New instabilites of unsteady transonic flows with non-equilibrium phase transition are presented including unsymmetric flow patterns with moving oblique shock systems in supersonic nozzles with perfectly symmetric shapes. The phenomena were first detected when performing experiments in our supersonic wind tunnel with atmospheric supply and could be perfectly reproduced by numerical simulations based on the Euler equations, i.e. neglecting the viscosity of the fluid. The formation of the liquid phase is modelled using the classical nucleation theory for the steady state together with the Hertz–Knudsen droplet growth law and yields qualitatively and quantitatively excellent agreement with experiments in the unsteady flow regime with high-frequency oscillations including the unstable transient change of the structure from symmetric to unsymmetric flow.

For engineering applications the sudden increase or decrease of the frequency by a factor 2 or more and of the pressure amplitude at the bifurcation limits is of immediate practical interest, e.g. for flutter excitation of turbomachinery blading.

Weak free-stream turbulence excites modulated Tollmien–Schlichting (T–S) waves in a laminar boundary layer that grow in magnitude with downstream distance and ultimately lead to the formation of turbulent spots and then fully turbulent flow. Hot-wire experiments have indicated that the development of localized large-amplitude ‘events’ in the velocity records are the essential precursor to the eventual formation of turbulent spots in the flow field. Traditional global Fourier techniques are unable to resolve the localized nature of these events and hence provide little useful information concerning the physical processes responsible for this breakdown process.

This investigation used sequences of computer-generated deterministic white noise to excite a laminar boundary layer via a loudspeaker embedded in a flat-plate model. This form of excitation generated the modulated disturbance waves of interest a short distance downstream from the source in a repeatable and deterministic manner. Further downstream the pattern of flow breakdown and subsequent generation of turbulent spots was similar to that observed in naturally excited situations. By repeatedly exciting the boundary layer with a single white-noise sequence it was possible to examine the highly nonlinear stages of ‘event’ development and breakdown with a single hot-wire probe.

Two local analysis techniques, the wavelet transform (WT) and singular spectrum analysis (SSA), were used in conjunction with the white-noise excitation technique to examine the highly nonlinear flow mechanisms responsible for the localized formation of events that lead to the eventual breakdown to turbulence.

The collisionally induced random particle velocities in a rapid granular shear flow drive the diffusion of particles in manner directly analogous to the thermal diffusion of molecules or the eddy-induced diffusion in a turbulent flow. This paper reports measurements, via computer simulation, of the anisotropic diffusion tensor for a granular shear flow. The components are determined both by particle tracking and through velocity correlations, which are found to agree with reasonable accuracy. As might be expected from symmetry arguments, there are four non-zero components generated in a simple shear flow: the three diagonal components and one off-diagonal component.

The effects of Brownian motion alone and in combination with an interparticle force of hard-sphere type upon the particle configuration in a strongly sheared suspension are analysed. In the limit Pe→∞ under the influence of hydrodynamic interactions alone, the pair-distribution function of a dilute suspension of spheres has symmetry properties that yield a Newtonian constitutive behaviour and a zero self-diffusivity. Here, Pe=γ˛a2/2D is the Péclet number with γ˛ the shear rate, a the particle radius, and D the diffusivity of an isolated particle. Brownian diffusion at large Pe gives rise to an O(aPe−1) thin boundary layer at contact in which the effects of Brownian diffusion and advection balance, and the pair-distribution function is asymmetric within the boundary layer with a contact value of O(Pe0.78) in pure-straining motion; non-Newtonian effects, which scale as the product of the contact value and the O(a3Pe−1) layer volume, vanish as Pe−0.22 as Pe→∞.

Periodic axial motion of the inner cylinder in Taylor–Couette flow is used to delay transition to Taylor vortices. The outer cylinder is fixed. The marginal stability diagram of Taylor–Couette flow with simultaneous periodic axial motion of the inner cylinder is determined using flow visualization. For the range of parameters studied, the degree of enhanced stability is found to be greater than that predicted by Hu & Kelly (1995), and differences in the scaling with axial Reynolds number are found. The discrepancies are attributed to essential differences between the base flow in the open system considered by Hu & Kelly, where mass is conserved over one period of oscillation, and the base flow in the enclosed experimental apparatus, where mass is conserved at all sections at all times.

The linear stability of the flow in the annular gap between two infinitely long cylinders, driven by the constant rotation and harmonic oscillation in the axial direction of the inner cylinder, is analysed using Floquet theory. Closed form solutions for the basic flow are derived, both with and without the presence of endwalls. Recent experiments and theory using the narrow gap approximation have shown that the axial oscillations significantly stabilize the flow with respect to centrifugal instabilities. However, the agreement has only been qualitative. The present analysis reproduces the experimental results to well within experimental uncertainty. We have identified the major source of discrepency with the previous theory to be due to the lack of global endwall effects enforcing a net zero axial mass flux. Analysis of the basic flow indicates that the stabilization is primarily due to waves of azimuthal vorticity propagating inwards from the cylinder boundary layers due to the axial oscillations.

Experimental data obtained in various turbulent flows are analysed by means of orthogonal wavelet transforms. Several configurations are analysed: homogeneous grid turbulence at low and very low Reλ, and fully developed jet turbulence at moderate and high Reλ. It is shown by means of the wavelet decomposition in combination with the form of scaling named extended self-similarity that some statistical properties of fully developed turbulence may be extended to low-Reλ flows. Indeed, universal properties related to intermittency are observed down to Reλ≃10. Furthermore, the use of a new conditional averaging technique of velocity signals, based on the wavelet transform, permits the identification of the time signatures of coherent structures which may or may not be responsible for intermittency depending on the scale of the structure itself. It is shown that in grid turbulence, intermittency at the smallest scales is related to structures with small characteristic size and with a shape that may be related to the passage of vortex tubes. In jet turbulence, the longitudinal velocity component reveals that intermittency may be induced by structures with a size of the order of the integral length. This effect is interpreted as the signature of the characteristic jet mixing layer structures. The structures identified on the transverse velocity component of the jet case turn out on the other hand not to be affected by the mixing layer and the corresponding shape is again correlated with the signature of vortex tubes.

To continue our (Saddoughi & Veeravalli 1994) tests of the local-isotropy predictions of Kolmogorov's (1941) universal equilibrium theory in shear flows, we have taken hot-wire measurements of the velocity fluctuations in complex turbulent boundary layers at several Reynolds numbers. We have studied the plane-of-symmetry flow upstream of a 4 ft diameter, 6 ft long circular cylinder placed with its axis vertical in the zero-pressure-gradient turbulent boundary layer of the test-section ceiling in the 80 ft x 120 ft Full-Scale Aerodynamics Facility at NASA Ames Research Center.

The subtle impact of the spanwise scaling in nonlinear interactions between oblique instability waves and the induced longitudinal vortex field is considered theoretically for the case of a Rayleigh-unstable boundary-layer flow, at large Reynolds numbers. A classification is given of various flow regimes on the basis of Reynolds-stress mechanisms of mean vorticity generation, and a connection between low-amplitude non-parallel vortex/wave interactions and less-low-amplitude non-equilibrium critical-layer flows is discussed in more detail than in previous studies. Two new regimes of vortex/wave interaction for increased spanwise lengthscales are identified and studied. In the first, with the cross-scale just slightly larger than the boundary-layer thickness, the wave modulation is governed by an amplitude equation with a convolution and an ordinary integral term present due to nonlinear contributions from all three Reynolds-stress components in the cross-momentum balance. In the second regime the cross-scale is larger, and the wave modulation is found to be governed by an integral/partial differential equation. In both cases the main-flow non-parallelism contributes significantly to the coupled wave/vortex development.

A scalar patch forms spiral structure when it wraps around an isolated vortex. It is shown that this wind-up process leads to accelerated diffusion during a time range TS<t<TD. The lower limit TS is the time needed to create a well-defined spiral, and the upper limit TD is the diffusive time scale of the scalar field θ in the vortex. Whereas the scaling TD∼Pe1/3 is independent of the particular spiral topology, the accelerated decay of the scalar variance θ2[bar](t) for earlier times is directly linked to the space-filling property of the spiral and is found to scale as θ2[bar](0)−θ2[bar](t)∼ (Pe1/3t) 3(1−D′K). D′K is the Kolmogorov capacity of the spiral; it is defined in the range 1/2<D′K<1 and it is the most suitable measure of the spiral's space-filling property.

The approach of Visbeck, Marshall & Jones (1996) is used to explain the primary results of a recent laboratory study of isolated convection in a two-layer fluid reported by Narimousa (1996).

Magnetic reconnection at an X-type neutral point of a two-dimensional magnetic field is studied in an incompressible viscous resistive fluid whose flow is assumed to be slow enough that its inertia is negligible. In both the ideal and resistive magnetohydrodynamic approximations current singularities appear at the X-point and along the separatrices. It is shown here analytically that the combined effect of viscosity and resistivity can resolve these singularities with the flow crossing the separatrices. A wide class of exact solutions describing the structure of the flow and current density distribution is found. The results suggest that reconnection may occur with localized distributions of strong current density restricted to finite regions.

A boundary integral method is used to model the flow of capsules into pores. An axisymmetric configuration is considered where the capsule and the pore axis coincide. The channel is a cylinder with hyperbolic entrance and exit regions. The capsule has a discoidal unstressed shape, is filled with a Newtonian liquid and is enclosed by a very thin membrane with various elastic properties (neo-Hookean or area-incompressible). The motion of the internal capsule liquid and of the suspending fluid is governed by the Stokes equations whose solution is expressed as boundary integrals. Those are computed by a collocation technique, where points are distributed on the capsule interface, on the channel walls and on the entrance and exit sections of the flow domain. The capsule interface mechanics follow the theory of large deformations of elastic membranes. The numerical model uses a forward time-stepping method, where the position and the deformation of the capsule are computed at each time step.

The model allows the study of the effect of a number of parameters (capsule size and geometry, membrane elastic properties) on the flow. The entrance length in the pore, the steady additional pressure drop at equilibrium and the capsule deformed profiles are determined. It is found that the entrance of a capsule into a pore is not sensitive to downstream conditions; but the length of tube necessary to reach steady conditions depends strongly on capsule size and membrane behaviour. Bursting of capsules with a neo-Hookean membrane is predicted to occur through a phenomenon of continuous elongation. The flow of a capsule with a membrane that resists area dilatation depends strongly on particle size and shape.