Using stationary rakes of hot-wire anemometer probes, a series of temperature measurements have been conducted within rising buoyant thermals created by detonation of large-diameter gas-filled balloons. These atmospheric detonation simulation tests were performed at the SANDIA Laboratories Aerial Cable Test Facility, Kirtland AFB, during the late fall of 1973. All measurements were performed after pressure equilibrium (t > 1 s) but prior to completion of the toroid formation process and within the time required (t > 4 s) for the fireball to rise one diameter.

Based on an extensive processing of measured data for two detonation events, unique results describing the mean flow field and turbulent structure statistics for the early-time large-scale buoyant thermal have been determined. Final results include: mean-velocity and temperature data; temperature and temperature gradient intensities; space, auto- and ‘eddy-lifetime’ correlation scales; power-spectral densities; probability density distributions and approximate microscale data.

The present temperature data illustrate that the early-time rising fireball is characterized by a highly intermittent irregular top or cap, a constant (high-) temperature core and a thermal wake exhibiting a linear decay in mean temperature. Mean convection velocities for the fireball wake were measured to be approximately twice as large as fireball cap velocities (13.1 m/s). Maximum fireball temperatures (1100 °C) were in good agreement with peak brightness-temperature data determined from an independent IR measurements experiment. Core leading-edge mean-temperature gradients compare favourably with predictions (10 °C/cm) whereas trailing-edge gradients (0.4 °C/cm) are smaller than predicted results (3 °C/cm).

Normalized temperature intensities at the fireball top and within the thermal wake were substantial (≈ 0.6) in contrast with quiescent fireball core levels (0.1). Moving-frame autocorrelation times (‘eddy lifetimes’, 0.17 + 0.04 s) were approximately four times larger than measured autocorrelation times. This result illustrates that the early-time fireball eddy structure is highly persistent, a finding which tends to substantiate those radar models for large-scale fireballs which postulate relatively slow ‘smearing’ of early-time electron density gradients. Wake integral scales, determined from vertical space correlation data, were approximately 5% of the fireball mean radius. Probability density distributions for the fireball thermal wake were ‘spiky’ in nature, with some evidence of bimodal behaviour, and slightly skewed to the negative side of their normalized values. Normalized spectra data, in general, follow a − &5/3; falloff behaviour for several decades in spectral power. The noted large ‘spread’ in the inertial subrange is consistent with measured turbulence Reynolds numbers (2000) and with the large-scale fully developed turbulent structure for the GEST fireballs (ReD = 3 × 107). Wake microscale data, estimated from temperature and temperature-gradient intensity data and the isotropic turbulence assumption, varied from 2 to 4 ern and were in favourable agreement with predicted microscale magnitudes.

We investigate the interaction of concentration fields of passive tracer with velocity fields characterizing geostrophic turbulence. We develop and compare results from equilibrium statistical mechanics, from turbulence-closure theory and from numerical simulation. A consistent account emerges. Among the results we show (1) that velocity fields efficiently scatter tracer variance to all scales, (2) that tracer variance evolves toward an equilibrium spectrum which is different from the equilibrium spectrum for vorticity variance, and (3) that intermittency of the tracer field is characteristic of a cascade of tracer variance across wavenumber space. The greater efficiency of the cascade of tracer variance relative to a vorticity cascade is due to wavenumber-local advective terms which affect tracer but not vorticity. We suggest that the more efficient tracer cascade results in shorter Lagrangian autocorrelation times for tracer than for vorticity.

We investigate the spatial flux of tracer when a uniform gradient of average tracer concentration is imposed. We show (1) that the spatial flux has dominant contributions from fluctuations on scales slightly larger than the dominant energetic scales, (2) that an effective eddy-diffusivity formulation is valid and that the diffusivity agrees with simple mixing-length estimates, and (3) that eddy diffusivity is significantly anisotropic if Rossby-wave propagation occurs. Meridional diffusivity is suppressed relative to zonal diffusivity.

We complement the study of stirring down from a uniform gradient with a numerical investigation of the stirring out of an initially concentrated spot. We see that eddy diffusivity can be a dangerous concept for such problems.

The time-dependent Navier-Stokes equations are integrated numerically for a finite-length concentric-cylinder geometry. The motion is initiated by an impulsive start of the inner cylinder from a state of rest. The transient development of a Taylor-vortex structure is discussed from the standpoint of the amplitude history, the onset time and vortex-front propagation; steady-state results are compared with previously published experimental results.

The flow of a rotating fluid over isolated three-dimensional topographic features has been investigated. Laboratory experiments have been conducted with a rotating water channel to determine the characteristics of the flow over and around truncated cylindrical disks and depressions located on the upper and lower bounding surfaces of the channel. The geometry of the rotating channel allowed the beta effect to be modelled and cases of beta-plane westward, beta-plane eastward and f-plane flows were studied. Flow patterns revealed by the use of an electrolytic precipitation technique are presented, and the flow behaviour is quantified in terms of a characteristic speed of the flow through a circular cylinder circumscribing the topography in the vicinity of the channel midplane. Case studies are presented for a range of values of Rossby number, Ekman number, beta parameter, and cylinder height-to-radius ratio. The vorticity equation and associated boundary conditions are discussed for the cases studied in the laboratory and appropriate numerical solutions are obtained. The laboratory and numerical experiments demonstrate the character of the horizontal steering of fluid by the topographic features as a function of the system parameters. Comparisons between laboratory and numerical experiments are presented and shown to be in good agreement.

Some aspects of the radial filling of a finite rotating cylinder are considered in the limit of a small Ekman number E. Three main cases are distinguished by the value of τF, the ratio of filling and spin-up times. When τF [Lt ] 1 the effect of the Ekman layers is unimportant and new fluid accumulates behind that already contained by an essentially radial flux. For τF ∼ 1 the Ekman layers are active and entering fluid is added both ahead and behind the initially contained fluid core. which undergoes a process similar to spin-up with the notable difference that here the Ekman layers are non-divergent. In both cases the Rossby number ε is 0(1). When τF [Gt ] 1, ε is small and the Ekman layers control the (quasi-steady) filling. The new fluid is then transported through boundary layers and spread on the moving front from the inside throughout an E¼ layer imbedded in a weak E1/3 layer.

It is shown that for a thin airfoil with small camber and small angle of attack moving in a periodic gust pattern, the unsteady lift caused by the gust can be constructed by linear superposition to the Sears lift of three independent components accounting separately for the effects of airfoil thickness, airfoil camber and non-zero angle of attack to the mean flow. This is true in spite of the nonlinear dependence of the unsteady flow on the mean potential flow of the airfoil. Specific lift formulas are derived and analysed to assess the importance of mean flow angle of attack and airfoil camber on the gust response.

The energy-transmission characteristics of an array of open convergent-channel-type wavebreakers to a normally incident wavetrain is studied experimentally and theoretically. A model of the wavebreaker transmission response to a sinusoidal incident wavetrain on a constant-depth ocean is developed as a boundary-value problem within the framework of linearized water-wave theory. This results in an integral equation based on a Green-function solution to the Helmholtz equation, which is solved numerically for each of several wavebreaker geometries over a range of incident wavelengths. Experiments on fixed model wavebreakers performed in an open wave tank are described, and results are compared with the numerical predictions. Theory and experiment indicate that the convergent-channel design is effective in attenuating the transmitted wave at resonant values of the incident wavelength λ that scale on the channel length L. Forces experienced by each half-wavebreaker are largely transverse; the calculated longitudinal forces for the fixed breakwater are small compared to those on a solid wall except at one resonance near L/λ = 0.5. Experiments indicate that this last condition does not occur for a floating breakwater, where the corresponding transmission of wave energy is high.

… in hydrodynamic turbulence … the fate of vortices extending in the direction of motion is of great importance (J. M. Burgers 1948).

We examine an elementary model of the dynamics of streamwise vorticity in a plane mixing layer. We assume that the vorticity is unidirectional and subjected to a two-dimensional spatially uniform strain, positive along the direction of vorticity. The equations of motion are solved numerically with initial conditions corresponding to a strain-viscous-diffusion balance for a layer with a sinusoidal variation of vorticity. The numerical results are interpreted physically and compared to those of an asymptotic analysis of the same problem by Neu. It is found that strained vortex sheets are fundamentally unstable unless their local strength nowhere exceeds a constant (somewhat larger than 2) times the square root of the product of strain and viscosity. The instability manifests itself by the spanwise redistribution of the vorticity towards the regions of maximum strength. This is accompanied by the local rotation of the layer and the intensification of the vorticity. The end result of this evolution is a set of discrete round vortices whose structure is well approximated by that of axially symmetric vortices in an axially symmetric strain. The phenomenon can proceed (possibly simultaneously) on two separate lengthscales and with two correspondingly different timescales. The first lengthscale is the initial spanwise extent of vorticity of a given sign. The second, relevant to initially thin and spanwise slowly varying vortex layers, is proportional to the layer thickness. The two types of vorticity focusing or collapse are studied separately. The effect of the first on the diffusion rate of a scalar across the layer is calculated. The second is examined in detail for a spanwise-uniform layer: First we solve the eigenvalue problem for infinitesimal perturbations and then use the eigenfunctions as initial conditions for a numerical finite-differences solution. We find that the initial instability is similar to that of unstrained layers, in that roll-up and pairings also follow. However, at each stage a strain-diffusion balance eventually imposes the same cross-sectional lengthscale and each of these events leads to an intensification of the local value of the vorticity.

The parameters upon which collapse and its timescale depend are related to those which are known to govern a mixing layer. The results suggest that the conditions for collapse of strained vortex sheets into concentrated round vortices are easily met in a mixing layer, even at low Reynolds numbers, so that these structures whose size is the Taylor microscale are far more plausibly typical than are vortex sheets on that scale. We found that they raise significantly the diffusion rate of scalar attributes by enhancing the rate of growth of material surfaces across which diffusion takes place. Finally, experimental methods that rely on the visualization of the gradient of scalar concentration are shown to be unable to reveal the presence of streamwise vorticity unless that vorticity has already gathered into concentrated vortex tubes.

Near-inertial oscillations associated with downward energy propagation are commonly observed in the upper ocean. Stern (1977) has suggested that these observations may be internal-inertial waves over-reflected from the shear zone at the base of the mixed layer. In this paper we develop a criterion for over-reflection as a function of wavenumber and frequency for a class of shear flows in the mixed layer. By examining the vertical profile of the vertical wave action flux we demonstrate that the source of the over-reflection is the shear at the base of the mixed layer, which is maintained by the wind-induced turbulent Reynolds stress, here parametrized as a body force. The relationship between over-reflection and the wave-induced Lagrangian-mean flow is determined. We also determine a criterion for unstable waves, and show that these are contiguous in wavenumber-frequency space with points of resonant over-reflection. However, the growth rates of these unstable waves are quite small, and in practice unstable waves will be indistinguishable from waves generated by over-reflection.

The vortex patterns which occur in coflowing jets and wakes at moderate Reynolds numbers (of order 500) are examined in detail. Flow visualization is used in conjunction with a flying hot-wire system which allows instantaneous velocity vector fields to be rapidly measured and related to the smoke patterns. The structures were made perfectly periodic in time by artificial stimulation. The experiments were therefore completely deterministic. This newly developed data-acquisition technique does not require the use of Taylor's hypothesis for inferring patterns from a fixed streamwise position. It therefore allows the vector fields of rapidly evolving patterns to be produced. It also allows the phenomenon of three-dimensional vortex pairing to be studied. The classification of patterns and conjectured topologies made by Perry & Lim (1978a, b) and the interpretations of Perry, Lim & Chong (1980) and Perry & Watmuff (1981) are examined. In the light of more-detailed measurements, it is found that some of these interpretations require modification.

Vortex ‘skeleton’ models of the patterns are constructed and it is found that the Biot-Savart law gives vector fields which are in reasonable agreement with the experiments. It is also found that the power-spectral density of a periodic array of eddies can be explained in terms of potential flow vortices.

Under the assumptions of zero gravity, of negligible viscous effects and of small surface deformations, the problem of the axisymmetric free vibrations of a liquid drop immersed in an outer fluid and in partial contact with a spherical bowl has been analysed. Using the Green function method and expanding the velocity potentials in series of Legendre polynomials, the problem has been reduced to the solution of a single integral equation whose kernel has been expressed in analytical form. It is found that, in comparison with an isolated drop, constrained drops have an additional vibration mode which reduces to a zero-frequency rigid motion as the support size tends to zero, while the remaining ones approach the modes predicted by Lamb for a free drop.

The vibration modes have been numerically calculated for different sizes of the supported surface and compared with the experimental results of Bisch, Lasek & Rodot (1982).

Oscillatory viscous flow in a tapered channel is analysed under conditions of fixed stroke volume. A lubrication theory is developed for small taper and the general result is steady bidirectional drift and an induced steady pressure gradient. The characteristics of the drift profiles change significantly as the Womersley parameter is increased. For large values difficulties arise in the matched asymptotics method which are resolved by introducing a steady drift layer that is much thicker than the Stokes layer. This double boundary layer does not arise in pressure-cycled oscillations. Both Eulerian and Lagrangian drift are examined. The results are compared qualitatively to experimental observations which primarily focus on the application to ventilation in the lung.

A model equation is derived for calculating transformation and propagation of Stokes waves. With the assumption that the water depth is slowly varying, the model equation, which is a nonlinear Schrödinger equation with variable coefficients, describes the forward-scattering wavefield. The model equation is used to investigate the wave convergence over a semicircular shoal. Numerical results are compared with experimental data (Whalin 1971). Nonlinear effects, which generate higher-harmonic wave components, are definitely important in the focusing zone. Mean free-surface set-downs over the shoal are also computed.

Experiments on the instability of the interface in two-phase displacements in Hele-Shaw cells were conducted using air and a viscous oil as the working fluids. The experiments had two objectives: (i) to provide quantitative measurements of the growth constants of the instability which occurs when a less-viscous fluid displaces a more-viscous one, and (ii) to compare the measured dispersion relations with the predictions of the recent theory of Park & Homsy (1984). The experiments were made by analysing the growth characteristics of between 10 and 20 Fourier modes describing the shape of the interface between displaced and displacing fluids, using still photography. For capillary numbers Ca = μU/γ less than approximately 4 × 10−3 the agreement is only fair, owing to substantial edge effects produced by a nearly static contact line near the lateral boundaries of the cell. For 4 × 10−3 < Ca < 1 × 10−2 theory and experiment agree to within the accuracy of the measurements. Location and verification of the behaviour of modes near the predicted cut-off wavenumber give partial verification of the theory of Park & Homsy.

Wave propagation through a thin-walled cylindrical orthotropic viscoelastic initially stressed tube filled with a Newtonian fluid is discussed. Special attention is drawn to the influence of the initial stretch on the wave propagation. It is shown that initial stretching of real arteries enhances the propagation of blood pressure pulses in mammalian arteries. The dispersion equation for the initial-value problem of a semi-infinite tube is also derived. It is shown that the speed of propagation and the attenuation vary with the distance from the support. The results obtained for the axial wave mode provide an explanation for the experimental observations, which is not possible with the results obtained for the infinite tube.

We study the flow of two immiscible fluids of different viscosities and equal density through a pipe under a pressure gradient. This problem has a continuum of solutions corresponding to arbitrarily prescribed interface shapes. The question therefore arises as to which of these solutions are stable and thus observable. Experiments have shown a tendency for the thinner fluid to encapsulate the thicker one. This has been ‘explained’ by the viscous-dissipation principle, which postulates that the amount of viscous dissipation is minimized for a given flow rate. For a circular pipe, this predicts a concentric configuration with the more viscous fluid located at the core. A linear stability analysis, which is carried out numerically, shows that while this configuration is stable when the more viscous fluid occupies most of the pipe, it is not stable when there is more of the thin fluid. Therefore the dissipation principle does not always hold, and the volume ratio is a crucial factor.

High-viscosity liquids hate to work. Low-viscosity liquids are the victims of the laziness of high-viscosity liquids because they are easy to push around.

The arrangement of components in steady flow of immiscible liquids is typically non-unique. The problem of selection of arrangements is defined here and is studied by variational methods under the hypothesis that the realized arrangements are the ones that maximize the speed on exterior boundaries for prescribed boundary tractions, or the ones that minimize the tractions for prescribed speeds. The arrangements which minimize tractions also minimize the dissipation by putting low-viscosity liquid in regions of high shear. The variational problem is used as a guide to intuition in the design and interpretation of experiments when results of analysis of stability are unavailable. In fact we always observe some kind of shielding of high-viscosity liquid. This can occur by sheet coating in which low-viscosity liquid encapsulates high-viscosity liquid, or through the formation of rigidly rotating masses of high-viscosity liquid which we call rollers. In other cases we get emulsions of low-viscosity liquid in a high-viscosity foam. The emulsions arise from a fingering instability. The low-viscosity liquid fingers into the high-viscosity liquid and then low-viscosity bubbles are pinched off the fingers. The emulsions seem to have a very low effective viscosity and they shield the high-viscosity liquid from shearing. In the problem of Taylor instability with two fluids, low-viscosity Taylor cells are separated by stable high-viscosity rollers.

A combination of analysis and testing has been utilized to develop a theory of jet-flap thrust recovery at the low speeds and high deflection angles characteristic of V/STOL lift systems. The contribution of jet mixing to the loss of thrust recovery has been computed with a viscid/inviscid interaction analysis. The results of this computation are compared to surface pressure and wake survey measurements made with a two-dimensional jet-flapped airfoil model. It is concluded that the jet-mixing drag causes a small loss of recovery at small values of the jet-thrust coefficient and deflect, an angle. However, at larger values of either jet parameter, the mainstream separates from the airfoil, producing a large loss of recovery. The loss increases suddenly, since it is due to bursting of the leading-edge separation bubble.

The speed of travelling azimuthal waves on Taylor vortices in a circular Couette system (with the inner cylinder rotating and the outer cylinder at rest) has been determined in laboratory experiments conducted as a function of Reynolds number R, radius ratio of the cylinders η, average axial wavelength $\overline{\lambda}$, number of waves m1 and the aspect ratio Γ (the ratio of the fluid height to the gap between the cylinders). Wave speeds have also been determined numerically for axially periodic flows in infinite-length cylinders by solving the Navier-Stokes equation with a pseudospectral technique where each Taylor-vortex pair is represented with 32 axial modes, 32 azimuthal modes (in an azimuthal angle of 2π/m1) and 33 radial modes. Above the onset of wavy-vortex flow the wave speed for a given η decreases with increasing R until it reaches a plateau that persists for some range in R. In the radius-ratio range examined in our experiments we find that the wave speed in the plateau region increases monotonically from 0.14Ω at η = 0.630 to 0.45Ω at η = 0.950 (where the wave speed is expressed in terms of the rotation frequency Ω of the inner cylinder). There is a much weaker dependence of the wave speed on $\overline{\lambda}$, m1 and Γ. For three sets of parameter values (R, $\overline{\lambda}$, η and m1) the wave speeds have been measured, extrapolated to infinite aspect ratio, and compared with the numerically computed values. For each of these three cases the agreement is within 0.1 %.

This work describes the development and characterization of an experimental system employing laser-induced Rayleigh light scattering with digital data acquisition as a time-resolved quantitative concentration probe in the turbulent flow field of a binary gas mixture. Equations for the expected signal and noise levels are given. Estimates of these parameters for the experimental system used here are in satisfactory agreement with experiment. It is demonstrated that the laser Rayleigh-light-scattering technique provides measurements having high spatial and temporal resolution for various locations within the concentration flow field. Measurements at various positions in the flow field of an axisymmetric methane jet issuing into a slow flow of air are reported and, where possible, compared with appropriate literature results. The statistical properties of the turbulent concentration fluctuations are found to be in good agreement with other independent measurements. Conditionally sampled measurements are also reported and shown to behave in the same manner as the limited number of similar measurements in the literature. The capability of calculating power spectra and correlation functions for the time behaviour of the methane concentration is also demonstrated. Raman and Rayleigh scattering techniques are compared as measurement techniques of scalar values in turbulent flow fields.