This paper treats a liquid-metal flow through a sharp elbow connecting two constant-area, rectangular ducts with thin metal walls. There is a uniform, strong magnetic field in the plane of the centrelines of the ducts. An analytical solution with a series of eigenfunctions is possible for two sectors of the geometry, while a finite-difference relaxation solution is used for the third sector. The analytical and numerical solutions are coupled at the common boundaries by a combination of a Galerkin minimization of a residual and of integrals of the basic conservation laws over cells adjacent to each boundary. Results are presented for the three-dimensional pressure, electric potential function and fluid velocity. The pressure drop due to the three-dimensional effects near the elbow is also presented. The eigenfunction series represents a quite general solution for any three-dimensional flow in a rectangular duct with a skewed magnetic field.

Turbulent boundary layers were altered with a tandem array of manipulators arranged to produce a maximum drag reduction. The Reynolds number based on the momentum thickness, Reθ, at the first manipulator position was between 1700 and 2400. Temperature was used as a passive contaminant to explore the dynamical relationship between the near-wall and outer regions of the manipulated layer. Heat was introduced by warming the wall uniformly to 15°C above the ambient temperature or with a line heater in the wake of the manipulator. Temperature and velocity measurements showed a reduction in fluctuation amplitude and a strong decrease in larger scale mixing accompanied by a reduction of the Taylor microscale and integral lengthscale. Isocorrelations indicated that the eddy size was decreased in all three directions. The net result of the manipulators was a marked decrease in the entrainment of irrotational fluid into the boundary layer. The results suggest that the manipulators do not directly affect the wall region but rather decrease the entrainment, and hence the growth of the boundary layer, leading to possible drag reduction.

Experimental and numerical investigations are performed for the situation of steady recirculating combined-convection water flows in a cylindrical duct. The experimental results are presented as photographs from which information regarding the stream-function and temperature distributions within the water can be deduced. The experimental flows, which have Reynolds number in the range 15 < Re < 31, are modelled numerically using an elliptic finite-difference formulation and a multigrid solution technique. The results for stream function and temperature are compared with the experimental results and agreement is found to be generally very good. Plots of flow average temperature, local Nusselt number, average Nusselt number and friction factor times Reynolds number are also presented for each flow situation considered.

Steady two-dimensional free-surface flows of an inviscid and incompressible fluid emerging from a nozzle and falling under gravity are calculated numerically. The nozzle is aimed at an angle β above the horizontal. It is shown that there are flows for which the fluid falls down along the underside of the nozzle and other flows which split into two sheets. The latter flows occur for each value of β when the Froude number F is greater than a critical value. Local solutions are constructed to describe the limiting behaviour of the flows as F → 0 and as F → ∞.

Mean velocity profiles have been measured in the wake of a two-dimensional airfoil with and without mass injection through a slit along its rear end. In particular, four cases have been documented: (a) a pure wake (no injection), (b) a weak wake (some injection), (c) a momentumless wake (injection adjusted to provide a thrust which exactly cancels the model's drag), and (d) a weak jet (more injection than necessary to cancel the drag). These mean velocity profiles clearly show the difference in momentum deficit for the four cases. When non-dimensionalized, the velocity profiles are self-similar.

Smoke-wire flow visualizations are also presented for both the near wake (0 < x/d < 30) and the far wake (45 < x/d < 75). The characteristic geometry of large-scale turbulent vortical structures is easily identifiable for the wake and jet cases, while the structures for the momentumless state are neither wake-like nor jet-like. Beyond about 45 diameters downstream, turbulent structures for the momentumless case become quite weak and can barely be observed.

For the momentumless wake at Re = 5400, the axial, lateral, and transverse turbulence intensities as well as the Reynolds stress were measured. Similarity of the axial and the transverse turbulence intensities was observed; the overall shape of those profiles is Gaussian except for the very near-wake region. The mean centreline velocity difference decays much faster (x−0.92) than the axial turbulent intensity (x−0.81). Consequently, the mean shear practically disappears far downstream; the flow becomes nearly isotropic beyond about 45 body diameters from the model. This turbulence behaviour is quite different from that of plane wakes or jets but rather closer to the case of grid turbulence.

An experimental study of the onset of chaos in a linear array of forced vortices is presented. The vortices are driven by electromagnetic forces in a layer of electrolyte. The system is found to behave like a chain of nonlinearly coupled oscillators, each oscillator being sustained by a pair of vortices. Systems with a small number of vortices exhibit scenarios characterized by a small number of degrees of freedom. Increasing the number of vortices leads to a rapid increase of the complexity of the regimes of transition to chaos. For moderately long systems, quasi-periodicity preceding the onset of chaos and intermittent behaviour is observed.

A revised formal solution of the vibrating ribbon problem of hydrodynamic stability is presented. The initial formulation of Gaster (1965) is modified by application of the Briggs method and a careful treatment of the complex double Fourier transform inversions. Expressions are obtained in a natural way for the discrete spectrum as well as for the four branches of the continuous spectra. These correspond to discrete and branch-cut singularities in the complex wavenumber plane. The solutions from the continuous spectra decay both upstream and downstream of the ribbon, with the decay in the upstream direction being much more rapid than that in the downstream direction. Comments and clarification of related prior work are made.

The continuous transformation of one flow into another of higher or lower energy while preserving the potential vorticity of all particles can be accomplished by advection with an artificial velocity field. Since isolated extremal energy states are stable states, this method can be used to find stable stationary flows on a prescribed isovortical sheet. A series of numerical simulations of this method for two-dimensional fluids that demonstrates its feasibility and utility is presented. Additionally, a corollary to Arnol'd's nonlinear stability theorems is discussed, which shows that there can be at most two Arnol'd stable states per isovortical sheet.

In addition to the Hamiltonian functional itself, non-canonical Hamiltonian dynamical systems generally possess integral invariants known as ‘Casimir functionals’. In the case of the Euler equations for a perfect fluid, the Casimir functionals correspond to the vortex topology, whose invariance derives from the particle-relabelling symmetry of the underlying Lagrangian equations of motion. In a recent paper, Vallis, Carnevale & Young (1989) have presented algorithms for finding steady states of the Euler equations that represent extrema of energy subject to given vortex topology, and are therefore stable. The purpose of this note is to point out a very general method for modifying any Hamiltonian dynamical system into an algorithm that is analogous to those of Vallis et al. in that it will systematically increase or decrease the energy of the system while preserving all of the Casimir invariants. By incorporating momentum into the extremization procedure, the algorithm is able to find steadily-translating as well as steady stable states. The method is applied to a variety of perfect-fluid systems, including Euler flow as well as compressible and incompressible stratified flow.

Direct numerical simulations of the transient flow in a side-heated cavity have been conducted for a Rayleigh Number of 2 × 109, an aspect ratio of 1 and a Prandtl Number of 7.1. The results show the presence of both long-period and short-period oscillations. The long-period oscillation is a cavity-scale mode produced by the tilting of the isotherms. The short-period oscillations are shown to be the result of two distinct boundary-layer instabilities. Whereas the latter oscillations can produce large deviations in the observed temperature records, they are relatively shortlived and have only a minor influence on the evolution of the flow towards steady state. The suggestion of the existence of an internal hydraulic jump in such flows has been investigated and found to be incorrect.

An axisymmetric hot-air jet discharging into cold ambient air is investigated experimentally. We consider the transitional regime, that is, Reynolds numbers at which the jet is initially laminar. In the first part of the paper it is demonstrated by several different experiments that, for sufficiently low Reynolds number and a ratio of jet exit to ambient density below approximately 0.7, global oscillations of the ‘jet column’ become self-excited, a behaviour which is related to local absolute instability in the potential core region. The onset of the global oscillations is identified as a Hopf bifurcation and two axisymmetric global modes are observed below the critical density ratio. Finally, it is shown that in the (self-excited) limit-cycle regime the spreading of the hot jet is intermittently quite spectacular, with half-angles in excess of 45°. Using flow visualization, this large spreading of low-density jets is related to the generation of strong ‘side jets’ emanating from the jet column.

An initial localized eddy was generated in a rotating tank by a source–sink method to study the behaviour of an isolated barotropic eddy on a β-plane. The evolution of the eddy was compared with the laboratory experiments by Firing & Beardsley (1976) and by Takematsu & Kita (1985, 1988), confirming the northwestward (southwestward) translation of a cyclonic (anticyclonic) isolated eddy due to nonlinear effects. Anticyclonic eddies were contrasted with cyclonic eddies in the tank experiment, showing a cyclonic–anticyclonic asymmetry due to the topographic β as a substitute for the planetary β. The fluid experiment was simulated well by numerical simulation based on the quasi-geostrophic vorticity equation. Numerical experiments verified the northwestward (southwestward) translation both for an initially Gaussian and initially Rankine-type isolated cyclonic (anticyclonic) eddy.