A family of velocity profiles with reversed flow, typical of those found in separated flows, are examined for their linear instability properties. Specifically, a family of modified Falkner-Skan profiles are analyzed for the onset of absolute instability as the magnitude of the reversed flow increases. The mode of instability associated with the inflection point in the vicinity of the dividing streamline is found to become absolutely unstable as the peak reversed flow approaches about thirty percent of the free stream value. The family of profiles were used to construct generic models of separation bubble and study the possible onset of global instability in the representative spatially-developing flows. (C) Elsevier, Paris.
The formation of three-dimensional vortices in spatially-growing incompressible mixing layers is investigated in Large-Eddy Simulation at zero molecular viscosity, with the aid of the Filtered Structure Function subgrid-scale model proposed in Ducros et nl. (1996, J. Fluid Mech., 326, pp. 1-36). Up to the second pairing at least, strong sensitivity to the nature of the random upstream perturbations and the spanwise size of the domain is observed. In addition to 'unequal' pairings between Kelvin-Helmholtz billows having undergone a different number of pairings and destructive 'translative-pairing-and-tearing' events, the two types of flow patterns obtained in the temporal Direct Numerical Simulations of Comte et ni. (1992, Phys. Fluids A, 4, 2761-2778), are recovered, namely, highly three-dimensional vortex lattices undergoing local or helical pairings, as in the experiments of Chandrsuda et al.(1978, J. Fluid Mech. 85), or quasi-two-dimensional billows undergoing successive pairings while stretching streamwise vortices in between each other, as observed by Bernal and Roshko (1986, J. Fluid Mech., 170, 499-525). These streamwise vortices form in a succession of stages involving local roll-up and pairing, as conjectured by Lin and Corcos (1984, J. Fluid Mech., 141). Streamwise vortices are also found in a mixing layer formed within a solid-propellant rocket engine. At the wall of the outlet nozzle, they interact and possibly merge with Dean-Gortler-type vortices. (C) Elsevier, Paris.
Various identification and visualization methods of vortical structures, especially of slender vortices, are critically reviewed with a special attention to their objectivity. The sectional-swirl-and-pressure-minimum scheme is presented as a new identification method and applied to homogeneous turbulence. Since the physical quantities associated with an individual vortex can be analyzed separately, this new scheme enables us to investigate quantitatively various physical characteristics related to vortices, such as the variations of the core shape, the circulation and the vorticity vector along a vortex and the temporal evolution of arbitrarily selected vortices. (C) Elsevier, Paris.
It is now well-known that the wake transition regime for a circular cylinder involves two modes of small-scale three-dimensional instability, modes "A" and "B", occurring in different Reynolds number ranges. These modes are quite distinct in spanwise lengthscale and in symmetry, and they are found to scale on different physical features of the how. Mode A has a large spanwise wavelength of around 3-4 cylinder diameters, and scales on the larger physical structure in the flow, namely the core of the primary Karman vortices. The feedback from one vortex to the next gives an out-of-phase streamwise vortex pattern for this mode. In contrast, the mode B instability has a distinctly smaller spanwise wevelength (1 diameter) which scales on the smaller physical structure in the flow, namely the braid shear layer. The symmetry of mode B is determined by the reverse flow behind the bluff cylinder, leading to a system of streamwise vortices which are in phase between successive half cycles. The symmetries of both modes are the same as the ones found in the vortex system evolving from perturbed plane wakes studied by Meiburg and Lasheras (1988) and Lasheras and Meiburg (1990). Furthermore, the question of the physical origin of these three-dimensional instabilities is addressed. We present evidence that they are linked to general instability mechanisms found in two-dimensional linear flows. In particular, mode A seems to be a result of an elliptic instability of the near-wake vortex cores; predictions based on elliptic instability theory concerning the initial perturbation shape and the spanwise wevelength are in good agreement with experimental observations. For the mode B instability,it is suggested that it is a manifestation of a hyperbolic instability of the stagnation point flow found in the braid shear layer linking the primary vortices. (C) Elsevier, Paris.
The receptivity of a laminar boundary layer to free stream disturbances has been experimentally investigated through the introduction of deterministic localized disturbances upstream of a hat plate mounted in a wind tunnel. Hot-wire measurements indicate that the spanwise gradient of the normal velocity component (and hence the streamwise vorticity) plays an essential role in the transfer of disturbance energy into the boundary layer. Inside the laminar boundary layer the disturbances were found to give rise to the formation of longitudinal structures of alternating high and low streamwise velocity. Similar streaky structures exist in laminar boundary layers exposed to free stream turbulence, in which the disturbance amplitude increases in linear proportion to the displacement thickness. In the present study the perturbation amplitude of the streaks was always decaying for the initial amplitudes used, in contrast to the growing fluctuations that are observed in the presence of free stream turbulence. This points out the importance of the continuous influence from the free stream turbulence along the boundary layer edge. (C) Elsevier, Paris.
The main purpose of this paper is to bring about a better balance between views of the exaggerated importance of concentrated vorticity, on one hand, and the underestimated role of three kinds of regions other than concentrated vorticity: i - 'structureless' background, ii - regions of strong vorticity/strain (self) interaction and strong enstrophy generation, and iii - regions with negative enstrophy production, on the other hand, with the emphasis on the latter. Results of experiments on turbulent grid flow and DNS of decaying turbulent how in a periodic 'box' at the same Reynolds number (Re-lambda approximate to 75) are used in order to demonstrate that all these regions are strongly non-Gaussian, dynamically significant and possess structure. It is argued that due to the strong nonlocality of turbulence in physical space all the four regions are in continuous interaction and are strongly correlated. Thus the answer to the question posed in the title is that - though important - regions of concentrated vorticity are not as important as is commonly believed. (C) Elsevier, Paris.
The present investigation has been undertaken in order to better understand the development of free, plane liquid jets. Both the development of the basic laminar flow as well as its stability have been investigated theoretically and experimentally. The velocity field and free surface location of a liquid jet emanating from a plane channel was calculated numerically and the velocity and surface relaxation lengths were determined. Calculated velocity profile distributions were in good agreement with Pitot tube measurements. Temporal linear stability calculations were performed using the calculated velocity distributions. The calculations showed five unstable modes, three sinuous and two dilatational. Four of these modes have been reported earlier and one of the sinuous modes is considered to be 'new'. The linear stability calculations include surface tension as well as viscosity in the liquid and gas. Hot wire anemometry measurements of controlled forced disturbances showed that waves in the experimental jet also were sinuous and that the amplitude distribution was in fair agreement with theoretical results. Shadowgraph visualisations showed the evolution of the waves on the surface of the jet and it was found that the waves break up downstream the nozzle. This break-up was visualized by particle visualisations, which showed that it creates strong streamwise streaks in the jet. (C) Elsevier, Paris.
The asymptotic behaviour of the motion of an incompressible fluid between a stationary and a rotating disc with a low aspect ratio and a radial inflow is analyzed assuming a small Ekman number. Two distinct solutions are obtained for the central core flow behaviour, depending on whether or not there is a superposed inflow, and general integral relations are presented. An experimental study is performed in air. Detailed measurements provide data for the radial and circumferential mean velocity components, Reynolds stress components and static pressure on the stator, for several values of the significant dimensionless parameters. This experimental investigation shows that it is relevant to consider the dimensionless inflow rate as a significant parameter. Comparisons between the analytical solutions and the experimental data are in agreement with the features of the asymptotic model and are used to provide a better physical understanding of the flow. (C) Elsevier, Paris.
The recently discovered concentration of vorticity in slender vortex tubes in turbulent flow fields has motivated the investigation of a class of vortices with elliptical streamlines. As a prototype of this flow, long vortices confined in a rectangular cavity and driven by tangentially moting walls are studied. These vortices are characterized by a large rate of plane strain at the core. The quasi-two-dimensional flow is found to be unstable at small Reynolds numbers, if the eccentricity of the streamlines, i.e. the strain rate, is sufficiently large. The three-dimensional supercritical flow is found to be steady with a wavelength of the order of the vortex core diameter. The flow pattern appears in the form of rectangular cells that are very robust. Good agreement between experiment and numerical calculations is obtained. It is argued that the instability found is due to the elliptic instability mechanism. (C) Elsevier, Paris.
Thermal convection for an incompressible Herschel-Bulkley fluid along an annular duct, whose inner cylinder is rotating and outer is at rest, is analyzed numerically and experimentally. The outer cylinder is heated at constant heat flux density and the inner one is assumed adiabatic. The first part of this study deals with the effect of the rheological behavior of the fluid and that of the rotation of the inner cylinder on the flow field and heat transfer coefficient. All the physical properties are assumed constant and the flow is assumed fully developed. The critical Rossby number Ro(c) = (R-1 Omega/U-d)(c), for which the dimension of the plug flow is reduced to zero is determined with respect to the Bow behavior index, the radius ratio and the Herschel-Bulkley number for axial flow. The rotation of the inner cylinder induces a decrease of the axial velocity gradient at the outer cylinder thereby reducing the heat transfer between the heated wall and the fluid. The second part of this study introduces the variation of the consistency K with temperature and analyzes the evolution of the Bow pattern and heat transfer coefficient along the heating zone. Two cases are distinguished depending on the Rossby number: (i) Ro < Ro(c), the plug Bow dimension increases along the heating zone; (ii) Po < Ro(c), the decrease of K with temperature leads to the reappearance of the plug Bow. For high angular velocities, it is possible to have a plug zone attached to the outer cylinder. Finally, a correlation is proposed for the Nusselt number. It shows clearly that the effect of thermodependency of K on the heat transfer becomes more important with increasing rotational velocity of the inner cylinder. (C) Elsevier, Paris.
Bifurcations from the quiescent state of three dimensional water wave solutions of a sixth order model equation are analysed. The equation in question is a generalization of the Kadomtsev-Petviashvili equation, and is obtained due to the presence of certain surface effects. These effects are caused either by a surface tension with Bond number close to 1/3, or by an elastic ice-sheet floating on the water surface. The equation describing travelling waves is reduced to a system of ordinary differential equations on a center manifold. Solutions having the form of a solitary wave with damped oscillations, propagating in a channel, are obtained. In the direction transverse to the propagation they satisfy boundary conditions which are either periodic or of Dirichlet type. In the periodic case we find both asymmetric and symmetric waves. In particular, some of these solutions fill a gap in the speeds of the travelling waves where no two-dimensional solitary waves exist. We show that the critical spectra of the linear operators of the model equation and of the full water wave problem are identical. (C) Elsevier, Paris.
Two different vortex sheet models are used to study the transition from absolute to convective instability in variable-density swirling jet flows. It is found that swirl enhances the tendency for absolute instability in a jet issuing into a non-swirling medium when the vortical core of the swirling how is small compared to the jet radius. When the size of the vortical core approximate the size of the let, the effect of swirl on promoting absolute instability is quite weak. The vend toward absolute instability is accentuated when the jet is heated relative to the ambient. If the how external to the jet also possesses swirl, the tendency tox ard absolute instability is increased when the jet shear layer is centrifugally unstable according to Rayleigh's criterion (i.e., the circulation decreases with increasing radius) and is decreased when the shear layer is centrifugally stable. (C) Elsevier, Paris.
Exact similarity solutions for the impingement of two viscous, immiscible oblique stagnation flows forming a flat interface are given. The problem is governed by three parameters: the ratios of density rho = rho(1)/rho(2) and of viscosity mu = mu(1)/mu(2) of the two fluids and R = tan theta(1)/tan theta(2) where theta(1) and theta(2) are the asymptotic angles of the incident streamlines in each fluid layer. For given values of rho, mu, and theta(2), the compatible flows in the lower fluid, as measured by the strain rate ratio beta = beta(1)/beta(2) of the two fluids and the asymptotic angle of incidence theta(1), are found such that the interface remains horizontal in a uniform gravitational field. For rho = 1, explicit solutions show that a family of co-current and counter-current shears supporting a flat interface exist for all finite, nonzero values of R. Far rho = 1, the normal stress interfacial boundary conditions restricts the flow to a unique combination of asymptotic far-field shear and Hiemenz stagnation-point flow in each fluid layer. The displacement thicknesses in each layer are always positive when the fluid densities are not equal, but vanish simultaneously as rho > 1. At each value of rho the interfacial velocities increase with increasing viscosity ratio mu. As a generalization of the present oblique two-fluid stagnation-point how problem, we discuss how the hat interface may be inclined with respect to the horizontal in a uniform, gravitational field. (C) Elsevier, Paris.
A uniform now of a gas condensing onto its plane condensed phase (commonly known as the half-space problem of condensation) is considered. The problem is studied analytically on the basis of the Boltzmann equation when the flow is in a transonic region. The paper clarifies the analytical structure of the solution, especially the mechanism by which the range of the parameters (the Bow speed, pressure, and temperature of the uniform How blowing from infinity) where a steady solution exists changes abruptly (from a surface to a domain in the parameter space) when the How speed passes the sonic speed, the correspondence of a family of supersonic solutions to a subsonic solution, etc. The solutions constructed analytically are compared with new numerical solutions near the sonic point. (C) Elsevier, Paris.
This paper represents an initial analysis of unsteady gaseous Bows in a rectangular microchannel under usual pressure and temperature conditions. The effect of depth and aspect ratios of the cross-section is investigated. With most fluid-based mechanical microsystems of snail internal dimensions and subject to normal pressure and temperature conditions, flow is rarefied with slip at the walls. This flow is then modeled by the Navier-Stokes equations combined with slip and temperature jump conditions at the walls. These conditions are represented by Maxwell-Smoluchowski first order equations. By concentrating essentially on the pulsed sinusoidal regime, it is shown that the instantaneous flow rate amplitude, as well as the band pass of the microchannel are underestimated when slip at the walls is not taken into account. The frequency response of two microchannels connected in series with different cross-sectional areas is also studied. Finally, the proposed model can serve as a tool giving information about the current feasibilities of pressure sensors for the measurement of the dynamic characteristics of gaseous flows in microchannels. (C) Elsevier, Paris.
The behaviour of small liquid drops, hanging from a circular disk and approaching a Rat wail at a different temperature is studied experimentally and numerically. If the pendant drop and the solid surface are at the same temperature and if the liquid wets the solid, the drop spreads over the surface forming a liquid bridge in times of the order of milliseconds. If the upper disk is heated and/or the solid surface is cooled, then the drop does not wet the wall. even if pressed against the surface, bur it is deformed in a completely reversible way, similarly to an elastic material (e.g. like a rubber balloon). To investigate this unusual and intriguing phenomenon, a systematic experimental programme has been carried out on silicone oils (with different viscosities) and on diesel oils. At the same time the problem was studied numerically under the assumption that a thin air film exists between the drop and the solid surface. This film is formed by the entrainment of the surrounding air caused by the Marangoni How directed, along the liquid surface, from the upper disk towards the contact zone. If suitable conditions are established, the pressure in the air film balances the pressure necessary to deform the liquid drop, preventing the wetting of the solid surface. The experimental results agree with the proposed numerical model. In particular the computed equilibrium air film thicknesses are compared with the thicknesses measured with a background illumination system and with an interferometric technique; a good agreement is found between numerical and experimental results, for different liquids and different geometrical configurations. (C) Elsevier, Paris.
Low-temperature superfluid turbulence is studied experimentally in a Helium swirling flow and numerically with the Gross-Pitaevskii equation in the geometry of the Taylor-Green (TG) vortex flow. Numerically, it was found in Nore er al. (1997a, b) that the kinetic energy transfer in the superfluid TG vortex is comparable to that of the viscous TG vortex and that the energy spectrum of the superflow is compatible with Kolmogrorov's scaling. The vorticity dynamics of the superflow are similar to that of the viscous flow. In both cases, many vortex reconnection events happen throughout the how. Experimentally, power measurements and pressure fluctuation spectra show very little difference above and far below the superfluid transition temperature, where the normal-fluid component of Helium is negligible (less than 5% in mass at T = 1.2 K). (C) Elsevier, Paris.
Previous studies on boundary layer transition at moderate levels of free stream turbulence (FST) have shown that the transition process can be promoted by the introduction of Tollmien-Schlichting (TS) waves. In the present work the interaction between localized boundary layer disturbances and controlled TS-waves is studied experimentally. The localized disturbances are generated either from a controlled free stream perturbation, or by means of suction or injection through a slot in the hat plate surface. Both methods result in boundary layer disturbances dominated by elongated streamwise streaks of high and low velocity in the streamwise component. A strong interaction is observed preferably for high frequency TS-waves, which are damped when generated separately, and the interaction starts as a local amplification of a wide band of low-frequency oblique waves. The later stages of the transition process can be identified as a non-linear interaction between the oblique structures, leading to regeneration of new and stronger streamwise streaks. (C) Elsevier, Paris.
Experimental measurements performed under conditions which reproduce most of the dynamical characteristics of the natural evolution of vorticity filaments in turbulent flows are presented here. Strong deviations from the Burgers vortex (which is a non-confirmed stretched vortex model) are observed and analyzed. (C) Elsevier, Paris.
The present theoretical and experimental knowledge of the intense intermittent events in high Reynolds number turbulence is reviewed. An attempt is made to relate the two main streams of research in this area: the multifractal description and the coherent filaments identified in numerical simulations. It is concluded that, although both approaches can be expressed in a common language, they are inconsistent in detail and both are incomplete. While the multifractal approach is a kinematic description without dynamics, the present understanding of the scaling and dynamics of the coherent vortices requires the existence of stable laminar structures of arbitrarily large Reynolds numbers, and probably represents only one of a hierarchy of intermittent objects. It is suggested that the vortices may not survive at very high values of Rex, and that the problem extends to all the intermittent structures of turbulence. It is shown that the filaments should dominate the structure functions in a range of scales that goes from beyond the Kolmogorov scale for p infinity (usually expected as p > infinity.) (C) Elsevier, Paris.