The results of experimental studies on the nonlinear evolution of perturbation waves in the turbulent wake behind a flat plate are presented. Sinuous perturbations at several amplitudes and frequencies were introduced into the wake by oscillating a small trailing-edge flap. The Strouhal numbers of the perturbations were specially chosen so that the downstream location of the neutral point (where the spatial amplification rate obtained from linear theory vanishes) was well within the range of measurements. The streamwise evolution of the waves and their effect on the growth of the turbulent wake was investigated. The amplitude of the coherent Reynolds stress varied significantly with x and changed sign downstream of the neutral point. This resulted in rather strong changes in the spreading rate of the mean flow with x. At high forcing levels, dramatic deviations from the square-root behaviour of the unforced wake occurred. Although the development of the mean flow depended strongly on the forcing level, there were some common features in the overall response, which are discussed. The measured coherent Reynolds stress changed sign in the neighbourhood of the neutral point as predicted by linear theory. The normalized mean velocity profiles changed shape as a result of nonlinear interactions but relaxed to a new self-similar shape far downstream from the neutral point. Detailed measurements of the turbulent and coherent Reynolds stresses are presented and the latter are compared to linear stability theory predictions.

A horizontal density gradient may be steepened to form a front if the horizontal flow which it drives is convergent. This convergence may be caused by an initial nonlinearity in the density gradient (as described by Simpson & Linden 1989). A quadratic density profile is analysed to illustrate the mechanism, and it is shown how the flow and the density profile interact to intensify and concentrate the front near a horizontal boundary. Linear and curved density profiles in a container of finite length are also studied: the most favourable location for frontogenesis is found to be where the flow emerges into a region of significant curvature after passing through a maximum of the density gradient.

The effects of boundary mixing on the transport of a buoyant cloud along an incline were investigated using a laboratory experiment. A fixed volume of a negatively buoyant substance (a suspension of aluminium particles or a saline solution) was introduced onto a rough inclined plane, which was submerged in homogeneous water and could make planar oscillations so as to produce turbulence. At weak turbulence intensities, the buoyant input flowed down the slope as a well-defined gravity current. As the intensity of turbulence became stronger, however, the buoyant input diffused away into the interior of the fluid. The frontal velocity of the gravity current, the density structure and the growth of the thickness of the buoyant cloud were measured, and their dependencies on the intensity of turbulence at the boundary were determined. A criterion which predicts the transition from gravity-current-dominated transport to turbulent-diffusion-dominated transport was found. Scaling arguments were developed to explain the experimental results.

Small-amplitude oscillations of viscous, capillary bridges are characterized by their frequency and rate of damping. In turn, these depend on the surface tension and viscosity of the liquid, the dimensions of the bridge, the axial and azimuthal wavenumbers of each excited mode and the relative magnitude of gravity. Both analytical and numerical methods have been employed in studying these effects. Increasing the gravitational Bond number decreases the eigenvalues in addition to modifying the well-known Rayleigh stability limit for meniscus breakup. At high Reynolds numbers results from inviscid and boundary-layer theories are recovered. At very low Reynolds numbers oscillations become overdamped. The analysis is applicable in measuring properties of semiconductor and ceramic materials at high temperatures under well-controlled conditions. Such data are quite scarce.

The steady, two-dimensional flows and interface shapes of the rimming flow of Newtonian and viscoelastic liquid films are studied by finite-element analysis. The viscoelastic flow calculations are based on the elastic-viscous split stress (EVSS) formulation for differential constitutive models. The EVSS formulation is derived by taking into account the mathematical type of the momentum, continuity and constitutive equations and is extended in this paper to calculation of free-surface flows. Calculations for a viscous Newtonian fluid demonstrate the balance between viscous forces and gravity which sets the shape of the interface of the liquid film coating the inside of the rotating cylinder. The liquid shape evolves from a concentric and circular film at high rotation rates to become thicker on the rising surface as the rotation rate is lowered. No steady flows with continuous films are found to exist below a minimum rotation rate, Ω = Ωc, where the family of flows evolves back toward higher values of Ω. Multiple solutions are predicted for a range of rotation rates, Ω > Ωc, and unstable flows develop a pronounced bulge on the rising side of the film. Asymptotic analysis for a thin film predicts this limiting rotation rate. Adding viscoelasticity to the liquid, as modelled by the Giesekus constitutive equation, leads to the existence of steady solutions at lower rotation rates and causes the bulge to appear on stable films. The minimum rotation rate for steady, viscoelastic flow shifts to lower values as the time constant of the fluid is increased.

The flow of a stratified fluid toward a line sink in a rotating channel of finite width and depth is studied. The withdrawal flow is shown to be established by a set of Kelvin shear waves trapped within a distance of Nh/fn from the right-hand side wall (f > 0) looking in the direction of propagation, where n = 1, 2,… is the vertical mode number. In addition there are a set of waves (Poincaré modes) which propagate away from the sink with a cross-channel modal structure. The withdrawal flow has a boundary-layer structure: far from the right-hand wall the flow resembles that of McDonald & Imberger (1991), whereas close to the right-hand wall the development of the vertical structure of the withdrawal flow resembles that of the non-rotating case due to the presence of Kelvin shear waves. In a narrow channel Kelvin shear waves dominate the establishment of the withdrawal flow. The withdrawal flow is investigated for large times compared to the inertial period, where it is shown that the width of the boundary layer is of the same order as the distance downstream from the sink. The flow within the boundary layer is unsteady as the withdrawal layer thickness δ continues to collapse indefinitely, while outside the boundary layer it is steady with δ ∼ fL/N, L being the horizontal lengthscale downstream from the sink. A scaling analysis is developed for the narrow channel case in which the cross-channel velocity can be ignored. The results are applied to actual field data, where it is shown that the effect of rotation may explain why previous non-rotating theories have been inaccurate in predicting withdrawal layer thickness.

Unsteady convection of an initially homogeneous fluid in a vertical slot is investigated theoretically in the limit of large Rayleigh and Prandtl/Schmidt numbers. The motion is driven by prescribed fluxes of heat or mass at the vertical walls of the slot. The ‘heat-up’ problem is considered, i.e. the fluxes are specified to change instantaneously from zero to finite constant values. Perturbation methods are used to compute approximate solutions for the initial period and for the slow approach to the asymptotic state. Numerical solutions of the full problem are also given. It is shown that a significant stratification is set up after short time and that the system thereafter evolves as a strongly stratified fluid on a timescale that is proportional to $Ra^{\frac{2}{9}}$. During the latter part of the process, linear buoyancy layers of thickness $\sim Ra^{\frac{2}{9}}$ appear on the vertical walls. On the horizontal walls, there are nonlinear boundary layers of thickness $\sim Ra^{-\frac{1}{9}}$, whose structure is akin to that of a Stewartson E¼ layer. The theoretical predictions are found to be in good agreement with experimental results.