A tensorially consistent near-wall second-order closure model is formulated. Redistributive terms in the Reynolds stress equations are modelled by an elliptic relaxation equation in order to represent strongly non-homogeneous effects produced by the presence of walls; this replaces the quasi-homogeneous algebraic models that are usually employed, and avoids the need for ad hoc damping functions. A quasi-homogeneous model appears as the source term in the elliptic relaxation equation-here we use the simple Rotta return to isotropy and isotropization of production formulae. The formulation of the model equations enables appropriate boundary conditions to be satisfied.

The model is solved for channel flow and boundary layers with zero and adverse pressure gradients. Good predictions of Reynolds stress components, mean flow, skin friction and displacement thickness are obtained in various comparisons to experimental and direct numerical simulation data.

The model is also applied to a boundary layer flowing along a wall with a 90°, constant-radius, convex bend. Because the model is of a general, tensorially invariant form, special modifications for curvature effects are not needed; the equations are simply transformed to curvilinear coordinates. The model predicts many important features of this flow. These include: the abrupt drop of skin friction and Stanton number at the start of the curve, and their more gradual recovery after the bend; the suppression of turbulent intensity in the outer part of the boundary layer; a region of negative (counter-gradient) Reynolds shear stress; and recovery from curvature in the form of a Reynolds stress ‘bore’ propagating out from the surface. A shortcoming of the present model is that it overpredicts the rate of this recovery.

A heat flux model is developed. It is shown that curvature effects on heat transfer can also be accounted for automatically by a tensorially invariant formulation.

The properties of two-dimensional steady periodic interfacial gravity waves between two fluids in relative motion and of constant vorticities and finite depths are investigated analytically and numerically. Particular attention is given to the effect of uniform vorticity, in the presence of a current velocity, on the two factors (identified in the literature as dynamical and geometrical limits) which limit the existence of steady gravity wave Solutions. The dynamical limit to the existence of steady Solutions is found to be significantly influenced by the uniform vorticity of the lower fluid. In particular, the effect of non-zero vorticity is qualitatively different between a very shallow and a relatively deep lower fluid. Profiles and flow fields corresponding to very steep waves are calculated for a wide range of parameter values. The effect of uniform vorticity on the interfacial wave structure is demonstrated through a direct comparison with irrotational waves. For negative vorticity and high current velocity, a new flow structure is found, consisting of a closed eddy attached to the interface below the crest. Resemblance with shallow water waves breaking under strong air flow, (described in the experimental literature as roll waves) is noted.

This paper is a description of an experimental study of round, turbulent jets and plumes, investigating the effects of buoyancy on the fractal structure. The jets and plumes are formed by injecting fluid from a small source, with diameter, d, of 0.508 mm, into a stationary body of water contained in a tall tank of dimensions 1.75 m high by 0.6 m by 0.6 m. For both jets and plumes the Reynolds number at the source was in the range 800 to 1800, and the flow was observed in the far field at distances 250d to 550d. In the case of the plumes momentum still dominated near the source so that the flow was fully turbulent before buoyancy forces had a significant effect. The source fluid was dyed with fluorescein, and the flow was illuminated by a ‘thick’ sheet of light (thick in the sense of many Kolmogorov scales) effectively giving a projection rather than a true two–dimensional slice. The fractal dimensions of contours of concentration on this projection were measured, with care taken to normalize with respect to the local intensity and lengthscales. There were no significant differences in the results for jets and plumes, so the smaller scales of motion seem unaffected by the presence of buoyancy forces, The fractal dimension was found and to be a function of threshold intensity, with an apparent minimum of 1.23. This may be an artefact of the noise level, however, and an estimated value for the zero–intensity threshold of 1.16 may be important, though the use of a single value for the fractal dimension is questionable. The implications of the results for measurements where no account has been taken of local scales is discussed.

An analysis is made of solute transport through a fluid within a long, but finite, channel or pipe whose walls remain parallel but oscillate transversely. When the fluid is viscous, the wall motion causes steady Streaming. Axial dispersion of solute is calculated over a wide parameter range, and mean longitudinal transport is found to be greatly enhanced when the steady-streaming Reynolds number is much greater than unity. The results are applied to low-volume high-frequency Ventilation of the human lung.

We investigate, using theoretical and computational techniques, the processes that lead to the drag force on a rigid surface that has two—dimensional undulations of length L and height H (with H/L [Lt ] 1) caused by the flow of a turbulent boundary layer of thickness h. The recent asymptotic analyses of Sykes (1980) and Hunt, Leibovich & Richards (1988) of the linear changes induced in a turbulent boundary layer that flows over an undulating surface are extended in order to calculate the leading-order contribution to the drag. It is assumed that L is much less than the natural lengthscale h* = hU0/u* over which the boundary layer evolves (u* is the unperturbed friction velocity and U0 a mean velocity scale in the approach flow). At leading order, the perturbation to the drag force caused by the undulations arises from a pressure asymmetry at the surface that is produced by the thickening of the perturbed boundary layer in the lee of the undulation. This we term non-separated sheltering to distinguish it from the mechanism proposed by Jeffreys (1925). Order of magnitude estimates are derived for the other mechanisms that contribute to the drag; the next largest is shown to be smaller than the non-separated sheltering effect by O(u*/U0). The theoretical value of the drag induced by the non-separated sheltering effect is in good agreement with both the values obtained by numerical integration of the nonlinear equations with a second-order-closure model and experiments. Although the analytical solution is developed using the mixing-length model for the Reynolds stresses, this model is used only in the inner region, where the perturbation shear stress has a significant effect on the mean flow. The analytical perturbation shear stresses are approximately equal to the results from a higher-order closure model, except where there is strong acceleration or deceleration. The asymptotic theory and the results obtained using the numerical model show that the perturbations to the Reynolds stresses in the outer region do not directly contribute a significant part of the drag. This explains why several previous analyses and computations that use the mixing-length model inappropriately throughout the flow lead to values of the drag force that are too large by up to 100%.

Recently it has been demonstrated that three-dimensionality can play an important role in dictating the stability of any Görtler vortices which a particular boundary layer may support. According to a linearized theory, vortices within a high Görtler number flow can take one of two possible forms within a two-dimensional flow supplemented by a small crossflow of size O(Re-½G⅗), where Re is the Reynolds number of the flow and G the Görtler number. Bassom & Hall (1991) showed that these forms are characterized by O(1)-wavenumber inviscid disturbances and larger $O(G^{\frac {1}{5}})$-wave-number modes which are trapped within a thin layer adjacent to the bounding surface. Here we concentrate on the latter, essentially viscous, vortices. These modes are unstable in the absence of crossflow but the imposition of small crossflow has a stabilizing effect. Bassom & Hall (1991) demonstrated the existence of neutrally stable vortices for certain crossflow/wavenumber combinations and here we describe the weakly nonlinear stability properties of these disturbances. It is shown conclusively that the effect of crossflow is to stabilize the nonlinear modes and the calculations herein allow stable finite-amplitude vortices to be found. Predictions are made concerning the likelihood of observing some of these viscous modes within a practical setting and asymptotic work permits discussion of the stability properties of modes with wavenumbers that are small relative to the implied $O(G^{\frac {1}{5}})$ scaling.

A study has been made of the instability and the subsequent breakdown of axisymmetric jets of helium/air mixtures emerging into ambient air. Although the density of the nozzle gas is less than that of the ambient fluid, the jet is essentially non-buoyant. Two kinds of instability are observed in the near field, depending upon the mean flow parameters. When the ratio of the exiting nozzle fluid density to ambient fluid density is ρe/ρ∞ > 0.6, shear-layer fluctuations evolve in a fashion similar to that observed in constant-density jets: the power spectrum near the nozzle is determined by weak background disturbances whose subsequent spatial amplification agrees closely with the spatial stability theory. When the density ratio is less than 0.6, an intense oscillatory instability may also arise. The overall behaviour of this latter mode (to be called the ‘oscillating’ mode) is shown to depend solely upon the density ratio and upon D/θ, where D is the nozzle diameter and θ is the momentum thickness of the boundary layer at the nozzle exit. The behaviour of this mode is found to be independent of the Reynolds number, within the range covered by the present experiments. This is even true in the immediate vicinity of the nozzle where, unlike in the case of shear-layer modes, the intensity of the oscillating mode is independent of background disturbances. The streamwise growth rate associated with the oscillating mode is not abnormally large, however. The frequency of the oscillating mode compares well with predictions based on a spatio-temporal theory, but not with those of the standard spatial theory.

From high-speed films it is found that the overall structure of the oscillating mode repeats itself with extreme regularity. The high degree of repeatability of the oscillating mode, in association with a strong pairing process, leads to abnormally large centreline velocity fluctuation, with its root-mean-square value being about 30 % of the nozzle exit velocity. Energetic and highly regular pairing is found also to lead to the early and abrupt breakdown of the potential core. The regularity often extends even to the finer structure immediately downstream of the breakdown. An attempt is made to explain these special features both in terms of the large-amplitude vorticity field, and in terms of the theoretically predicted space–time evolution of wave packets.

The effects of almost neutrally buoyant plastic particles and heavy glass particles on grid-generated turbulence were studied experimentally in a water flow facility. From measured velocities of both the solid and liquid phases, drag and slip velocities of the particles and energy spectra and dissipation rates of the liquid phase were estimated. A monotonic increase in the dissipation rate of the turbulence energy with particle concentration was observed. The increase in energy dissipation rate for suspensions of glass particles was about twice that of suspensions of plastic particles. The increase in dissipation was larger than that predicted by a simple model based on the slip velocities between the phases. It is speculated that the particles enhance the transfer of energy to smaller eddies extending the dissipation spectrum to smaller scales. Since only part of the high wavenumber end of the energy spectrum could be resolved, this speculation cannot be conclusively demonstrated by the present experimental data. The measured velocity spectra do show that the particles increase the isotropy of the flow field and modify the high wavenumber end of the turbulence energy spectrum.