in the water discharge. The model is found to agree with laboratory experiments. Further, by use of this model, flow in a river where the water discharge oscillates weakly around a constant mean value has been treated. Hereby the variation in the phase differences between sediment transport, water depth and water discharge with the period of the oscillation is calculated. The results agree qualitatively with observations.

Calculations of finite amplitude convection in cubic boxes containing fluid-saturated porous material are reported for Rayleigh numbers R as large as 150. Steady two- or three-dimensional convection can always be forced by appropriate choice of initial conditions. Randomly chosen initial conditions will result in either two- or three-dimensional convection. Although there is a non-uniqueness associated with initial conditions which makes possible either two- or three-dimensional convection, the non-uniqueness is limited in the sense that only one two-dimensional or one three-dimensional solution appears to be realizable. Two-dimensional flows have larger Nusselt numbers than three-dimensional flows for R [lsim ] 97; the opposite is true for R [gsim ] 97.

Two inequalities are proposed for the purpose of bounding from below the mean shear U′o(z) in turbulent channel flow. The first of these inequalities pertains to the energetics of the boundary layer, and the second pertains to the logarithmic form of the asymptote to Uo. These inequalities imply a maximum value of von Kármán's constant, the numerical value of which lies between the measurements of Laufer (1951) and the value obtained from bulk discharge measurements in a pipe. The formalism, which contains no adjustable parameters, is then applied to the turbulent thermal convection problem, and a lower bound for the mean temperature $\overline{T}_o(z)$ is obtained. The minimum value of the latter at large distances from the boundary is in fair agreement with Townsend's (1959) measurements. Although the proposed inequalities have not been deduced from the equations of motion, they provide facts which may be useful in the search for new variational formulations of theturbulent transport problem.

Surface tension provides a restoring force which cannot reasonably be ignored for water waves of short crest-to-crest length. Even for large wavelengths its presence precludes any sharp corner developing on the free surface. In this paper we begin an investigation of the effects of surface tension on steep water waves. The work of Longuet-Higgins (1975) is generalized to show how the integral properties of the wave train are affected. In particular it is shown that for pure capillary waves in deep water the mean fluxes of energy, mass and momentum are given by 3Tc, 2T/c and 4T − V respectively, where c is the phase velocity, T the kinetic energy and V the potential energy.

Also the exact solution for the wave profile of deep-water pure capillary waves (Crapper 1957) is used to obtain wave profiles, all with the same mean level. This yields the unexpected result that the height of the wave crest above the mean level is not a monotonic function of wave steepness.

With subsequent papers this work will form one limiting case of the general problem of deep-water gravity—capillary waves.

By means of similarity principles an analytical solution is constructed for the development of the linear flow field due to the instantaneous application of a constant point force in an infinite liquid. If the force is applied at the origin O and if ν denotes distance from O, ν denotes the coefficient of kinematic viscosity of the fluid and t the time from the application of the force, the solution constructed exhibits the following features. Initially the flow field set up has a dipole structure with centre at O and axis along the direction of the impressed force. At a station r this dipole structure persists so long as 4νt [Lt ] r2. In an axial cross-section the field lines form two sets of closed loops about two stagnation points in the equatorial plane. The stagnation points occur at r = 1.76(νt)½ and thus propagate to infinity with speed 0.88(ν/t)½. The steady state is reached algebraically.

Two integral invariants of Shuto's (1974) generalization of the Korteweg—de Vries equation for a unidirectional wave in a channel of gradually varying breadth b and depth d are derived. The second-order (in amplitude) invariant measures energy, as expected, but the first-order invariant measures mass divided by b½d¼; accordingly, mass is conserved only if either the mean free-surface displacement vanishes or bd½ is constant. This difficulty is associated with the reflected wave that is excited by the channel variation but neglected in the KdV approximation. The total mass flux is resolved into a primary (KdV) flux and a residual flux that is proportional to the mean displacement of the primary wave. The reflected wave associated with the residual flux is constructed by neglecting both nonlinearity and dispersion (even though both are significant for the primary wave). The results are applied to a slowly varying cnoidal wave, which is fully determined by conservation of mass and energy and the known results for a uniform channel, and to a slowly varying solitary wave, for which mass is not conserved and both trailing and reflected residuals are excited. The development of the Boussinesq equations for a gradually varying channel and their reduction to Shuto's equation are sketched in an appendix.