The structure and evolution of homogeneous stably stratified sheared turbulence have been investigated through direct numerical simulation. In these simulations the primary dimensionless parameter is the Richardson number which measures the relative importance of stratification and mean shear.

For Richardson numbers less than the transition value the Reynolds stress and vertical density flux are down-gradient. Some of the vertical kinetic energy gained indirectly through production is expended in creating potential energy. Included in this shear-dominated regime is the stationary Richardson number at which the turbulent kinetic energy is constant in time although the spectra are evolving. At low dimensionless shear rate the stationary Richardson number increases with increasing Reynolds number.

At the transition Richardson number the maximum anisotropy and energy partition are achieved. For larger Richardson numbers potential energy is released into vertical kinetic energy and the vertical density flux becomes counter-gradient. The associated production reversal enhances the decay rate of the turbulent kinetic energy.

The effects of other dimensionless parameters have been investigated. After initial transients the developed flow is rather insensitive to the presence of significant initial potential energy. An increase in the Schmidt number increases the effect of stable stratification, e.g. the counter-gradient vertical density flux occurs earlier.

In the shear dominated case the down-gradient fluxes are produced by the pumping of fluid through coherent hairpin-shaped vorticity. In the buoyancy dominated flow the counter-gradient fluid parcels induce helical vorticity structures as they move toward a position of neutral buoyancy.

The effective phase change from fluid behaviour to solid behaviour, that too often occurs in granular flow and brings with it such unwelcome events as funnel flows in hoppers and clogging of other material handling devices, is studied using a discrete particle computer simulation of a Couette flow with gravity. This simulation exhibits the full range of granular flow behaviour, from a stagnant solid-like material, through a quasi-static transition zone, to a rapid granular flow. The most important result is that the first movement in the material just above the static bed occurs in a quasi-static mode at a fixed value of the stress ratio τxy/τyy. Thus, it appears that the primary transition from solid to fluid behaviour is a yield-like phenomenon and can be described by a Mohr-Coulomb-type failure criterion.

The present experiments are an extension of previous studies on nearly homogeneous, parallel, shear flows and represent an attempt to study the effects of curvature on sheared turbulence in relative isolation from wall and entrainment effects. Uniformly sheared turbulence was allowed to reach a state of transverse statistical homogeneity in a straight rectangular duct: it was then passed into a curved duct, also of rectangular cross-section. The near homogeneity of the turbulence and the near uniformity of the shear were preserved. In the present experiments, the parameter S = (Uc/Rc)(dU/dn) spanned a wide range, from approximately -0.50 to over 1.0 (Uc is the centreline velocity, dU/dn the mean shear and Rc the radius of curvature on the centreline of the duct). Variation of S was achieved by using two curved tunnel sections as well as by adjusting the shear. Measurements indicate that the growth of the turbulent stresses and lengthscales was enhanced for S < 0 and suppressed for S > 0. For S > 0.05, the stresses decayed. In cases where sufficiently large total strain was achieved, the stresses seemed to grow or decay roughly exponentially and to develop in a quasi-self-preserving manner. The magnitude of the dimensionless shear stress decreased monotonically with increasing S, while, for sufficiently large positive values of S, this quantity reversed sign, to achieve the same sense as the mean shear. Measurements of the integral lengthscales and the Taylor microscales are presented and their dependence upon curvature discussed. The results in ‘mildly curved’ flows are used to derive approximate expressions for the dependence upon S of the various terms in the Reynolds stress equations, including the pressure-strain rate covariance tensor.

The conditions for hydraulic control to occur in a continuously stratified fluid are discussed, using density as a vertical coordinate in place of height. A suitable definition of Froude number, which varies with depth, is given. Three conditions for control emerge. One is that the flow be everywhere well-behaved; another is that control occurs when the local long-wave speed vanishes. These are shown to be equivalent. The location of the control is determined indirectly by the Froude number, which occurs as the coefficient in an ordinary differential equation; the Froude number must be somewhere less than a critical value for control to occur. The third condition requires the coalescence of two different solutions for the same boundary conditions at the point of control. It is shown that this requirement is non-trivial: examples given include a simple control by topography, a virtual control, and a control by a constriction. A direct connection with layered theory is produced. Brief discussions of bidirectional flow (where the isopycnal surface of zero velocity must be flat) and weak shocks are given.

The buoyancy-driven motion of a train of viscous drops settling or rising along the axis of a vertical cylindrical tube is investigated. Under the assumption of creeping flow, the evolution of the drops is computed numerically using a boundary integral method that employs the axisymmetric periodic Green's function for flow in a cylindrical tube. Given the drop volume and assuming that the viscosity of the drops is equal to that of the suspending fluid, the motion is studied as a function of the radius of the tube, the separation between the drops, and the Bond number. Two classes of drops are considered: compact drops whose effective radius is smaller than the radius of the tube, and elongated drops whose effective radius is larger than the radius of the tube. It is found that compact drops may have a variety of steady shapes including prolate and oblate, dimpled tops, and shapes containing pockets of entrained ambient fluid. When the surface tension is sufficiently small, compact drops become unstable, evolving to prolate rings with elongated tails. The terminal velocity of compact drops is discussed and compared with that predicted by previous asymptotic analyses for spherical drops. Steady elongated drops assume the shape of long axisymmetric fingers consisting of a nearly cylindrical main body and two curved ends. Relationships between the terminal velocity of elongated drops, the gap between the drops and the wall of the tube, and the Bond number are established. The results are discussed with reference to previous analyses and laboratory measurements for inviscid bubbles.

The solidification of melts can be profoundly influenced by convection. In alloys, compositional convection can be driven by solute gradients generated as one component of the alloy is preferentially incorporated within the solid, even when the thermal field is stabilizing. In this paper, two modes of compositional convection during solidification from below are uncovered using a linear-stability analysis: one, which we shall call the ‘mushy-layer mode’, is driven by buoyant residual fluid within a mushy layer, or porous medium, of dendritic crystals; the other, which we shall call the ‘boundary-layer mode’ is associated with a narrow compositional boundary layer in the melt just above the mush-liquid interface. Either mode can be the first to become unstable depending on the thermodynamical and physical properties of the alloy. The marginally stable eigenfunctions suggest that the boundary-layer mode results in fine-scale convection in the melt above the mushy layer and leaves the interstitial fluid of the mushy layer virtually stagnant. In contrast, the mushy-layer mode causes perturbations to the solid fraction of the mushy layer that are indicative of a tendency to form chimneys, which are vertical channels of reduced or zero solid fraction that have been observed experimentally. Particular attention is focused on the mushy-layer mode and its dependence upon the thermodynamical properties of the alloy. The results of this analysis are used to make a number of interpretations of earlier experimental studies such as the observations that some systems are less prone to form chimneys and that the regions of melt in these systems evolve to supersaturated conditions, while the melt evolves to unsaturated conditions once chimneys have formed. In addition, good quantitative agreement is found between the results of the linear-stability analysis and the experimental results of Tait & Jaupart (1992) for the onset of the mushy-layer mode of convection.

Transient internal temperature distributions of vaporizing droplets have been carefully measured, using fine thermocouples at 1 atm. and 1000 K. Droplet diameters are fixed at 2000 ± 50 μm with Reynolds numbers being 17, 60 or 100. Fuels tested are JP-10, n-decane and JP-10 thickened with polystyrene. The effects of Reynolds number and liquid viscosity on internal temperature distribution and heating mechanism have been examined. Experimental results indicate that liquid viscosity or circulation intensity strongly affects the temperature distribution and heating mechanism. In contrast, the temperature distributions associated with the three different Reynolds numbers have shown little difference for both low- and high-viscosity cases. For the low-viscosity JP-10 droplets at Reynolds numbers up to 100, where the vortex model of Sirignano and coworkers (Prakash & Sirignano 1978; Tong & Sirignano 1983) has been claimed to be applicable, the vortex model appears qualitatively correct but quantitatively inaccurate. Physical reasons for the deviation have been discussed. Solutions of the full Navier-Stokes equations appear to accord better with the experimental temperature distributions. Circulative heat transport decreases progressively as liquid viscosity increases. A semi-empirical effective conductivity model for high-viscosity cases yields a very good simulation of the experimental temperature distributions at all the Reynolds numbers when proper effective conductivity factors are chosen. A discussion on internal droplet dynamics and heating mechanisms in physical terms has been provided.