Turbulence-driven secondary motion (known as secondary flow of Prandtl's second kind) is the result of the anisotropy of Reynolds stresses. It is associated with internal or external turbulent flow in the vicinity of streamwise corners. In the last six decades the flow along the streamwise internal corner has attracted the attention of many researchers, but it is only recently at the University of Melbourne that an experimental investigation on a flow over an external corner has been undertaken. Although the turbulence-driven secondary motions are generally much smaller than those resulting from skewing of the mean spanwise vorticity (known as secondary flow of Prandtl's first kind), they have a pronounced effect on peripheral wall shear stress distributions and heat transfer rates in the corner region. In the present study the details of turbulence-driven secondary motion over the external corner are explored experimentally and a counter-rotating helical streamwise vortex pair symmetrically placed around the corner bisector is found. As expected, all mean velocity and Reynolds stress profiles on both surfaces at the same spanwise distance from the corner agree quite well, having nominal deviation. The secondary flow is observed to be directed away from the corner bisector and then flow back towards the wall. It is also revealed that far from the corner, the flow develops as a nominal two-dimensional flat-plate boundary-layer flow.

A new depth-integrated equation is derived to model a time-harmonic motion of small-amplitude waves in water of variable depth. The new equation, which is referred to as the complementary mild-slope equation here, is derived from Hamilton's principle in terms of stream function. In the formulation, the continuity equation is satisfied exactly in the fluid domain. Also satisfied exactly are the kinematic boundary conditions at the still water level and the uneven sea bottom. The numerical results of the present model are compared to the exact linear theory and the existing mild-slope equations that have been derived from the velocity-potential formulation. The computed results give better agreement with those of the exact linear theory than the other mild-slope equations. Comparison shows that the new equation provides accurate results for a bottom slope up to 1.

Friction factor data from two recent pipe flow experiments are combined to provide a comprehensive picture of the friction factor variation for Reynolds numbers from 10 to 36,000,000.

The three-dimensional linear instability of axisymmetric flow between exactly counter-rotating disks is studied numerically. The dynamics are governed by two parameters, the Reynolds number $Re$ based on cylinder radius and disk rotation speed and the height-to-radius ratio $\Gamma$. The stability analysis performed for $0.5 \,{\le}\, \Gamma \,{\le}\, 3$ shows that non-axisymmetric modes are dominant and stationary and that the critical azimuthal wavenumber is a decreasing function of $\Gamma$. The patterns of the dominant perturbations are analysed and a physical mechanism related to a shear layer instability is discussed. No evidence of complex dynamical behaviour is seen in the neighbourhood of the 1:2 codimension-two point when the $m\,{=}\,2$ threshold precedes that of $m\,{=}\,1$. Axisymmetric instabilities are also calculated; these may be stationary or Hopf bifurcations. Their thresholds are always higher than those of non-axisymmetric modes.

The objective of the study is to develop a closed-loop control scheme that is capable of preserving the columnar swirling flow state in the finite-length pipe model of Wang & Rusak (1996a). The base state consists of a solid body rotation superimposed on axial plug flow, with two dimensionless parameters: the swirl $\Omega$ and the pipe aspect ratio $L$. The linear stability properties of the columnar base state are documented and shown to give rise to unstable global modes above a critical swirl level $\Omega_1$, thereby triggering vortex breakdown. Our study focuses on the derivation of a control method in order to quench the linear development of the Wang & Rusak instability. An optimal control approach is then devised for a reduced-order system which is obtained by a suitable projection on a low-order subspace of the $N$ least-stable eigenmodes. The actuator consists of perturbations of the inlet circulation and its time history is selected so as to minimize a cost-functional incorporating both the state energy and the control energy. A Riccati-based formulation leads to the determination of the optimal gain matrix for the low-order system. When applied to the full linear system, the feedback law for $N=4$ succeeds in maintaining the columnar base state for swirl levels as high as 13% above global onset. The control scheme is found to be robust with respect to noise and to uncertainties in parameter settings. It remains effective even under partial-state information conditions.

The goal of this study is to understand the effect of latent heat release on entrainment in cumulus clouds by employing a laboratory analogue consisting of a volumetrically heated turbulent axisymmetric jet. The jet fluid is volumetrically heated in an off-source manner to simulate condensation heat release in clouds. The experimental set-up is similar to Bhat & Narasimha (1996), and the current application of wholefield velocimetry and thermometry has allowed us to probe in detail the velocity and temperature fields within the heat injection zone (HIZ) for the first time, leading to several new results. We are able to demarcate three distinct zones within the HIZ based primarily on the nature of the cross-stream velocity profile, and we present sharp differences in flow properties in these zones. Thermochromic liquid crystal-based temperature visualizations have revealed details about the complex interplay of velocity, local concentration and temperature leading to a physically coherent understanding of this flow. We also provide evidence using linear stochastic estimates (LSE) to show that large eddies are disrupted in the latter part of the HIZ; the disruption of large eddies is linked to the change in the nature of the cross-stream velocity profile. While our results have confirmed certain previously reported observations such as a reduction in scalar width, we have measured significantly larger r.m.s. values within the HIZ than previously reported, which is corroborated by direct numerical simulation results.

We focus on the bulge in the scalar and velocity width at the start of the HIZ and link it to the excess deceleration of the centreline velocity there. Ideas proposed by Tso & Hussain (1989) are used to explain the eventual reduction of jet width with buoyancy addition. We also employ LSE to show that eddies are laterally compressed in ordinary jets, and that the surviving ones become more circular with heat addition in accordance with Lumley's (1971) hypothesis. Our primary conclusion differs from Bhat & Narasimha (1996) in that we measure a mass flux that exceeds that of an unheated jet throughout the HIZ. Further, we show that a step-increase in momentum flux corresponds to a step-increase in mass flux.

We present the first laboratory evidence of internal gravity wave tunnelling through weakly stratified fluid patches and we derive analytic theories for energy transmission by the waves in two distinct circumstances. In one, the computed transmission coefficient is directly analogous to the textbook calculation for quantum tunnelling of a free electron incident upon a potential barrier. In the other, we consider the partial reflection and transmission of internal waves through a mixed region bounded by discontinuities in the density profile. The results reveal a linear resonance between vertically propagating internal waves and interfacial waves that exist on either flank of the mixing region. The resonance permits perfect transmission of internal waves that would otherwise strongly reflect from the weakly stratified region. We discuss a specific application of our results to deep convective storm-generated internal waves that tunnel through the mesosphere to the ionosphere.

A multi-scale asymptotic theory is derived for the evolution and interaction of currents and surface gravity waves in water of finite depth, under conditions typical of coastal shelf waters outside the surf zone. The theory provides a practical and useful model with which wave–current coupling may be explored without the necessity of resolving features of the flow on space and time scales of the primary gravity-wave oscillations. The essential nature of the dynamical interaction is currents modulating the slowly evolving phase of the wave field and waves providing both phase-averaged forcing of long infra-gravity waves and wave-averaged vortex and Bernoulli-head forces and hydrostatic static set-up for the low-frequency current and sea-level evolution equations. Analogous relations are derived for wave-averaged material tracers and density stratification that include advection by horizontal Stokes drift and by a vertical Stokes pseudo-velocity that is the incompressible companion to the horizontal Stokes velocity. Illustrative solutions are analysed for the special case of depth-independent currents and tracers associated with an incident surface wave field and a vortex with O(1) Rossby number above continental shelf topography.

In this paper we consider the stability of the flow produced by an infinite rotating disk. A large-Reynolds-number asymptotic theory is developed to obtain the non-parallel correction to the local absolute instability (AI) found for this flow by Lingwood (1995), who used the parallel-flow approximation. Our asymptotic theory is based on the inviscid AI underlying the viscous AI and so is expected to give the non-parallel correction to the upper branch of Lingwood's neutral curve for the AI. It is found that non-parallel terms have a destabilizing effect on the AI. Also, it is shown that, although the position of the neutral curve for convective instability is known to depend on choice of measurement quantity, for AI it does not. However, in relating the asymptotic non-parallel results to the numerical parallel results at large Reynolds numbers, it is found that Lingwood's viscous AI does not, after all, asymptote towards the inviscid results. Instead, Lingwood's family of branch points is distinct from a second family of branch points that do asymptote towards the inviscid limit. We show that these two families of branch points are related by a ‘super branch point’ at which three spatial branches connect simultaneously. Lingwood's branch points, in fact, have a viscous long-wave origin, and will therefore be subjected to non-parallel effects that are some power of the Reynolds number larger than if they had been of inviscid origin.

We study the potential flow of a second-order fluid over a sphere or an ellipse. The normal stress at the surface of the body is calculated and has contributions from the inertia, viscous and viscoelastic effects. We investigate the effects of Reynolds number and body size on the normal stress; for the ellipse, various angles of attack and aspect ratios are also studied. The effect of the viscoelastic terms is opposite to that of inertia; the normal stress at a point of stagnation can change from compression to tension. This causes long bodies to turn into the stream and causes spherical bodies to chain. For a rising gas bubble, the effect of the viscoelastic and viscous terms in the normal stress is to extend the rear end so that it tends to the cusped trailing edge observed in experiments.

A simultaneous technique employing particle image velocimetry (PIV) and shadowgraphy was used to study vertical slug flow in non-Newtonian fluids. Two aqueous solutions of 0.8 and 1.0 wt% carboxymethylcellulose (CMC) were studied and the flow field around individual Taylor bubbles fully characterized. The rheological fluid properties and pipe dimension yielded Reynolds numbers of 8 and 4 and Deborah numbers of 0.2 and 0.4. A negative wake was found downstream of the Taylor bubbles in both fluids. Below the bubble trailing edge, along the axis region, the fluid flows in the opposite direction to the bubble (negative wake), originating rotational liquid movements in adjacent regions. Even far downward from the bubble, rotational liquid movements are clearly seen and measured. In the 1.0 wt% CMC solution, the bubble trailing edge has the shape of a two-dimensional cusp. This two-dimensional cusp, of small dimensions, is seen in different orientations during the bubble rise-indicating a fast rotational movement. The asymmetrical shape of the trailing edge is responsible for small asymmetries in the flow in the wake region (three-dimensional flow). The asymmetrical shape associated with the rotational movement is responsible for an unsteady flow of small amplitude. In the 0.8 wt% CMC solution, the shape of the trailing edge changes during the bubble rise. An axisymmetric axial oscillation a continuous expansion and contraction of the trailing edge, is the origin of this behaviour. This oscillatory movement is responsible for an unsteady flow of small amplitude in the wake region.

The velocity fluctuations present in macroscopically homogeneous suspensions of neutrally buoyant non-Brownian spheres undergoing simple shear flow, and their dependence on the microstructure developed by the suspensions, are investigated in the limit of vanishingly small Reynolds numbers using Stokesian dynamics simulations. We show that, in the dilute limit, the standard deviation of the velocity fluctuations (the so-called suspension temperature) is proportional to the volume fraction, in both the transverse and the flow directions, and that a theoretical prediction, which considers only the hydrodynamic interactions between isolated pairs of spheres, is in good agreement with the numerical results at low concentrations. We also simulate the velocity fluctuations that would result from a random hard-sphere distribution of spheres in simple shear flow, and thereby investigate the effects of the microstructure on the velocity fluctuations. Analogous results are discussed for the fluctuations in the angular velocity of the suspended spheres. In addition, we present the probability density functions for all the linear and angular velocity components, and for three different concentrations, showing a transition from a Gaussian to an exponential and finally to a stretched exponential functional form as the volume fraction is decreased.

The simulations include a non-hydrodynamic repulsive force between the spheres which, although extremely short range, leads to the development of fore–aft asymmetric distributions for large enough volume fractions, if the range of that force is kept unchanged. On the other hand, we show that, although the pair distribution function recovers its fore–aft symmetry in dilute suspensions, it remains anisotropic and that this anisotropy can be accurately predicted theoretically from the two-sphere solution by assuming the complete absence of any permanent doublets of spheres.

We also present a simple correction to the analysis of laser-Doppler velocimetry measurements, which substantially improves the interpretation of these measurements at low volume fractions even though it involves only the angular velocity of a single sphere in the vorticity direction.

Finally, in an Appendix, we show that, in the dilute limit, the whole velocity autocorrelation function can be predicted using again only two-particle encounters.

The problem of vortical motions in the surf zone is simplified by taking the bottom topography to be piecewise flat while allowing finite-height jumps in depth between flat regions. The motion of an arbitrary number of singular vortices is cast into Hamiltonian form and the rule for relating Hamiltonians in conformally equivalent domains derived. Examples are given of a singular vortex pair colliding head-on with a step, of a vortex propagating along a curved coast to cross a step, and of a vortex being swept past a circular island straddling a step. Surf-zone vortices are then modelled as finite-area vortex patches and their motion followed by contour dynamics. It is shown that the paths of singular vortices can yield highly accurate explicit predictions of the paths of the centroids of vortex patches. Possible applications to surf-zone rip currents are noted.

We present the results of a combined experimental and theoretical investigation of the family of free-surface flows generated by obliquely colliding laminar jets. We present a parameter study of the flow, and describe the rich variety of forms observed. When the jet Reynolds number is sufficiently high, the jet collision generates a thin fluid sheet that evolves under the combined influence of surface tension and fluid inertia. The resulting flow may take the form of a fluid chain: a succession of mutually orthogonal links, each composed of a thin oval film bound by relatively thick fluid rims. The dependence of the form of the fluid chains on the governing parameters is examined experimentally. An accompanying theoretical model describing the form of a fluid sheet bound by stable rims is found to yield good agreement with the observed chain shapes. In another parameter regime, the fluid chain structure becomes unstable, giving rise to a striking new flow structure resembling fluid fishbones. The fishbones are demonstrated to be the result of a Rayleigh–Plateau instability of the sheet's bounding rims being amplified by the centripetal force associated with the flow along the curved rims.

Of particular importance to the development of models for isolated vortex ring dynamics in a real fluid is knowledge of ambient fluid entrainment by the ring. This time-dependent process dictates changes in the volume of fluid that must share impulse delivered by the vortex ring generator. Therefore fluid entrainment is also of immediate significance to the unsteady forces that arise due to the presence of vortex rings in starting flows. Applications ranging from industrial and transportation, to animal locomotion and cardiac flows, are currently being investigated to understand the dynamical role of the observed vortex ring structures. Despite this growing interest, fully empirical measurements of fluid entrainment by isolated vortex rings have remained elusive. The primary difficulties arise in defining the unsteady boundary of the ring, as well as an inability to maintain the vortex ring in the test section sufficiently long to facilitate measurements. We present a new technique for entrainment measurement that utilizes a coaxial counter-flow to retard translation of vortex rings generated from a piston–cylinder apparatus, so that their growth due to fluid entrainment can be observed. Instantaneous streamlines of the flow are used to determine the unsteady vortex ring boundary and compute ambient fluid entrainment. Measurements indicate that the entrainment process does not promote self-similar vortex ring growth, but instead consists of a rapid convection-based entrainment phase during ring formation, followed by a slower diffusive mechanism that entrains ambient fluid into the isolated vortex ring. Entrained fluid typically constitutes 30% to 40% of the total volume of fluid carried with the vortex ring. Various counter-flow protocols were used to substantially manipulate the diffusive entrainment process, producing rings with entrained fluid fractions up to 65%. Measurements of vortex ring growth rate and vorticity distribution during diffusive entrainment are used to explain those observed effects, and a model is developed to relate the governing parameters of isolated vortex ring evolution. Measurement results are compared with previous studies of the process, and implications for the dynamics of starting flows are suggested.

A large-eddy simulation technique is described for computing Rayleigh–Taylor instability. The method is based on high-wavenumber-preserving subgrid-scale models, combined with high-resolution numerical methods. The technique is verified to match linear stability theory and validated against direct numerical simulation data. The method is used to simulate Rayleigh–Taylor instability at a grid resolution of $1152^3$. The growth rate is found to depend on the mixing rate. A mixing transition is observed in the flow, during which an inertial range begins to form in the velocity spectrum and the rate of growth of the mixing zone is temporarily reduced. By measuring growth of the layer in units of dominant initial wavelength, criteria are established for reaching the hypothetical self-similar state of the mixing layer. A relation is obtained between the rate of growth of the mixing layer and the net mass flux through the plane associated with the initial location of the interface. A mix-dependent Atwood number is defined, which correlates well with the entrainment rate, suggesting that internal mixing reduces the layer's growth rate.

The wall-jetting effect in Mach reflections in viscous pseudo-steady flows (as obtained in shock tubes) is investigated numerically. The W-modification of Godunov's scheme has been modified to solve the Navier–Stokes equations using a splitting into physical processes. The viscous terms are approximated using an explicit scheme with central differences in space and a two-step Runge–Kutta method in time. Two analytical models are considered. The first is a self-similar viscous flow model in which we consider a flow field with characteristic size $L$, and assume that as the characteristic size grows from 0 to $L$, the viscosity of the gas ahead of the shock wave varies from 0 to $\mu_{0}$. Consequently, the flow can be made self-similar by using the parameter $\textit{Re}\,{=}\,\rho_{0}a_{0}L/\mu_{0}$. The second is a real non-stationary viscous flow, in which the molecular viscosity during the growth of a characteristic size from 0 to $L$ remains constant and is equal $\mu_{0}$. As a result the viscous effects are only partially accounted for in the self-similar viscous flow model in comparison to a real non-stationary viscous flow model, since they are smaller in the former case. The present investigation complements our previous investigation of the wall-jetting effect in Mach reflection in inviscid pseudo-steady flows (Henderson et al. 2003).