The effects of vortex generators and periodic excitation on vorticity dynamics and the phenomenon of axis switching in a free asymmetric jet are studied experimentally. Most of the data reported are for a 3:1 rectangular jet at a Reynolds number of 450 000 and a Mach number of 0.31. The vortex generators are in the form of ‘delta tabs’, triangular-shaped protrusions into the flow, placed at the nozzle exit. With suitable placement of the tabs, axis switching could be either stopped or augmented. Two mechanisms are identified governing the phenomenon. One, as described by previous researchers, is due to the difference in induced velocities for different segments of a rolled-up azimuthal vortical structure. The other is due to the induced velocities of streamwise vortex pairs in the flow. While the former mechanism, referred to here as the ωθ-dynamics, is responsible for a rapid axis switching in periodically forced jets, e.g. screeching supersonic jets, the effect of the tabs is governed mainly by the latter mechanism, referred to as the ωx-dynamics. Both dynamics can be active in a natural asymmetric jet; the tendency for axis switching caused by the ωθ-dynamics may be, depending on the streamwise vorticity distribution, either resisted or enhanced by the ωx-dynamics. While this simple framework qualitatively explains the various observations made on axis switching, mechanisms actually in play may be much more complex. The two dynamics are not independent as the flow field is replete with both azimuthal and streamwise vortical structures which continually interact. Phase-averaged measurements for a periodically forced case, over a volume of the flow field, are carried out in an effort to gain insight into the dynamics of these vortical structures. The results are used to examine such processes as the reorientation of the azimuthal vortices, the resultant evolution of streamwise vortex pairs, as well as the redistribution of streamwise vortices originating from secondary flow within the nozzle.

Shock wave propagation arising from steady one-dimensional motion of a piston in a granular gas composed of inelastically colliding particles is treated theoretically. A self-similar long-time solution is obtained in the strong shock wave approximation for all values of the upstream gas volumetric concentration v0. Closed form expressions for the long-time shock wave speed and the granular pressure on the piston are obtained. These quantities are shown to be independent of the particle collisional properties, provided their impacts are accompanied by kinetic energy losses. The shock wave speed of such non-conservative gases is shown to be less than that for molecular gases by a factor of about 2.

The effect of particle kinetic energy dissipation is to form a stagnant layer (solid block), on the surface of the moving piston, with density equal to the maximal packing density, vM. The thickness of this densely packed layer increases indefinitely with time. The layer is separated from the shock front by a fluidized region of agitated (chaotically moving) particles. The (long-time, constant) thickness of this layer, as well as the kinetic energy (granular temperature) distribution within it are calculated for various values of particle restitution and surface roughness coefficients. The asymptotic cases of dilute (v0 [Lt ] 1) and dense (v0 ∼ vM) granular gases are treated analytically, using the corresponding expressions for the equilibrium radial distribution functions and the pertinent equations of state. The thickness of the fluidized region is shown to be independent of the piston velocity.

The calculated results are discussed in relation to the problem of vibrofluidized granular layers, wherein shock and expansion waves were registered. The average granular kinetic energy in the fluidized region behind the shock front calculated here compared favourably with that measured and calculated (Goldshtein et al. 1995) for vibrofluidized layers of spherical granules.

The mechanisms of heat and mass transport in a side-heated square cavity filled with a near-critical fluid are explored, with special emphasis on the interplay between buoyancy-driven convection and the Piston Effect. The Navier–Stokes equations for a near-critical van der Waals gas are solved numerically by means of an acoustically filtered, finite-volume method. The results have revealed some striking behaviour compared with that obtained for normally compressible gases: (i) heat equilibration is still achieved rapidly, as under zero-g conditions, by the Piston Effect before convection has time to enhance heat transport; (ii) mass equilibration is achieved on a much longer time scale by quasi-isothermal buoyant convection; (iii) due to the very high compressibility, a stagnation-point effect similar to that encountered in high-speed flows provokes an overheating of the upper wall; and (iv) a significant difference to the convective single-roll pattern generated under the same conditions in normal CO2 is found, in the form of a double-roll convective structure.

Experimental investigations in the three-dimensional boundary layer of a swept flat plate with the pressure gradient induced from outside are aimed at enhancing knowledge of the transition process in the presence of pure crossflow instability. The development of disturbances is characterized by the occurrence of both stationary and travelling instability modes, by early nonlinear development and by complex dependence upon the environmental conditions. Experiments under natural conditions of transition showed a good correspondence of the identified modes with those predicted by local linear stability theory. The disturbance growth, however, is generally overpredicted. Controlled excitation of crossflow vortices allowing measurements closer to the linear range of amplification confirmed this result. Nonlinear effects such as interaction between stationary disturbances and base flow and between travelling and stationary modes have already been observed when the naturally excited instabilities become of measurable size.

The most striking feature of the disturbance development is the complex dependence on initial conditions. Experiments under systematically varied environments showed that surface roughness represents the key parameter responsible for the initiation of stationary crossflow vortices. In contrast to two-dimensional boundary layers, free-stream turbulence influences the transition process indirectly. Only for turbulence levels Tu > 0.2% and smooth surfaces do the travelling instability waves dominate. The location of the final breakdown of laminar flow is clearly determined by the saturation amplitude of crossflow vortices. The receptivity to sound, two-dimensional surface roughness and non-uniformities of the test-section mean flow was found to be very weak.

The asymptotic flow structure is considered for a viscous–inviscid conical interaction, in particular that between a swept shock wave and a boundary layer. A flow model is devised based on the three-layer interaction concept. Assuming conicity of the inviscid flow regions, a viscous layer structure is established that is compatible with the inviscid outer flow, and which produces a geometrically conical surface flow pattern. This result is obtained from a dimensional analysis, which reveals similarity of the viscous layer in cross-flow planes at different radial distances from the conical origin. The results of this analysis provide a tool for the quantitative interpretation of surface flow visualizations in terms of the related topological structure of the flow in the cross-flow plane. This method is illustrated by application to the surface flow visualization of a Mach 3 shock-wave/boundary-layer interaction.

In the idealized problem of homogeneous isotropic stationary inertial-range turbulence the rate of relative dispersion of an ensemble of tracer pairs can be characterized by a constant C0. In order to compute this constant with random-flight equations, however, it is necessary first to know the values of two other constants, C1 and C2, that occur in the two-particle velocity-component relations of Lagrangian tracers (Faller 1992).

C1 and C2 are found by an elaborate trial and error procedure in a new two-tracer random-flight model of dispersion that matches input and output values of these two variates. The constant C0 is then computed using the Lagrangian relations and is found to be significantly smaller than when the Eulerian Kármán/Howarth correlations are used.

The probability density distribution of tracer separations has a kurtosis slightly larger than that of a comparable Gaussian distribution. At small spacings the frequency of tracer spacings is six to ten times larger than would be expected from a Gaussian distribution. The distribution function for the speed of separation of the Lagrangian tracers has a negative skewness similar to that found for two-point Eulerian velocities.

The growth rates of gravity waves are computed from linear, inviscid stability theory for wind velocity profiles that are representative of the mean flow in a turbulent boundary layer. The energy transfer to the waves is largely concentrated in an angle (to the wind) interval that broadens with increasing wind speed and narrows with increasing wavelength. At sufficiently high wind speeds and sufficiently short wavelengths, the waves of maximum growth rate propagate at an oblique angle to the wind. The connection with bimodal directional distributions of observed spectra is discussed.

The present study aims at relating lift and drag to flow structures around a delta wing of elliptic section. Aerodynamic forces are analysed in terms of fluid elements of non-zero vorticity and density gradient. The flow regime considered is Mα = 0.6 ∼ 1.8 and α = 5° ∼ 19°, where Mα denotes the free-stream Mach number and α the angle of attack. Let ρ denote the density, u velocity, and ω vorticity. It is found that there are two major source elements Re(x) and Ve(x) which contribute about 95% or even more to the aerodynamic forces for all the cases under consideration, \[R_e({\bm x})=-\frac{1}{2} {\bm u}^2 \nabla\rho \cdot \nabla\phi\quad {\rm and}\quad V_e ({\bm x}) = -\rho{\bm u}\times {\bm \omega}\cdot \nabla\phi,\] where θ is an acyclic potential, generated by the delta wing moving with unit velocity in the negative direction of the force (lift or drag). All the physical quantities are non-dimensionalized. Detailed force contributions are analysed in terms of the flow structures and the elements Re(x) and Ve(x). The source elements Re(x) and Ve(x) are concentrated in the following regions: the boundary layer in front of (below) the delta wing, the primary and secondary vortices over the delta wing, and a region of expansion around the leading edge. It is shown that Ve(x) due to vorticity prevails as the source of forces at relatively low Mach number, Mα < 0.7. Above about Mα = 0.75, Re(x) due to compressibility generally becomes the dominating contributor to the lift, while the overall contribution from Ve(x) decreases with increasing Mα, and even becomes negative at Mα = 1.2 for the lift, and at a higher Mα for the drag. The analysis is carried out with the aid of detailed numerical results by solving the Reynolds-averaged Navier–Stokes equations, which are in close agreement with experiments in comparisons of the surface pressure distributions.

Gravity-driven granular flow of slightly frictional particles down an inclined, bumpy chute is studied. A modified kinetic model which includes the frictional energy loss effects is used, and the boundary conditions for a bumpy wall with small friction are derived by ensuring the balance of momentum and energy. At the free surface, the condition of vanishing of the solid volume fraction is used. The mean velocity, the fluctuation kinetic energy and the solid volume fraction profiles are evaluated. It is shown that steady granular gravity flow down a bumpy frictional chute could be achieved at arbitrary inclination angles. The computational results also show that the slip velocity may vary considerably depending on the granular layer height, the surface boundary roughness, the friction coefficient and the inclination angles. The model predictions are compared with the existing experimental and simulation data, and good agreement is observed. In particular, the model can well predicate the features of the variation of solid volume fraction and fluctuation energy profiles for different particle–wall friction coefficients and wall roughnesses.

Ensemble averaging combined with multiple scattering ideas is applied to the Stokes flow over a stochastic rough surface. The surface roughness is modelled by compact protrusions on an underlying smooth surface. It is established that the effect of the roughness on the flow far from the boundary may be represented by replacing the no-slip condition on the exact boundary by a partial slip condition on the smooth surface. An approximate analysis is presented for a sparse distribution of arbitrarily shaped protrusions and explicit numerical results are given for hemispheres. Analogous conclusions for the two-dimensional case are obtained. It is shown that in certain cases a traction force develops on the surface at an angle with the direction of the flow.

We consider the fluid flow induced when free-surface travelling waves pass over a submerged circular cylinder. The wave amplitude is assumed to be small, and a suitably defined Reynolds number large, so that perturbation methods may be employed. Particular attention is focused on the steady streaming motion, which induces circulation about the cylinder. The viscous forces acting on the cylinder are calculated and compared with the pressure forces which are solely responsible for the loading on the cylinder in a purely inviscid flow.

We discuss chaotic advection in three-dimensional unsteady incompressible laminar flow, and analyse in detail the most important novel advection phenomenon in these flows: the global dispersion of passive scalars in flows with two slow and one fast velocity components. We make a comprehensive study of the first model of an experimentally realizable flow to exhibit this resonance-induced dispersion: biaxial unsteady spherical Couette flow is a three-dimensional incompressible laminar flow with periodic time dependence derived analytically from the Navier–Stokes equations in the low-Reynolds-number limit.

We have investigated the lift force on a small isolated particle which is attached to a flat smooth surface and embedded within the viscous sublayer of the turbulent boundary layer over this surface. We have developed a novel experimental technique with which it is possible to measure both the mean and fluctuating lift force by gluing the particle on top of a silicium cantilever. The deflection of this cantilever is measured with a focused laser beam. The sensitivity of the focus detection system allows us to measure a lift force with an average value around 10−8N and with a standard deviation of approximately 5% of the mean. This means that our device is at least a factor of 100 more sensitive than previous devices and at the same time able to measure the lift forces on smaller particles. Data for the mean lift force (FL+) as a function of the particle radius (a+), where both parameters have been non-dimensionalized with the kinematic viscosity v and the friction velocity u*, are obtained in the range 0.3 < a+ < 2. The data support the relationship: FL+ = (56.9 ± 1.1) (a+)1.87±0.04. Also results on the fluctuating lift force have been obtained. We find that the ratio of the r.m.s. to the mean lift force is approximately 2.8.

The linear stability of elliptic pipe flow is considered for finite aspect ratios thereby bridging the gap between the small-aspect-ratio analysis of Davey & Salwen (1994) and the large-aspect-ratio asymptotics of Hocking (1977). The flow is found to become linearly unstable above an aspect ratio of about 10.4 to the spanwise-modulated analogue of the Orr-Sommerfeld mode to which plane Poiseuille flow first loses stability. This disturbance is found to possess a series of intense vortices along its critical layer at lateral stations far removed from the central minor axis. The critical Reynolds number appears to fall from infinity as the aspect ratio increases above 10.4, ultimately approaching Hocking's (1977) asymptotic result at much larger aspect ratios.

The different rise or sinking velocity for different sizes or types of particles gives different vertical sampling of a wind-affected shallow-water flow. This paper derives a mathematical model for the consequent horizontal fractionation of a dilute suspension of particles when the flow is a wind-influenced perturbation from the classical logarithmic open-channel flow. Simple approximations are given for the effective horizontal velocity and for the shear dispersion tensor which preserve the perfect duality between the sensitivity of sinking particles to bed stress and the sensitivity of rising particles to surface stress.

In this paper, we have identified a new mechanism which can promote rapid growth of three-dimensional disturbances. The mechanism involves the interaction between a planar mode and an oblique mode, or a pair of oblique modes, which are phase-locked in the sense that they have the same phase speed. This allows a powerful nonlinear interaction to take place within the common critical layer(s). The disturbance is not required to form a subharmonic resonant triad, and hence the mechanism operates under much less restrictive conditions than does subharmonic resonance (although it is somewhat less powerful). We show that the quadratic interaction between the planar mode and the oblique modes drives an exceptionally large forced mode with the difference frequency, which in turn interacts with the planar mode to contribute the dominant nonlinear effect. This interaction can cause the oblique modes to grow super-exponentially provided that their magnitude is sufficiently small. As a result of the super-exponential growth, the oblique mode may soon become strong enough to produce a feedback effect on the planar mode, so that the interactions eventually become fully coupled. This subsequent stage takes slightly different forms depending on whether a single or a pair of oblique modes is present. Both cases are investigated. Particular attention is paid to symmetric plane shear layers, e.g. a planar wake or jet, for which subharmonic resonance of sinuous modes is inactive.