A numerical experiment has been carried out to evaluate two of the methods available for finding the time-averaged mean velocity and the Reynolds stresses of a turbulent flow field using hot wires. The conventional method is based on the series expansion of the response equation, subsequent truncation of the series and time averaging. The improved method is based on squaring and time averaging without neglecting any terms. The method adopted to evaluate these two methods is based on the Monte Carlo simulation of a pseudo turbulent flow field using random-number generators and the corresponding hot-wire response, for a prescribed set of conditions, by assuming an appropriate model for the hot-wire response. The simulated hot-wire response and the calibration constants are then perturbed about their mean values to study the effects of errors in these quantities. The perturbed response is used to compute the time-averaged flow field by the two methods. The deviation of these values from the generated pseudo values, averaged over large number of trials, is used as the criterion to evaluate the methods. This procedure is also used to estimate the errors due to truncation in the conventional method, to study the effect of turbulence-intensity levels and to study the effects of measurement errors. The results indicate that the choice of the method for determining the time-averaged quantities should be based on the turbulence-intensity level and the measurement errors likely to be encountered. The conventional method yields reliable mean-velocity results for turbulence intensities as high as 50% with second-order turbulence correction. If measurement errors are within reasonable limits and the turbulence level is below 20%, the conventional method yields reliable results for Reynolds stresses. The improved method should be used to determine the time-averaged flow field for turbulence intensity above 40–50%. The error in the yaw sensitivity parameter k has an insignificant effect on the mean velocity and Reynolds stresses computed by both methods. By accurately determining the sensitivity s of the hot wire, the accuracy of the measured mean velocity and Reynolds stresses can be improved significantly. An improved method of carrying out the uncertainty analysis for measurements, based on the Monte Carlo technique, has also been outlined.

The analog of Whitham's law of conservation of wave action density is derived in the case of Rayleigh instability waves. The analysis allows for wave propagation in two space dimensions, non-unidirectionality of the background flow velocity profiles and weak horizontal nonuniformity and unsteadiness of those profiles. The small disturbance equations of motion in the Eulerian flow description are subject to a change of dependent variable in which the new variable represents the pressure-driven part of a disturbance material coordinate function as a function of the Cartesian spatial coordinates and time. Several variational principles expressing the physics of the small disturbance equations of motion are presented in terms of this new variable. A law of conservation of ‘bilinear wave action density’ is derived by a method intermediate between those of Jimenez and Whitham (1976) and Hayes (1970a). The distinction between the observed square amplitude of an amplified wavetrain and the wave action density is discussed. Three types of algebraic focusing are discussed, the first being the far-field ‘caustics’, the second being near-field ‘movable singularities’, and the third being a focusing mechanism due to Landahl (1972) which we here derive under somewhat weaker hypotheses.

Detailed information is provided in this paper on the physics of momentum transfer in bubble-driven liquid flows. Experimental information is obtained on the flow around bubbles and on the axisymmetric bubble-driven liquid flow inside liquid-filled cylinders located with their axes in the vertical direction. A laser-Doppler anemometer extended for particulate two-phase flows is employed for these measurements to yield local fluid velocity information as well as the rise velocity of bubbles. The bubble top radius and the bubble shape were also found from these measurements.

Utilizing experimentally gained information and employing the basic equations for particulate two-phase flows, permits finite difference equations to be formulated that allow bubble-driven liquid flows to be computed. Results are presented for boundary conditions corresponding to those of the experimental studies. Comparisons of numerical and experimental results are shown to be in good agreement. This is taken as a justification to employ the developed computer programs to carry out parameter studies for bubble-driven liquid flow inside circular cylinders. Results of these studies are presented and discussed.

An experimental investigation of entrainment and mixing in reacting and non-reacting turbulent mixing layers at large Schmidt number is presented. In non-reacting cases, a passive scalar is used to measure the probability density function (p.d.f.) of the composition field. Chemically reacting experiments employ a diffusion-limited acid–base reaction to directly measure the extent of molecular mixing. The measurements make use of laser-induced fluorescence diagnostics and high-speed, real-time digital image-acquisition techniques.

Our results show that the vortical structures in the mixing layer initially roll-up with a large excess of fluid from the high-speed stream entrapped in the cores. During the mixing transition, not only does the amount of mixed fluid increase, but its composition also changes. It is found that the range of compositions of the mixed fluid, above the mixing transition and also throughout the transition region, is essentially uniform across the entire transverse extent of the layer. Our measurements indicate that the probability of finding unmixed fluid in the centre of the layer, above the mixing transition, can be as high as 0.45. In addition, the mean concentration of mixed fluid across the layer is found to be approximately constant at a value corresponding to the entrainment ratio. Comparisons with gas-phase data show that the normalized amount of chemical product formed in the liquid layer, at high Reynolds number, is 50% less than the corresponding quantity measured in the gas-phase case. We therefore conclude that Schmidt number plays a role in turbulent mixing of high-Reynolds-number flows.

The structure of the pressure and velocity fields in the air above mechanically generated water waves was investigated in order to evaluate their contribution to the transfer of momentum and energy from wind to water waves. The measurements were taken in a transformed Eulerian wave-following frame of reference, in a wind-wave research facility at Stanford University.

The organized component of the fluctuating static pressure at the channel roof was found to contain contributions from both the sound field and the reflected water wave. The acoustic contributions were accounted for by appropriately correcting the pressure amplitude and phase (relative to the wave) and its contribution to the momentum and energy exchange. The wave-induced pressure coefficient at the fundamental mode shows in general an exponential decay behaviour with height, but the rate of decay is different from that predicted by potential-flow theory. The wave-induced pressure phase relative to the wave remains fairly constant throughout the boundary layer, except when the ratio of the wave speed to the freestream velocity, c/Uδ0 = 0.78 and 0.68. This phase difference was found to be about 130° during active wave generation, with the pressure lagging the wave. The momentum and energy transfer rates supported by the waves were found to be dominated by the wave-induced pressure, but the transfer of the corresponding total quantities to both waves and currents may or may not be so dominated, depending on the ratio c/Uδ0. The direct contribution of the wave-induced Reynolds stresses to the transfer processes is negligible.

A quantitative experimental study of the two-dimensional inverse energy cascade is presented. The flow is electrically driven in a horizontal layer of mercury and three-dimensional perturbations are suppressed by means of a uniform magnetic field, so that the flow can be well approximated by a two-dimensional Navier–Stokes equation with a steady forcing term and a linear friction due to the Hartmann layer. Turbulence is produced by the instability of a periodic square network of 36 electrically driven alternating vortices. The inverse cascade is limited at large scales, either by the linear friction or by the finite size of the domain, depending on the experimental parameters. In the first case, $k^{-\frac{5}{3}$ spectra are measured and the corresponding two-dimensional Kolmogorov constant is in the range 3–7. In the second case, a condensation of the turbulent energy in the lowest mode, corresponding to a spontaneous mean global rotation, is observed. Such a condensation was predicted by Kraichnan (1967) from statistical thermodynamics arguments, but without the symmetry breaking. Random reversals of the rotation sense, owing to turbulent fluctuations, are more and more sparse as friction is decreased. The lowest mode fluctuations and the small scales are statistically independent.

Transition in a pipe flow with a superimposed sinusoidal modulation has been studied in a straight circular water pipe using laser-Doppler anemometer (LDA) techniques. This study has determined the stability–transition boundary in the three-dimensional parameter space defined by the mean and modulation Reynolds numbers Rem, Remω and the frequency parameter λ. Furthermore, it documents the mean passage frequency Fp of ‘turbulent plugs’ as functions of Rem’ Remω and λ. This study also delineates the conditions when plugs occur randomly in time (as in the steady flow) or phase-locked with the excitation. The periodic flow requires a new definition of the transitional Reynolds number Rer, identified on the basis of the rate of change of Fp with Rem. The extent of increase or decrease in Rer from the corresponding steady flow value depends on λ and Remω. At any Rem and Remω, maximum stabilization occurs at λ ≈ 5. With increasing Remω, the ‘stabilization bandwidth’ of modulation frequencies increases and then abruptly decreases after levelling off. The maximum stabilization bandwidth depends strongly on Rem, decreasing with increasing Rem. Previously reported observations of turbulence during deceleration, followed by a relaminarization during acceleration, can be explained in terms of a new phenomenon: namely, periodic modulation produces longitudinally periodic cells of turbulent fluid ‘plugs’ which differ in structural details from ‘puffs’ or ‘slugs’ in steady transitional pipe flows and are called patches. The length of a patch could be increased continuously from zero to the entire pipe length by increasing Rem. This tends to question the concept that all turbulent plugs (and even the fully-turbulent pipe flow) consists of many identical elementary plugs as basic ‘building blocks’.

The flow-induced surface instabilities of Kramer-type compliant surfaces are investigated by a variety of theoretical approaches. This class of instability includes all those modes of instability for which the mechanism of generation involves essentially inviscid processes. The results should be applicable to all compliant surfaces that could be modelled theoretically by a thin elastic plate, with or without applied longitudinal tension, supported on a springy elastic foundation. with or without a viscous fluid substrate; material damping is also taken into account through the viscoelastic properties of the solid constituents of the coatings.

The simple case of a potential main flow is studied first. The eigenmodes for this case are subjected to an energy analysis following the methods of Landahl (1962). Instabilities that grow both in space and time are then considered, and absolute and convective instabilities identified and analysed.

The effects of irreversible processes on the flow-induced surface instabilities are investigated. The shear flow in the boundary layer gives rise to a fluctuating pressure component which is out of phase with the surface motion. This leads to an irreversible transfer of energy from the main stream to the compliant surface. This mechanism is studied in detail and is shown to be responsible for travelling-wave flutter. Simple results are obtained for the critical velocity, wavenumber and stability boundaries. These last are shown to be in good agreement with the results obtained by the numerical integration of the Orr–Sommerfeld equation. An analysis of the effects of a viscous fluid substrate and of material damping is then carried out. The simpler inviscid theory is shown to predict values of the maximum growth rate which are, again, in good agreement with the results obtained by the numerical integration of the Orr–Sommerfeld equation provided that the instability is fairly weak.

Compliant surfaces of finite length are analysed in the limit as wave-length tends to zero. In this way the static-divergence instability is predicted. Simple formulae for critical velocity and wavenumber are derived. These are in exact agreement with the results of the simpler infinite-length theory. But, whereas a substantial level of damping is required for the instability on a surface of infinite length, static divergence grows fastest in the absence of damping on a surface of finite length.

The Hall effect in the magnetohydrodynamic (MHD) channel flow of a plasma leads to the presence of transverse Lorentz forces. The non-uniform distribution of these body forces may cause secondary flows to develop; these can exert a significant influence on the plasma momentum, thermal and electrical behaviour. The effect is predicted to be large for envisioned large-scale MHD devices. An experimental study of this phenomenon is described. The apparatus consisted of a laboratory-scale MHD channel in which a controlled net axial current was applied. Plasma velocities were measured using laser-Doppler anemometry. The results demonstrate that transverse Lorentz forces can drive intense secondary flows at a value of the magnetic interaction parameter based on the Hall current of approximately one. The peak measured transverse velocities were 15% of the bulk velocity. Qualitatively, the basic character of the large-scale secondary flow structure was in accord with a simple model based on a first-order distribution of the axial current density. Measurements were also made under a variety of conditions of the profiles of mean axial velocity and of the axial and transverse components of turbulence intensity, of electrode surface temperatures and of plasma voltage distributions. These results all support the conclusion that convective transport by MHD secondary flow caused significant asymmetries to develop in the cross-plane distribution of scalar quantities.

A method for calculating transonic potential flow past a multi-element aerofoil configuration is presented. The method is a hybrid method that is based upon a compressible-flow panel method, valid for subcritical flow, and a finite-difference method that is suitable for supercritical flow calculations. The effectiveness of the proposed method is demonstrated, first by application to a single aerofoil and then to a three-element aerofoil.

Three different Navier-Stokes computational models of incompressible viscoussublayer turbulence have been developed. Comparison of computed turbulence quantities with experiment is made for the mean streamwise velocity, Reynolds stress, correlation coefficient and dissipation; for the r.m.s. fluctuation intensities of streamwise vorticity, Reynolds stress and three velocity components; and for the skewness and flatness of fluctuating streamwise velocity and Reynolds stress. The comparison is good for the first three of these quantities, and reasonably good for most of the remainder.

Special computer runs with a very fine mesh and small Courant number were made to define the limiting power-law behaviour of turbulence near a wall. Such behaviour was found to be confined to about 0.3 wall units from the wall, and to be: linear for streamwise turbulence, spanwise turbulence, vorticity normal to the wall, and for the departures from their respective wall values of dissipation, streamwise vorticity and spanwise vorticity; second power for turbulence normal to the wall; third power for Reynolds stress; and a constant value of the correlation coefficient for Reynolds stress. A simple physical explanation is given for the third-power variation of Reynolds stress and for the broad generality of this limiting variation.

Applications are made to Reynolds-average turbulence modelling: damping functions for Reynolds stress in eddy-viscosity models are derived that are compatible with the near-wall limiting behaviour; and new wall boundary conditions for dissipation in k-ε models are developed that are similarly compatible.

We determine the circumstances under which baroclinic instability in the Charney model subjected to localized time-periodic forcing manifests itself as a wavetrain that oscillates at the source frequency and amplifies in space with distance from the source; analytical and numerical results describing the salient characteristics of such waves are presented. The spatially amplifying disturbance is a hitherto unsuspected part of the response to a pulsating source, and coexists with the more familiar neutral Rossby wavetrains; it is likely to play a role in a wide range of atmospheric and oceanic phenomena.

The central results rely on a careful application of a causality criterion due to Briggs. These results illustrate a practical means of attacking spatial instability problems, which can be applied to a broad class of systems besides the one at hand. We have found that the Charney problem with positive vertical shear is not absolutely unstable, so long as the wind at the ground is non-negative. This implies that spatial instability and forced stationary-wave problems are well posed in an open domain under typical atmospheric circumstances.

The amplifying waves appear on the downstream side of the source, have eastward (downstream) phase propagation and have wavelengths that increase monotonically with decreasing frequency, becoming infinite at zero frequency. When the surface wind is not too large, the spatial amplification rate has a single maximum near the frequency ωm = (f/N)Uz, where f is the Coriolis parameter, N is the stability frequency and Uz is the vertical shear; the rate approaches zero at zero frequency and asymptotes algebraically to zero at large frequency for any positive surface wind. Distinct Charney and Green modes do not appear until the surface wind is made very large. The amplification rate at ωm becomes infinite as surface wind approaches zero, suggesting a mechanism for the concentration of eddy activity.

We also discuss the relationship of these results to the structure of low- and high-frequency atmospheric variability.

Experiments are described in which the populations of metastable levels in ionizing argon are measured through spatially resolved hook interferometry. The results are compared with the present model for shock-induced ionization and a recently proposed mechanism to explain observed flow instabilities. It is found that the experimental measurements support the presently accepted model, which states that electron–atom collisions play the dominant role in the excitation process, but contradicts recent proposals which predict a rapid build-up of anomalously high metastable populations through atom–atom collisions.

The problem of Rayleigh–Taylor instability is reexamined within the framework of incompressible, inviscid and irrotational fluid flow in a bounded three-dimensional domain. A relation proposed by Pimbley (1976) between the slope and the amplitude of the interface at the rigid boundary is adopted as the interface boundary condition. Steady solutions are derived in approximate form by using bifurcation theory. It is shown that under the conditions given some of the steady solutions exhibit the features of the well-known bubbles-and-spikes configuration and can be stable to infinitesimal disturbances.

The objective of this work is an experimental study of laminar mixing in several kinds of two-dimensional cavity flows by means of material line and blob deformation in a new experimental system consisting of two sets of roller pairs connected by belts. The apparatus can be adjusted to produce a range of aspect ratios (0.067–10), Reynolds numbers (0.1–100), and various kinds of flow fields with one or two moving boundaries. Flow visualization is conducted by marking underneath the free surface of the flow with a tracer solution of low diffusivity and of approximately the same density and viscosity as the flowing fluid. The effects of the initial location of the material blob, relative motion of the two bands, and minor changes in the geometry of the flow region are investigated experimentally.

The alternate periodic motion of two bands in a cavity flow is an example of a laminar flow which might lead to chaotic mixing. The governing parameter is the dimensionless frequency of oscillation of the walls f which, under the proper conditions, is able to produce horseshoe functions of various types. The deformation of blobs is central to the understanding of mixing and can be studied to identify horseshoe functions. It is found that the efficiency of mixing depends strongly on the value of f and that there exists an optimal value of f that produces the best mixing in a given time.

We rederive Brinkman's equations for the flow of slow viscous fluid past a random distribution of identical obstacles using the Foldy's approximation. It is shown explicitly that such a derivation is valid for extremely dilute systems. We argue that Brinkman's equation can be used even in systems with lower porosity by proposing a model of porous media that has a very large number of scales.

A mathematical model of convection, obtained by truncation from the two-dimensional Boussinesq equations, is shown to exhibit a bifurcation from symmetrical cells to tilted non-symmetrical ones. A subsequent bifurcation leads to time-dependent flow with similarly tilted transient plumes and a large-scale Lagrangian mean flow. This change of symmetry is similar to that occurring with the advent of a large-scale flow and transient tilted plumes seen in laboratory experiments on turbulent convection at high Rayleigh number. Though not intended as a description of turbulent convection, the model does bring out in a theoretically tractable context the possibility of the spontaneous change of symmetry suggested by the experiments.

Further bifurcations of the model lead to stable chaotic phenomena as well. These are numerically found to occur in association with heteroclinic orbits. Some mathematical results clarifying this association are also presented.

The three-dimensional interactions of weak swept oblique shock and expansion waves and a turbulent boundary layer on a flat plate are investigated. Upstream influences in a single swept interaction are found to be consistent with a model of the flow involving shock/boundary-layer interaction characteristics. The model implies that there is more rapid thickening of the boundary layer close to the shock generator and this is seen to be consistent with surface streamline patterns. It is also found that a superposition principle, which is inherent in the triple-deck model of shock/boundary-layer interactions proposed by Lighthill, can be used to predict the pressure field and surface streamlines for the case of intersecting shock interactions and for the intersection of a shock with a weak expansion.

Topographic Rossby waves in elongated basins on the f-plane are studied by transforming the linear boundary-value problem for the mass transport stream function into a class of two-point boundary-value problems of which the independent spatial variable is the (curved) basin axis. The procedure for deriving the substitute problems is the Method of Weighted Residuals. What emerges is a vector differential equation and associated boundary conditions, its dimension indicating the order of the approximate model. It is shown that each substitute problem in the class entails the qualitative features typical of topographic waves, and increasing the order of the model corresponds to higher-order approximations. Equations are explicitly presented for cross-sectional distributions of the lake topography which has a power-law representation and permits the analysis of weak and strong topographies.

Straight channels in which the depth profile does not change with position along the axis are studied in detail. The dispersion relation is discussed and dispersion curves are shown for the three lowest-order models. Convergence properties are thereby uncovered and phase speed and group velocity properties are found as they depend on wavenumber and topography. Further, for the lowest two modes, cross-channel stream-function distributions are presented. Apart from further convergence properties these distributions show that for U-shaped channels wave activity is nearer to the shore than for V-shaped channels, important information in the design of mooring systems.

An analysis of topographic Rossby wave reflection follows, which emphasizes the importance of the depth profile in the reflecting zone. Based on these results some lake solutions are presented.

The formation of vortex streets behind stationary cylinders is found to be caused by an absolute instability in the wake immediately behind the cylinder. The inviscid Orr–Sommerfeld equation is used together with measured profiles at Reynolds numbers of (a) Re = 56 when the absolute instability provides a Strouhal number of 0.13; and (b) Re = 140000 providing a Strouhal number of 0.21, both in agreement with experimental values. At the subcritical Re = 34 the instability is of the convective type; i.e. the disturbance decays, being convected away once the external disturbance is removed, in agreement with experimental observations. Finally, the instability of the mode which causes a symmetric array of vortices is shown to be always of the convective type.