This paper addresses the cross-stream migration of rigid rods undergoing diffusion and advection in parabolic flow between flat plates – a simple model of a polymer that possesses internal (rotational) degrees of freedom for which the probability distribution depends upon the local shear rate. Unequivocal results on the observable concentration profiles across the channel are obtained from a finite–difference solution of the full Fokker–Planck equation in the space of lateral position y and azimuthal angle φ, the polar angle θ being constrained to π/2 for simplicity. Steric confinement and hydrodynamic wall effects, operative within thin boundary layers, are neglected. These calculations indicate that rods should migrate toward the walls. For widely separated rotational and translational timescales asymptotic analysis gives effective transport coefficients for this migration. Based upon angular distributions at arbitrary rotational Péclet number – obtained here by a least–squares collocation method using trigonometric basis functions – accumulation at the walls is confirmed quantitatively by the effective transport coefficients. The results are extended to free rotation using spherical harmonics as the basis functions in the (φ, θ) orientation space. Finally, a critique is given of the traditional thermodynamic arguments for polymer migration as they would apply to purely rotational internal degrees of freedom.

We consider fibre migration across streamlines in a suspension under plane Poiseuille flow. The flow investigated lies between two infinite, parallel plates separated by a distance comparable to the length of a suspended fibre. We consider the weak flow limit such that Brownian motion strongly affects the fibre position and orientation. Under these conditions, the fibre distribution, fibre mobility and fluid velocity field all vary on scales comparable to the fibre's length thus complicating a traditional volumeaveraging approach to solving this problem. Therefore, we use a non-local derivation of the stress. The resulting fully coupled problem for the fluid velocity, fibre stress contribution and fibre distribution function is solved self-consistently in the limit of strong Brownian motion. When calculated in this manner, we show that at steady state the fibres’ centre-of-mass distribution function shows a net migration of fibres away from the centre of the channel and towards the channel walls. The fibre migration occurs for all gap widths (0 ≤ λ ≤ 35) and fibre concentrations (0 ≤ c ≤ 1.0) investigated. Additionally, the fibre concentration reaches a maximum value around one fibre half-length from the channel walls. However, we find that the net fibre migration is a relatively small change over the fibre's uniform bulk distribution, and typically the centre-of-mass migration changes the uniform concentration profile by only a few percent.

This study concerns the flow around the base of a vertical, wall-mounted cylinder - a pile - exposed to waves. The study comprises (i) flow visualization of horseshoe-vortex flow in front of and the lee-wake-vortex flow behind the pile and (ii) bed shear stress measurements around the pile conducted in a wave flume, plus supplementary bed shear stress measurements carried out in an oscillatory-flow water tunnel. The Reynolds number range of the flume experiments is ReD = (2-9) x 103 and that of the tunnel experiments is ReD= 103—5 x 104, in which ReD is based on the pile size. Steadycurrent tests were also carried out for reference. The horseshoe-vortex flow (like leewake-vortex flow) is governed primarily by the Keulegan-Carpenter number, KC. The range of KC was from 0 to about 25 in the flume experiments, and from 4 to 120 in the tunnel experiments. The experiments were conducted mainly with circular piles. The results indicate that no horseshoe vortex exists for KC < 6. The size and lifespan of the horseshoe vortex increase with KC. The influence of the cross-sectional shape of the pile on the horseshoe vortex was investigated. The results show that a square pile with 90° orientation produces the largest horseshoe vortex while that with 45° orientation produces the smallest one, the circular-pile result being between the two. The influence of a superimposed current on the horseshoe vortex was also investigated. The range of the current-to-wave-induced-velocity ratio, Uc/Um, was from 0 to about 0.8. The overall effect of the superimposed current is to increase the size and lifespan of the horseshoe vortex. This effect increases with increasing Uc/Um. Regarding the near-bed lee-wake flow, the flow regimes observed for the two-dimensional free-cylinder case exist for the present case, too, but with one exception: in the present case, no transverse vortex street was observed in the so-called single-pair regime. The results show that the bed shear stress beneath the horseshoe vortex and in the lee-wake area is heavily influenced by KC. The amplification of the bed shear stress with respect to its undisturbed value is maximum (O(4)) at the side edges of the pile, in contrast to what occurs in steady currents where the maximum occurs at an angle of about 45° from the upstream edge of the pile with an amplification of O(10).

Experiments have been performed to examine the turbulence structure and development of a pair of counter-rotating wing-tip vortices. The vortices were generated by two rectangular NACA 0012 half wings placed tip to tip, separated by 0.25 chordlengths. Preliminary studies showed the vortices to be insensitive to the introduction of a probe and subject only to small wandering motions. Meaningful measurements could therefore be made using hot-wire probes. Three-component velocity measurements were made 10 and 30 chordlengths downstream of the wing leading edges for a chord Reynolds number of 260000.

At 10 chordlengths the vortex cores are laminar. True turbulence levels within them are low and vary little with radius. The turbulence that surrounds the cores is formed by the roll-up of and interaction of the wing wakes that spiral around them. This turbulence is stretched and organized but apparently not produced by the circulating mean velocity fields of the vortices.

At 30 chordlengths the vortex cores have become turbulent. True turbulence levels within them are larger and increase rapidly with radius. The turbulent region surrounding the cores has doubled in size and turbulence levels have not diminished, apparently being sustained by outward diffusion from the core regions. The distribution of the turbulence has also changed, the wake spirals having been replaced by a much more core-centred turbulence field.

This change in flow structure contrasts sharply with what is seen in the equivalent isolated tip vortex, produced when one of the wings is removed. Here the vortex core remains laminar and the turbulence surrounding it decays rapidly with downstream distance. This implies that the transition to turbulence in the cores of the vortex pair is stimulated by interaction between the vortices. Spectral measurements at 10 chordlengths suggest that short-wave instability may be the cause.

The linear instability of a viscous liquid flowing in a vertical sheet sandwiched between two viscous gases bounded externally by two vertical walls is investigated. The critical Weber number below which the flow is absolutely unstable and above which the flow is convectively unstable is found to be approximately equal to one and is weakly dependent on the rest of the parameters. The Weber number is defined as We ≡ ρ1 U20d/S where S is the surface tension, ρ1is the liquid density, U0 is the centreline velocity of the liquid sheet, and d is the half-thickness of the uniform liquid sheet. The sinuous mode is found to have a greater amplification rate than the varicose mode in the convective instability regime. While absolute instability is caused by the surface tension, convective instability is caused by the amplification of disturbances near the liquid-gas interface. The surface tension, and viscosities of liquids and gases all suppress the amplification of the convectively unstable disturbances. An increase in the gravitational force or the gas density results in an enhancement of the amplification rate.

Axisymmetric high-Reynolds-number laminar flows are simulated numerically. In particular, we consider the formation and propagation of single vortex rings from a circular orifice in a plane boundary, and pairs of vortex rings from a circular annulus in a plane boundary. During formation, single rings grow within an essentially potential flow, as in the similarity theory of Pullin (1979). When released they are shown to propagate in an almost inviscid manner, as described by Saffman (1970). Pairs of vortex rings, formed at a circular annulus, have been studied by Weidman & Riley (1993), both experimentally and computationally. They conclude from their observations that the behaviour of the rings depends primarily upon two parameters, namely the impulse applied to the fluid, during ring formation, and the gap width of the annulus. The results we present in this paper confirm the dependence of the flow on these parameters.

We consider dispersion in axisymmetric turbulence which lacks reflectional symmetry. A stochastic equation for the Lagrangian evolution of the velocity of a fluid particle, which is appropriate for infinite Reynolds number turbulence, is used to model the dispersion. Such equations are now common as Lagrangian dispersion models for atmospheric transport problems, but are only strictly well founded for isotropic homogeneous turbulence. It is the minimalist variation from this state of affairs that is considered here. Axisymmetry is the most highly symmetric turbulence that can be suitably analysed by these techniques, spherical symmetry being equivalent to full isotropy in the class of models considered. This simple relaxation of full symmetry leads to oscillations of the Lagrangian velocity autocorrelation, oscillatory growth of the dispersion, significant reduction of dispersion for fixed turbulence kinetic energy and dissipation rate, spiralling fluid-particle trajectories, and tracer fluxes orthogonal to gradients (skew diffusion). The mean fluid-particle angular momentum is an important parameter.

A systems theory framework is presented for the linear stabilization of two-dimensional laminar plane Poiseuille flow. The governing linearized Navier-Stokes equations are converted to control-theoretic models using a numerical discretization scheme. Fluid system poles, which are closely related to Orr-Sommerfeld eigenvalues, and fluid system zeros are computed using the control-theoretic models. It is shown that the location of system zeros, in addition to the well-studied system eigenvalues, are important in linear stability control. The location of system zeros determines the effect of feedback control on both stable and unstable eigenvalues. In addition, system zeros can be used to determine sensor locations that lead to simple feedback control schemes. Feedback controllers are designed that make a new fluid-actuator-sensorcontroller system linearly stable. Feedback control is shown to be robust to a wide range of Reynolds numbers. The systems theory concepts of modal controllability and observability are used to show that feedback control can lead to short periods of highamplitude transients that are unseen at the output. These transients may invalidate the linear model, stimulate nonlinear effects, and/or form a path of ‘bypass’ transition in a controlled system. Numerical simulations are presented to validate the stabilization of both single-wavenumber and multiple-wavenumber instabilities. Finally, it is shown that a controller designed upon linear theory also has a strong stabilizing effect on two-dimensional finite-amplitude disturbances. As a result, secondary instabilities due to infinitesimal three-dimensional disturbances in the presence of a finite-amplitude two-dimensional disturbance cease to exist.

Coherent structures (CS) near the wall (i.e. y + ≤ 60) in a numerically simulated turbulent channel flow are educed using a conditional sampling scheme which extracts the entire extent of dominant vortical structures. Such structures are detected from the instantaneous flow field using our newly developed vortex definition (Jeong & Hussain 1995) - a region of negative λ2, the second largest eigenvalue of the tensor SikSkj + ΩikΩkj - which accurately captures the structure details (unlike velocity-, vorticity- or pressure-based eduction). Extensive testing has shown that λ2 correctly captures vortical structures, even in the presence of the strong shear occurring near the wall of a boundary layer. We have shown that the dominant near-wall educed (i.e. ensemble averaged after proper alignment) CS are highly elongated quasi-streamwise vortices; the CS are inclined 9° in the vertical (x, y)-plane and tilted ±4° in the horizontal (x, z)-plane. The vortices of alternating sign overlap in x as a staggered array; there is no indication near the wall of hairpin vortices, not only in the educed data but also in instantaneous fields. Our model of the CS array reproduces nearly all experimentally observed events reported in the literature, such as VITA, Reynolds stress distribution, wall pressure variation, elongated low-speed streaks, spanwise shear, etc. In particular, a phase difference (in space) between streamwise and normal velocity fluctuations created by CS advection causes Q4 ('sweep’) events to dominate Q2 ('ejection’) and also creates counter-gradient Reynolds stresses (such as Ql and Q3 events) above and below the CS. We also show that these effects are adequately modelled by half of a Batchelor's dipole embedded in (and decoupled from) a background shear U(y). The CS tilting (in the (x, z)-plane) is found to be responsible for sustaining CS through redistribution of streamwise turbulent kinetic energy to normal and spanwise components via coherent pressure-strain effects.

We describe an experimental study of porous media convection (PMC) from onset to 8Rac. The goal of this work is to provide non-invasive imaging and high-precision heat transport measurements to test theories of convection in PMC. We obtain velocity information and visualize the convection patterns using magnetic resonance imaging (MRI). We study both ordered and disordered packings of mono-disperse spheres of diameter d = 3.204 ± 0.029 mm, in circular, rectangular, and hexagonal planforms. In general, the structure of the medium plays a role which is not predicted by theories which assume a homogeneous system. Disordered media are prepared by pouring mono-disperse spheres into the container. Large ordered regions of close packing for the spheres, with grain boundaries and isolated defects, characterize these media. The defects and grain boundaries play an important role in pattern formation in disordered media. Any deviation from close packing produces a region of larger porosity, hence locally larger permeability. The result is spatial variations in the Rayleigh number, Ra. We define the critical Ra, Rac, as the Rayleigh number at the onset of convection in the ordered regions. We find that stable localized convective regions exist around grain boundaries and defects at Ra < Rac. These remain as pinning sites for the convection patterns in the ordered regions as Ra increases above Rac up to 5Rac, the highest Ra studied in the disordered media. In ordered media, spheres are packed such that the only deviations from close packing occur within a thin (<d) region near the vertical walls. Stable localized convection begins at 0.5Rac in the wall regions but appears to play only a weak role in the pattern formation of the interior regions (bulk), since different stable patterns are observed in the bulk at the same Ra after each cycling of Ra below Rac, even for similar patterns of small rolls in the wall regions. The experiments provide a test of the following predictions for PMC: (i) that straight parallel rolls should be linearly stable for Rac < Ra < 5Rac; (ii) that at onset, the rolls should have a dimensionless wavevector qc = π; (iii) that at the upper end of this range rolls should lose stability to cross-rolls; (iv) that the initial slope of the Nusselt curve should be 2; (v) that there should be a rapid decay of vertical vorticity - hence no complex flows, such as those which occur for Rayleigh- Benard convection (RBC) within the nominal regime of stable parallel rolls. These predictions are in partial agreement with our findings for the bulk convection in the ordered media. We observe roll-like structures which relax rapidly to stable patterns between Rac and 5Rac. However we find a wavenumber which is 0.7π compared to π derived from linear stability theory. We find an asymmetry between the size of the upfiowing regions and downfiowing regions as Ra grows above Rac. The ratio of the volume of the upfiowing to the volume of the downfiowing regions decreases as Ra increases and leads to a novel time-dependent state, which does not consist of cross-rolls. This time-dependent state begins at 6Rac and is observed up to 8Rac, the largest Ra which we studied. It seems likely that the occurrence of this state is linked to departures from the Boussinesq approximation at higher Ra. We also find that the slope of the Nusselt curve is 0.7, which does not agree with the predicted value of 2.

We present results for pattern formation at the onset of convection in fluid-saturated porous media obtained by a novel variation on the shadowgraphic technique (modified shadowgraphic technique). Both ordered and disordered media are used, each exhibiting distinct behaviour. Ordered porous media are constructed from grids of overlapping bars. Convective onset in this type of medium is characterized by a sharp, well-defined bifurcation to straight parallel rolls. The orientation of the convection rolls is determined by the number of bar layers, Nb; odd Nb leads to rolls with axes perpendicular to the direction of the top and bottom bars, and even Nb to rolls at 45° to the bars. Disordered porous layers are produced by stacking randomly drilled disks separated by spacers. In this system, we observe a rounded bifurcation to convection with localized convection near convective onset. More specifically, the flow patterns take on one of several different three-dimensional cellular structures after each cycling through convective onset. These observations may be described by two different mechanisms: random spatial fluctuations in the Rayleigh number (Zimmermann et al. 1993), and/or spatial variation in the thermal conductivity on the length scale of the convection wavelength (Braester & Vadasz 1993).

In premixed turbulent combustion, the modelling of the turbulent flux of the mean reaction progress variable remains somewhat controversial. Classical gradient transport assumptions based on the eddy viscosity concept are often used while both experimental data and theoretical analysis have pointed out the existence of countergradient turbulent diffusion. Direct numerical simulation (DNS) is used in this paper to provide basic information on the turbulent flux of and study the occurrence of counter-gradient transport. The numerical configuration corresponds to twoor three-dimensional premixed flames in isotropic turbulent flow. The simulations correspond to various flame and flow conditions that are representative of flamelet combustion. They reveal that different flames will feature different turbulent transport properties and that these differences can be related to basic dynamical differences in the flame-flow interactions: counter-gradient diffusion occurs when the flow field near the flame is dominated by thermal dilatation due to chemical reaction, whereas gradient diffusion occurs when the flow field near the flame is dominated by the turbulent motions. The DNS-based analysis leads to a simple expression to describe the turbulent flux of , which in turn leads to a simple criterion to delineate between the gradient and counter-gradient turbulent diffusion regimes. This criterion suggests that the occurrence of one regime or the other is determined primarily by the ratio of turbulence intensity divided by the laminar flame speed, and by the flame heat release factor, τ ≡ (Tb — Tu)/Tu, where Tu and Tb are respectively the temperature within unburnt and burnt gas. Consistent with the Bray-Moss-Libby theory, counter-gradient (gradient) diffusion is promoted by low (high) values and high (low) values of τ. DNS also shows that these results are not restricted to the turbulent transport of . Similar results are found for the turbulent transport of flame surface density, Σ. The turbulent fluxes of and Σ are strongly correlated in the simulated flames and counter-gradient (gradient) diffusion of always coincides with counter-gradient (gradient) diffusion of Σ.

The wake of a finite cylinder with free ends and an aspect ratio of 21.4 is simulated in three-dimensions and analysed theoretically. Close to the primary-instability threshold, the flow is shown to settle on a limit cycle with a uniform frequency throughout the flow-field. About 20% above the primary-instability threshold, a secondary instability sets in and the limit cycle becomes unstable. The new attractor of the flow can be identified as a limit T2-torus characterized by two incommensurate frequencies. One of them is shown to evolve continuously from the primary-instability frequency, the other one, about 17 times smaller near the secondary-instability threshold, generates a slow modulation of the oscillations in the wake. The limit cycle and the limit torus are described in terms of their Fourier expansion and the spatial distribution of the most relevant Fourier components is investigated. The theoretical analysis and numerical results given shed some light on the mechanisms underlying a number of known but not satisfactorily explained three-dimensional effects in wakes of finite cylinders such as the ambiguity in the dominant Strouhal frequency, the existence of zones with different frequencies spanwise in the wake, the discreteness of coexisting frequencies observed in the wake as well as the spatial uniformity of the beating period. They moreover explain the Reynolds number variation of these effects and identify the recirculation around the cylinder ends as basically responsible for the onset of the secondary instability. The results are compared to the case of a cylinder with aspect ratio of 10.7 to determine the basic trends in aspect ratio dependence. It is shown that qualitatively the same behaviour is obtained, but that the secondary-instability threshold is shifted significantly upward to about twice the primary-instability threshold. Simulations of the wake of a finite NACA wing with incidence show that the form of the cross-section plays a minor role.

The effects of capillary waves are considered on the transfer of gas into (or out of) solution through a gas-liquid interface. The bulk liquid is assumed to be otherwise motionless in the analysis of a preliminary problem; in this problem, a concentration boundary layer is developed as a consequence of a first-order chemical reaction that is assumed to deplete the dissolved gas in the liquid. The reaction rate determines the asymptotic thickness of the concentration boundary layer. It is shown that gas transfer through the concentration boundary layer is most enhanced by the presence of capillary waves when there is vigorous removal of dissolved gases by chemical reaction - i.e. when the reaction is fast and the boundary layer is thin. The results of this theory are then measured against gas transfer through a turbulent, sheared interface in the context of a surface renewal model. Here it is the exchange, from time to time, of fluid between the interface and the bulk that leads to the development of a thin concentration boundary layer when the bulk fluid is not saturated with dissolved gas. Capillary waves are shown to thicken the concentration boundary layer at the interface and to increase the rate of gas transfer.

Finite-amplitude convection in rotating spherical fluid shells is considered for a variety of Prandtl numbers P and Rayleigh numbers Ra up to about 10 times the critical value. Convection at low Rayleigh numbers in the form of azimuthally periodic or weakly aperiodic drifting waves is characterized by relatively low heat transport, especially for P ≲ 1. The transition to strongly time-dependent convection leads to a rapid increase of the heat transport with increasing Rayleigh numbers. Onset of convection in the polar regions is delayed, but contributes a disproportionate fraction of the heat transport at high Rayleigh number. The differential rotation generated by convection, the distributions of helicity, and the role of asymmetry with respect to the equatorial plane are also studied.

A careful study of the existing literature available in the field of cavitation reveals the potential of ultrasonics as a tool for controlling and, if possible, eliminating certain types of hydrodynamic cavitation through the manipulation of nuclei size present in a flow. A glass venturi is taken to be an ideal device to study the cavitation phenomenon at its throat and its potential control. A piezoelectric transducer, driven at the crystal resonant frequency, is used to generate an acoustic pressure field and is termed an ‘ultrasonic nuclei manipulator (UNM)'. Electrolysis bubbles serve as artificial nuclei to produce travelling bubble cavitation at the venturi throat in the absence of a UNM but this cavitation is completely eliminated when a UNM is operative. This is made possible because the nuclei, which pass through the acoustic field first, cavitate, collapse violently and perhaps fragment and go into dissolution before reaching the venturi throat. Thus, the potential nuclei for travelling bubble cavitation at the venturi throat seem to be systematically destroyed through acoustic cavitation near the UNM. From the solution to the bubble dynamics equation, it has been shown that the potential energy of a bubble at its maximum radius due to an acoustic field is negligible compared to that for the hydrodynamic field. Hence, even though the control of hydrodynamic macro cavitation achieved in this way is at the expense of acoustic micro cavitation, it can still be considered to be a significant gain. These are some of the first results in this direction.

The relation, first written by Kolmogorov, between the third-order moment of the longitudinal velocity increment δu1 and the second-order moment of δu1 is presented in a slightly more general form relating the mean value of the product δu1(δui)2, where (δui)2 is the sum of the square of the three velocity increments, to the secondorder moment of δui. In this form, the relation is similar to that derived by Yaglom for the mean value of the product δu1(δuθ)2 where (δuθ)2 is the square of the temperature increment. Both equations reduce to a ‘four-thirds’ relation for inertialrange separations and differ only through the appearance of the molecular Prandtl number for very small separations. These results are confirmed by experiments in a turbulent wake, albeit at relatively small values of the turbulence Reynolds number.