The turbulence structure in zero-pressure-gradient boundary layers above smooth, rough and wavy surfaces was investigated. The mean flow, turbulence intensity and spectral data for both smooth and rough surfaces show support for the attached eddy hypothesis of Townsend (1976), the model for wall turbulence proposed by Perry & Chong (1982) and the extended version developed by Perry, Henbest & Chong (1986). Anomalies in hot-wire behaviour when measuring in the turbulent wall region of the flow were discovered and some of these have been resolved.

Spray combustion is analysed using a full simulation of the continuous gaseous carrier phase, while dilute-spray modelling is adopted for the discrete phase. The direct numerical simulation of the flow is performed in an Eulerian context and a Lagrangian description is used for the spray. The numerous physical parameters controlling spray flames are first studied to construct two synthetic model problems of spray combustion: a laminar spray flame that propagates freely over a train of droplets and a weakly turbulent spray-jet with coflowing preheated air. It is observed that the flame structures can be classified with respect to three dimensionless quantities, which characterize the fuel/air equivalence ratio within the core of the spray-jet, the ratio between the mean distance between the droplets and the flame thickness, and the ratio between an evaporation time and a flame time. A large variety of reaction zone topologies is found when varying those parameters, and they are scrutinized by distinguishing between premixed and diffusion combustion regimes. Partially premixed combustion is observed in most of the spray-jet flames and the spray parameters that make the flame transition from non-premixed to premixed combustion are determined. A combustion diagram for dilute-spray combustion is then proposed from the identification of those various regimes.

Liquid of viscosity $\mu$ moves slowly through a cylindrical tube of radius $R$ under the action of a pressure gradient. An immiscible force-free drop having viscosity $\lambda\mu$ almost fills the tube; surface tension between the liquids is $\gamma$. The drop moves relative to the tube walls with steady velocity $U$, so that both the capillary number ${\hbox{\it Ca}}\,{=}\,\mu U/\gamma$ and the Reynolds number are small. A thin film of uniform thickness $\epsilon R$ is formed between the drop and the wall. It is shown that Bretherton's (1961) scaling $\epsilon\propto{\hbox{\it Ca}}^{{2}/{3}}$ is appropriate for all values of $\lambda$, but with a coefficient of order unity that depends weakly on both $\lambda$ and ${\hbox{\it Ca}}$. The coefficient is determined using lubrication theory for the thin film coupled to a novel two-dimensional boundary-integral representation of the internal flow. It is found that as $\lambda$ increases from zero, the film thickness increases by a factor $4^{{2}/{3}}$ to a plateau value when ${\hbox{\it Ca}}^{-{1}/{3}}\,{\ll}\,\lambda\,{\ll}\,{\hbox{\it Ca}}^{-{2}/{3}}$ and then falls by a factor $2^{{2}/{3}}$ as $\lambda\,{\rightarrow}\,\infty$. The multi-region asymptotic structure of the flow is also discussed.

A mathematical model is presented for the high pressures and sudden velocity changes which may occur in the impact between a region of incompressible liquid and either a solid surface or a second liquid region. The theory rests upon the well-known idea of pressure impulse, for the sudden initiation of fluid motion in incompressible fluids. We consider the impulsive pressure field which occurs when a moving fluid region collides with a fixed target, such as when an ocean wave strikes a sea wall. The boundary conditions are given for modelling liquid-solid and liquid-liquid impact problems. For a given fluid domain, and a given velocity field just before impact, the theory gives information on the peak pressure distribution, and the velocity after impact. Solutions for problems in simple domains are presented, which give insight into the peak pressures exerted by a wave breaking against a sea wall, and a wave impacting in a confined space. An example of liquid-liquid impact is also examined. Results of particular interest include a relative insensitivity to the shape of the incident wave, and an increased pressure impulse when impact occurs in a confined space. The theory predicts that energy is lost from the bulk fluid motion and we suggest that this energy can be transferred to a thin jet of liquid which is projected away from the impact region.

An experimental study involving flow visualization and two-component LDV measurements has been undertaken to elucidate the deformation of an axisymmetric jet (ReD ≈ 1950 and 4160) caused by tabs placed at the nozzle exit. Previous studies have shown the profound distortion of high-speed jets with tabs and have demonstrated that a pair of counter-rotating streamwise vortices generated by each tab are responsible for the deformation of the jet core. This work illustrates the distortion as well as some of the more subtle features of the tab effect. Extensive visualizations taken simultaneously from two perspectives reveal the real-time evolution of complex three-dimensional flow structures. Velocity data show the expected overall distortion, and the existence and strength of the streamwise vortices responsible for this deformation. Furthermore, a second set of weaker streamwise vortices was detected near each tab, the size and location of which was consistent with a horseshoe vortex system. The data showed a widespread increase in both Reynolds normal and shear stresses and generally indicated the accelerated development of the mixing layer when tabs were inserted. A brief analysis employing vortex dynamics - an alternative to previous work which utilized pressure gradient arguments-is used to explain the tab effect, resulting in similar conclusions.

Mathematical methods of control theory are applied to the problem of control of fluid flow with the long-range objective of developing effective methods for the control of turbulent flows. The procedure of how to cast the problem of controlling turbulence into a problem in optimal control theory is presented using model problems through the formalism and language of control theory. Then we present a suboptimal control and feedback procedure for general stationary and time-dependent problems using methods of calculus of variations through the adjoint state and gradient algorithms. This suboptimal feedback control procedure is applied to the stochastic Burgers equation. Two types of controls are investigated: distributed and boundary controls. The control inputs are the momentum forcing for the distributed control and the boundary velocity for the boundary control. Costs to be minimized are defined as the sum of the mean-square velocity gradient inside the domain for the distributed control or the square velocity gradient at the wall for the boundary control; and in both cases a term was added to account for the implementation cost. Several cases of both controls have been numerically simulated to investigate the performances of the control algorithm. Most cases considered show significant reductions of the costs. Another version of the feedback procedure more effective for practical implementation has been considered and implemented, and the application of this algorithm also shows significant reductions of the costs. Finally, dependence of the control algorithm on the time-discretization method is discussed.

The dynamics of the sublayer and buffer regions of wall-bounded turbulent flows are analysed using autonomous numerical simulations in which the outer flow, and on some occasions specific wavelengths, are masked. The results are compared with a turbulent channel flow at moderate Reynolds number. Special emphasis is put on the largest flow scales. It is argued that in this region there are two kinds of large structures: long and narrow ones which are endogenous to the wall, in the sense of being only slightly modified by the presence or absence of an outer flow, and long and wide structures which extend to the outer flow and which are very different in the two cases. The latter carry little Reynolds stress near the wall in full simulations, and are largely absent from the autonomous ones. The former carry a large fraction of the stresses in the two cases, but are shown to be quasi-linear passive wakes of smaller structures, and they can be damped without modifying the dynamics of other spectral ranges. They can be modelled fairly accurately as being infinitely long, and it is argued that this is why good statistics are obtained in short or even in minimal simulation boxes. It is shown that this organization implies that the scaling of the near-wall streamwise fluctuations is anomalous.

The effect of gyrotaxis on the linear stability of a suspension of swimming, negatively buoyant micro-organisms is examined for a layer of finite depth. In the steady basic state there is no bulk fluid motion, and the upwards swimming of the cells is balanced by diffusion resulting from randomness in their shape, orientation and swimming behaviour. This leads to a bulk density stratification with denser fluid on top. The theory is based on the continuum model of Pedley, Hill & Kessler (1988), and employs both asymptotic and numerical analysis. The suspension is characterized by five dimensionless parameters: a Rayleigh number, a Schmidt number, a layer-depth parameter, a gyrotaxis number G, and a geometrical parameter measuring the ellipticity of the micro-organisms. For small values of G, the most unstable mode has a vanishing wavenumber, but for sufficiently large values of G, the predicted initial wavelength is finite, in agreement with experiments. The suspension becomes less stable as the layer depth is increased. Indeed, if the layer is sufficiently deep an initially homogeneous suspension is unstable, and the equilibrium state does not form. The theory of Pedley, Hill & Kessler (1988) for infinite depth is shown to be appropriate in that case. An unusual feature of the model is the existence of overstable or oscillatory modes which are driven by the gyrotactic response of the micro-organisms to the shear at the rigid boundaries of the layer. These modes occur at parameter values which could be realized in experiments.

The origin of meandering and braiding of alluvial rivers is re-analysed in terms of stability theory. The flow is described by a two-dimensional model, and the transportation of sediment is separated into bed-load transport and transport of suspended sediment, by use of the improved knowledge of sediment transport mechanisms achieved in recent years. The paper explains why it is important to distinguish between the sediment transported as bed load and that in suspension.

The analysis is able to predict whether a river remains stable or tends to meander or braid.

The results of the stability analysis are compared with laboratory experiments and data from natural rivers, and the agreement is satisfactory.

Here we study the dynamics of a bubble or drop as it is driven by a pressure gradient through a capillary tube. For the case of a straight capillary, the drop can either approach a steady-state shape or the rear of the drop develops a re-entrant cavity. Also, depending on the initial conditions, the drop can break apart into smaller drops. For flow through a constricted capillary tube, depending on the physical parameters of the problem, the drop can either move through the constriction or break into two or more pieces as it moves past the constriction. We study this snap-off process numerically and determine the effect of the physical parameters on the dynamics of the drop.

Using a ‘clean’ jet facility the relationship between the jet flow and its radiation field was studied experimentally in the Mach-number range 0.05 < Mj < 0.20 and a Reynolds-number range 6 × 104 < ReD < 2.3 × 105. The various acoustic source parameters such as strength, frequency and Mach number were varied systematically, and the far-field pressure measured simultaneously. On the basis of these measurements the nature of the sources in the initial shear layer could be characterized. The principal results, equally valid for unexcited and excited jets, are as follows: the acoustic sources are not convected but are located within a confined volume fixed with respect to the nozzle even though they are being generated by moving disturbances in the jet; they are associated with the nonlinear saturation of the unstable wave amplitudes of the shear layer occurring at the vortex-pairing locations; the radiation intensity varies nonlinearly with the source strength and is highly directional, exponential in character.

The neutral curve for stationary vortex disturbances in rotating-disk flow is computed up to a Reynolds number of 107 using the sixth-order system of linear stability equations which includes the effects of streamline curvature and Coriolis force. It is found that the neutral curve has two minima: one at R = 285.36 (upper branch) and the other at R = 440.88 (lower branch). At large Reynolds numbers, the upper branch tends to Stuart's asymptotic solution while the lower branch tends to a solution that is associated with the wave angle corresponding to the direction of zero mean wall shear.

Disturbances of arbitrary amplitude are superposed on a basic flow which is assumed to be steady and either (a) two-dimensional, homogeneous, and incompressible (rotating or non-rotating) or (b) stably stratified and quasi-geostrophic. Flow over shallow topography is allowed in either case. The basic flow, as well as the disturbance, is assumed to be subject neither to external forcing nor to dissipative processes like viscosity. An exact, local ‘wave-activity conservation theorem’ is derived in which the density A and flux F are second-order ‘wave properties’ or ‘disturbance properties’, meaning that they are O(a2) in magnitude as disturbance amplitude a → 0, and that they are evaluable correct to O(a2) from linear theory, to O(a3) from second-order theory, and so on to higher orders in a. For a disturbance in the form of a single, slowly varying, non-stationary Rossby wavetrain, $\overline{F}/\overline{A}$ reduces approximately to the Rossby-wave group velocity, where (${}^{-}$) is an appropriate averaging operator. F and A have the formal appearance of Eulerian quantities, but generally involve a multivalued function the correct branch of which requires a certain amount of Lagrangian information for its determination. It is shown that, in a certain sense, the construction of conservable, quasi-Eulerian wave properties like A is unique and that the multivaluedness is inescapable in general. The connection with the concepts of pseudoenergy (quasi-energy), pseudomomentum (quasi-momentum), and ‘Eliassen-Palm wave activity’ is noted.

The relationship of this and similar conservation theorems to dynamical fundamentals and to Arnol'd's nonlinear stability theorems is discussed in the light of recent advances in Hamiltonian dynamics. These show where such conservation theorems come from and how to construct them in other cases. An elementary proof of the Hamiltonian structure of two-dimensional Eulerian vortex dynamics is put on record, with explicit attention to the boundary conditions. The connection between Arnol'd's second stability theorem and the suppression of shear and self-tuning resonant instabilities by boundary constraints is discussed, and a finite-amplitude counterpart to Rayleigh's inflection-point theorem noted.

The flow of an ideal dissociating gas through a nearly conical nozzle is considered. The equations of one-dimensional motion are solved numerically assuming a simple rate equation together with a number of different values for the rate constant. These calculations suggest that deviations from chemical equilibrium will occur in the nozzle if the rate constant lies within a very wide range of values, and that, once such a deviation has begun, the gas will very rapidly ’freeze’. The dissociation fraction will then remain almost constant if the flow is expanded further, or even if it passes through a constant area section. An approximate method of solution, making use of this property of sudden ’freezing’ of the flow, has been developed and applied to the problem of estimating the deviations from equilibrium under a wide range of conditions. If all the assumptions made in this paper are accepted, then lack of chemical equilibrium may be expected in the working sections of hypersonic wind tunnels and shock tubes. The shape of an optimum nozzle is derived in order to minimize this departure from equilibrium.

It is shown that, while the test section conditions are greatly affected by ’freezing’, the flow behind a normal shock wave is only changed slightly. The heat transfer rate and drag of a blunt body are estimated to be reduced by only about 25% even if complete freezing occurs. However, the shock wave shape is shown to be rather more sensitive to departures from equilibrium.

We study the dynamics of turbulent boundary layer flow over a heterogeneous topography composed of roughness patches exhibiting relatively high and low correlation in the streamwise and spanwise directions, respectively (i.e. the roughness appears as streamwise-aligned ‘strips’). It has been reported that such roughness induces a spanwise-wall normal mean secondary flow in the form of mean streamwise vorticity associated with counter-rotating boundary-layer-scale circulations. Here, we demonstrate that this mean secondary flow is Prandtl’s secondary flow of the second kind, both driven and sustained by spatial gradients in the Reynolds-stress components, which cause a subsequent imbalance between production and dissipation of turbulent kinetic energy that necessitates secondary advective velocities. In reaching this conclusion, we study (i) secondary circulations due to spatial gradients of turbulent kinetic energy, and (ii) the production budgets of mean streamwise vorticity by gradients of the Reynolds stresses. We attribute the secondary flow phenomena to extreme peaks of surface stress on the relatively high-roughness regions and associated elevated turbulence production in the fluid immediately above. An optimized state is attained by entrainment of fluid exhibiting the lowest turbulent stresses – from above – and subsequent lateral ejection in order to preserve conservation of mass.

We investigate the dynamical and statistical features of turbulent Taylor–Couette flow (for a radius ratio 0.5) through three-dimensional direct numerical simulations (DNS) at Reynolds numbers ranging from 1000 to 8000. We show that in three-dimensional space the Görtler vortices are randomly distributed in banded regions on the wall, concentrating at the outflow boundaries of Taylor vortex cells, which spread over the entirecylinder surface with increasing Reynolds number. Görtler vortices cause streaky structures that form herringbone-like patterns near the wall. For the Reynolds numbers studied here, the average axial spacing of the streaks is approximately 100 viscous wall units, and the average tilting angle ranges from 16° to 20°. Simulationresults have been compared to the experimental data in the literature, and the flow dynamics and statistics are discussed in detail.

The description of entrainment in turbulent free jets is at the heart of physical models of some major flows in environmental science, from volcanic plumes to the dispersal of pollutant wastes. The classical approach relies on the assumption of complete self-similarity in the flows, which allows a simple parameterization of the dynamical variables in terms of constant scaling factors, but this hypothesis remains under debate. We use in this paper an original parameterization of entrainment and an extensive review of published experimental data to interpret the discrepancy between laboratory results in terms of the systematic evolution of the dynamic similarity of the flow as a function of downstream distance from the source. We show that both jets and plumes show a variety of local states of partial self-similarity in accordance with the theoretical analysis of George (1989), but that their global evolution tends to complete self-similarity via a universal route. Plumes reach this asymptotic regime faster than jets which suggests that buoyancy plays a role in more efficiently exciting large-scale modes of turbulence.

Artificially initiated turbulent spots in a Blasius boundary layer were investi- gated experimentally using hot-wire anemometers. Electrical discharges generated the spots, which grew in all directions rn they were swept downstream by the mean flow. A typical lateral spread angle of the spots is 10° to each side of t.he plane of symmetry. Conditional sampling methods were used to form ensemble-averaged data yielding the average shape of a spot and the mean flow field in its vicinity. Far downstream a spot exhibits conical similarity and all quantities measured seem to be independent of the type of disturbance which generated the spot in the first place.

In plan view, the spot has an arrowhead shape whose leading interface is convected downstream somewhat more slowly than the free-stream velocity near the plane of symmetry and at approximately half the free-stream velocity at the extreme spanwise location. The trailing interface is convected at a constant velocity throughout (UTE = 0·5 U∞). In this way the spot entrains laminar fluid through both interfaces, resulting in its elongation it proceeds downstream. The flow near the surface accelerates abruptly as the leading interface passes by, however the acceleration continues within the spot and the velocity attains a maximum near the trailing interface. There is therefore a continuous increase in skin friction towards the trailing interface. Further away from the surface the passage of the spot is marked by deceleration followed by acceleration after the ridge of the spot passes the measuring station. All changes in velocity occur monotonically without causing inflexions or kinks in the ensemble-averaged velocity profiles. Although the displacement and momentum thicknesses change quite rapidly within the spot, the shape factor is practically constant in the interior region (H = 1·5); and the velocity profiles may be very well represented by the universal logarithmic distribution. The spanwise velocity component W is everywhere directed outwards (i.e. away from the plane of symmetry) and increases with increasing z. The component of velocity normal to the surface is directed towards the plate near the leading interface and away from it in the remaining part of the spot.

Two-point velocity correlation measurements suggest that the spot may be represented by an arrowhead vortex tube which is convected downstream with a velocity equal to 65 yo of the free-stream velocity. Pluid which is entrained near the plane of symmetry acquires a helical motion towards the extremities of the spot. This motion helps to explain the lateral as well as the longitudinal spread of the spot.

Three-dimensional flow over two identical (solid or liquid) spheres which are held fixed relative to each other with the line connecting their centres normal to a uniform I stream is investigated numerically at Reynolds numbers 50, 100, and 150. We consider the lift, moment, and drag coefficients on the spheres and investigate their dependence on the distance between the two spheres. The computations show that, for a given Reynolds number, the two spheres are repelled when the spacing is of the order of the diameter but are weakly attracted at intermediate separation distances. For small spacing, the vortical structure of the near wake is significantly different from that of the axisymmetric wake that establishes at large separations. The partially confined flow passing between the two spheres entrains the flows coming around their other sides. Our results agree with available experimental and numerical data.