Direct numerical simulations (DNS) of the Navier–Stokes equations are used to investigate the role of the Klebanoff-mode in laminar–turbulent transition in a flatplate boundary layer. To model the effects of free-stream turbulence, volume forces are used to generate low-frequency streamwise vortices outside the boundary layer. A suction/blowing slot at the wall is used to generate a two-dimensional Tollmien–Schlichting (TS) wave inside the boundary layer. The characteristics of the fluctuations inside the boundary layer agree very well with those measured in experiments. It is shown how the interaction of the Klebanoff-mode with the two-dimensional TS-wave leads to the formation of three-dimensional TS-wavepackets. When the disturbance amplitudes reach a critical level, a fundamental resonance-type secondary instability causes the breakdown of the TS-wavepackets into turbulent spots.

The energy exchange between the kinetic and internal energies in non-premixed reacting compressible homogeneous turbulent shear flow is studied via data generated by direct numerical simulations (DNS). The chemical reaction is modelled by a one- step exothermic irreversible reaction with Arrhenius-type reaction rate. The results show that the heat release has a damping effect on the turbulent kinetic energy for the cases with variable transport properties. The growth rate of the turbulent kinetic energy is primarily in uenced by the reaction through temperature-induced changes in the solenoidal dissipation and modifications in the explicit dilatational terms (pressure–dilatation and dilatational dissipation). The production term in the scaled kinetic energy equation, which is proportional to the Reynolds shear stress anisotropy, is less affected by the heat release. However, the dilatational part of the production term increases during the time when the reaction is important. Additionally, the pressure–dilatation correlation, unlike the non-reacting case, transfers energy in the reacting cases, on the average, from the internal to the kinetic energy. Consequently, the dilatational part of the kinetic energy is enhanced by the reaction. On the contrary, the solenoidal part of the kinetic energy decreases in the reacting cases mainly due to an enhanced viscous dissipation. Similarly to the non-reacting case, it is found that the direct coupling between the solenoidal and dilatational parts of the kinetic energy is small. The structure of the flow with regard to the normal Reynolds stresses is affected by the heat of reaction. Compared to the non-reacting case, the kinetic energy in the direction of the mean velocity decreases during the time when the reaction is important, while it increases in the direction of the shear. This increase is due to the amplification of the dilatational kinetic energy in the x2-direction by the reaction. Moreover, the dilatational effects occur primarily in the direction of the shear. These effects are amplified if the heat release is increased or the reaction occurs at later times. The non-reacting models tested for the explicit dilatational terms are not supported by the DNS data for the reacting cases, although it appears that some of the assumptions employed in these models hold also in the presence of heat of reaction.

The incompressible fluid flow in a rectangular container driven by two facing sidewalls which move steadily in anti-parallel directions is investigated experimentally for Reynolds numbers up to 1200. The moving sidewalls are realized by two rotating cylinders of large radii tightly closing the cavity. The distance between the moving walls relative to the height of the cavity (aspect ratio) is Γ = 1.96. Laser-Doppler and hot-film techniques are employed to measure steady and time-dependent vortex flows. Beyond a first threshold robust, steady, three-dimensional cells bifurcate supercritically out of the basic flow state. Through a further instability the cellular flow becomes unstable to oscillations in the form of standing waves with the same wavelength as the underlying cellular flow. If both sidewalls move with the same velocity (symmetrical driving), the oscillatory instability is found to be tricritical. The dependence on two sidewall Reynolds numbers of the ranges of existence of steady and oscillatory cellular flows is explored. Flow symmetries and quantitative velocity measurements are presented for representative cases.

The air density fluctuations in the plumes of fully expanded, unheated free jets were investigated experimentally using a Rayleigh-scattering-based technique. The point measuring technique used a continuous-wave laser, fibre-optic transmission and photon counting electronics. The radial and centreline profiles of time-averaged density and root-mean-square density fluctuation provided a comparative description of jet growth. To measure density fluctuation spectra a two-photomultiplier-tube (PMT) technique was used. Cross-correlation between the two PMT signals significantly reduced the electronic shot noise contribution. The density fluctuation spectra were found to be remarkably similar for all Mach number jets. A detailed survey in fully expanded Mach 0.95, 1.4 and 1.8 jets further confirmed that the distribution of various Strouhal frequency fluctuations remained similar, except for a spatial stretching with increased Mach number. In spite of this similarity in flow fluctuations the noise sources in these three jets were found to be significantly different. Spark schlieren photographs and near-field microphone measurements confirmed that Mach wave radiation was present in the Mach 1.8 jet, and was absent in the Mach 0.95 jet. Direct correlation measurement between the flow density fluctuation (cause) and far-field sound pressure fluctuation (effect) shed further light on the sound generation process. For this purpose a microphone was kept fixed at a far-field point, mostly at a distance of 50 diameters and 30° to the flow direction, and the laser probe volume was moved from point to point in the flow. In the Mach 1.8 jet, where the convective velocity of Kelvin–Helmholtz instability waves exceeded the ambient sound speed, significant correlation was measured from the peripheral shear layer, while in the Mach 0.95 jet, where the instability waves had subsonic convective speed, no correlation could be measured. Although the same instability waves were present in both Mach 1.8 and 0.95 jets, the peripheral shear layer of the former was found to be an obvious noise source, while that of the latter was not. Further correlation studies along the jet centreline showed that behaviour in the region downstream of the potential core was similar in all Mach number jets tested, 0:6[les ]M[les ]1:8. Good correlation at low Strouhal frequencies was measured from this region, which started from downstream of the potential core and extended many diameters from there.

In this study we investigate the Kolmogorov flow (a shear flow with a sinusoidal velocity profile) in a weakly stratified, two-dimensional fluid. We derive amplitude equations for this system in the neighbourhood of the initial bifurcation to instability for both low and high Péclet numbers (strong and weak thermal diffusion, respectively). We solve amplitude equations numerically and find that, for low Péclet number, the stratification halts the cascade of energy from small to large scales at an intermediate wavenumber. For high Péclet number, we discover diffusively spreading, thermal boundary layers in which the stratification temporarily impedes, but does not saturate, the growth of the instability; the instability eventually mixes the temperature inside the boundary layers, so releasing itself from the stabilizing stratification there, and thereby grows more quickly. We solve the governing fluid equations numerically to compare with the asymptotic results, and to extend the exploration well beyond onset. We find that the arrest of the inverse cascade by stratification is a robust feature of the system, occurring at higher Reynolds, Richards and Péclet numbers – the flow patterns are invariably smaller than the domain size. At higher Péclet number, though the system creates slender regions in which the temperature gradient is concentrated within a more homogeneous background, there are no signs of the horizontally mixed layers separated by diffusive interfaces familiar from doubly diffusive systems.

This paper provides comparisons between experimental data and numerical results for impulsively started flows in a three-dimensional rectangular lid-driven cavity of aspect ratio 1:1:2 at Reynolds number 1000. The initial evolution of this flow is studied up to the dimensionless time t = 12 and is found both experimentally and numerically to exhibit high sensitivity to geometrical perturbations. Three different flow developments generated by very small changes in the boundary geometry are found in the experiments and are reproduced by the numerics. This indicates that even at moderate Reynolds numbers the predictability of three-dimensional incompressible viscous flows in bounded regions requires controlling the shape of the boundary and the values of the boundary conditions more carefully than needed in two dimensions.

A spatial two-dimensional version of the Zakharov equation describing the evolution of deep-water gravity waves is used to derive two fourth-order evolution equations, for the amplitudes of the surface elevation and of the velocity potential. The scaled form of the equations is presented.

The dynamics of a vortex subject to a localized stretching is numerically investigated. The structure of the flow is analysed in the case of an initially two-dimensional vortex surrounded by a periodic array of vortex rings localized far from its core. Amplified oscillations of both the axial vorticity and the stretching are found, in strong contrast with Burgers-like vortices. The resulting dynamics is the appearance, around the vortex, of successive vortical structures of smaller and smaller radius and alternate sign embedded in the previous vortical rings. The frequency scaling of the oscillations is recovered by linear analysis (Kelvin modes) but not the amplification nor the shape of the successive tori. An inviscid model based on structures is presented, which compares better with the numerical computations. These results suggest that the formalism of Kelvin waves is not sufficient to describe the full dynamics, which is instead related to the feedback of rotation on stretching and more conveniently described in terms of localized structures. We finally discuss the relative timescales of vortex stretching and of vortex reaction. The Burgers-like vortices, where there is no such reaction, turn out to correspond to a nearly pure strain field, slightly disturbed by rotation.

The onset of instability in a liquid annular jet enclosing another fluid, and surrounded by a gas in a pipe is analysed by use of a spectra-collocation method. The dynamic responses to the variation of different flow parameters are elucidated by use of numerical results. Two linearly independent convectively unstable interfacial modes of disturbances are found. In general, the para-sinuous mode has a larger amplification rate than the para-varicose mode. It is shown that to initiate encapsulation of core fluid with a uniform shell fluid, the growth of the para-sinuous mode must be promoted and the para-varicose mode must be suppressed. Suppression of the paravaricose mode in a finite range of wavenumbers is possible by varying the flow parameters. The effects of ten relevant parameters on instability are discussed. In certain parameter space, the annular jet becomes absolutely unstable with respect to the sinuous mode. The transition Weber number below which the flow is absolutely unstable and above which the flow is convectively unstable is found as a function of the Reynolds number when the rest of flow parameters are given. A successful encapsulation of core fluid with a uniform shell fluid is possible if the process is carried out outside of the parameter space of absolute instability, and if an external forcing is introduced at a frequency within a band in which the para-varicose mode is stable but the para-sinuous mode is convectively unstable.

The main objectives of this study are to suggest a proper boundary condition at the interface between a permeable block and turbulent channel flow and to investigate the characteristics of turbulent channel flow with permeable walls. The boundary condition suggested is an extended version of that applied to laminar channel flow by Beavers & Joseph (1967) and describes the behaviour of slip velocities in the streamwise and spanwise directions at the interface between the permeable block and turbulent channel flow. With the proposed boundary condition, direct numerical simulations of turbulent channel flow that is bounded by the permeable wall are performed and significant skin-friction reductions at the permeable wall are obtained with modification of overall flow structures. The viscous sublayer thickness is decreased and the near-wall vortical structures are significantly weakened by the permeable wall. The permeable wall also reduces the turbulence intensities, Reynolds shear stress, and pressure and vorticity fluctuations throughout the channel except very near the wall. The increase of some turbulence quantities there is due to the slip-velocity fluctuations at the wall. The boundary condition proposed for the permeable wall is validated by comparing solutions with those obtained from a separate direct numerical simulation using both the Brinkman equation for the interior of a permeable block and the Navier–Stokes equation for the main channel bounded by a permeable block.

We revisit Salmon's ‘Dirac bracket projection’ approach to constructing generalized semi-geostrophic equations. One of the obstacles to the method's applicability is that it leads to a sign-indefinite energy functional in the computational domain. In some instances this can cause severe failure of the model. We demonstrate in the simple context of shallow-water semi-geostrophy that the Hamiltonian remains positive definite when the asymptotic expansion at the heart of this method is carried to the next order. The resulting new model can be interpreted in the framework of regularization by Lagrangian averaging, which is currently receiving much attention.

Real-time holographic interferometry and shadowgraph visualization are used to study convection in the fluid between two concentric spheres when two distinct buoyancy forces are applied to the fluid. The heated inner sphere has a constant temperature that is greater than the constant temperature of the outer sphere by ΔT. In addition to the usual gravitational buoyancy from temperature induced density differences, another radial buoyancy is imposed by applying an a.c. voltage difference, ΔV between the inner and outer spheres. The resulting electric field gradient in this spherical capacitor produces a central polarization force. The temperature dependence of the dielectric constant results in the second buoyancy force that is especially large near the inner sphere. The normal buoyancy is always present and, within the parameter range explored in our experiment, always results in a large-scale cell that is axisymmetric about the vertical. We have found that this flow becomes unstable to toroidal or spiral rolls that form near the inner sphere and travel vertically upward when ΔT and ΔV are suffciently high. These rolls start near the centre sphere's equator and travel upward toward its top. The onset of this instability depends on both the temperature difference at onset ΔTc and the voltage difference at onset ΔVc and these two quantities appear to be related, within the parameter range accessible to our experimental system, by a power law ΔVc ∝ ΔT1/3c. Measurements of the heat transfer show that these travelling rolls increase the heat transfer at onset. Far above onset, the heat transfer may actually decrease with increasing ΔT. The travelling roll's frequency increases with increasing ΔT near onset and with increasing ΔV far above onset. These results have been interpreted in terms of a flow structure that includes a thermal boundary-layer-like behaviour. This layer has a radial width that increases from the bottom pole to an unstable ‘latitude’ near the equator where the rolls appear.

In this paper we report the results of an experimental study of periphyton–flow interactions conducted in a specially designed outdoor hydraulic flume. ‘Periphyton’ is a collective term for the micro-organisms which grow on stream beds, and includes algae, bacteria, and fungi, with algae usually the dominant and most conspicuous component. The main goals of the study are to identify potential effects of periphyton–flow interactions as well as the potential mechanisms of mass transfer in the near-bed region, which could influence periphyton growth and losses. The main results of the study may be summarized as follows.

A linear velocity distribution in the interfacial sublayer (i.e. below the roughness tops), and a logarithmic distribution above the roughness tops appeared to be reasonable approximations for both flow types, with and without periphyton on the bed. However, the appearance of periphyton on a rough bed shifts the origin of the bed upwards, increases the roughness length zo by 16–21%, and reduces the ratio of the mean velocity at the level of roughness tops to the shear velocity by ≈30%. In general, below the roughness tops the periphyton suppresses the mean velocities, the turbulent stresses, turbulence intensities, and vertical turbulent fluxes of the turbulent energy and turbulent shear stresses.

It was found that in flows without periphyton large-scale eddies successfully penetrate the interfacial sublayer. However, tufts of periphyton on the tops of the roughness elements significantly weaken the penetration processes leading to spatial de-correlation in the velocity field within the interfacial sublayer. The appearance of periphyton on the bed does not change appreciably the velocity spectra above the roughness tops but reduces the total spectral energy and generates a wide spectral peak in the interfacial sublayer. Most probably, this peak is formed by penetration of sweep events into the interfacial sublayer, ‘filtered’ by the periphyton tufts. Thus, sweep events may be the main mechanism responsible for the delivery of nutrients from the outer region to the biologically active interfacial sublayer. The potential effects of flow properties on the periphyton community are also discussed.

The vectoring of an incompressible, two-dimensional jet in a co-flowing stream is investigated by means of direct numerical simulation. The control input used to stimulate jet vectoring is accomplished through distributed suction from blunt-faced lips at the exit of the jet. The thrust vector methodology is based on suppression of global instabilities in the wake-shear layers formed between the co-flow and the jet. Once a critical suction volume flux needed to suppress these global instabilities is exceeded, local flow control can be realized through varying the distribution of suction across the base of the jet lips. It is found that the critical suction flux scales primarily with the ambient co-flow, not with the jet speed, and that lift-to-thrust ratios exceeding 15% can be realized. The effects of jet Reynolds number, jet-to- ambient velocity ratio, boundary-layer thickness, and geometric parameters on various performance characteristics are examined. It is also shown that the asymmetric flow control approach used for vectoring the jet can also be implemented in a symmetric configuration to enhance jet spreading. Significant increases in jet spreading can be realized when the symmetrically applied suction flux is sufficient to stimulate the sinuous mode of instability of the jet such that energetic apping motion ensues.

Turbulent plane jets are prototypical free shear flows of practical interest in propulsion, combustion and environmental flows. While considerable experimental research has been performed on planar jets, very few computational studies exist. To the authors' knowledge, this is the first computational study of spatially evolving three-dimensional planar turbulent jets utilizing direct numerical simulation. Jet growth rates as well as the mean velocity, mean scalar and Reynolds stress profiles compare well with experimental data. Coherency spectra, vorticity visualization and autospectra are obtained to identify inferred structures. The development of the initial shear layer instability, as well as the evolution into the jet column mode downstream is captured well.

The large- and small-scale anisotropies in the jet are discussed in detail. It is shown that, while the large scales in the flow field adjust slowly to variations in the local mean velocity gradients, the small scales adjust rapidly. Near the centreline of the jet, the small scales of turbulence are more isotropic. The mixing process is studied through analysis of the probability density functions of a passive scalar. Immediately after the rollup of vortical structures in the shear layers, the mixing process is dominated by large-scale engulfing of fluid. However, small-scale mixing dominates further downstream in the turbulent core of the self-similar region of the jet and a change from non-marching to marching PDFs is observed. Near the jet edges, the effects of large-scale engulfing of coflow fluid continue to influence the PDFs and non-marching type behaviour is observed.