The effect of rotation on the frequencies of oscillations of a liquid drop is investigated. It is assumed that the drop is imbedded in a fluid of the same or different density and that a constant surface tension acts on the interface. Rotation influences the oscillations through the Coriolis force and through the centrifugal distortion of the drop. For non-axisymmetric oscillations only the Coriolis force is important in first approximation and causes the expected splitting of the frequency for the two modes differing in their sign of circular polarization with respect to the axis of rotation. In the case of axisymmetric oscillations the centrifugal distortion and the Coriolis force combine to increase the frequency whenever the density ρi of the drop exceeds the density of ρ° of the surrounding fluid. For ρi < ρ° a decrease of the frequency of oscillation is possible for some modes of higher degree.

One-dimensional small-amplitude waves in which the local value of the fundamental derivative changes sign are examined. The undisturbed medium is taken to be a Navier–Stokes fluid which is at rest and uniform with a pressure and density such that the fundamental derivative is small. A weak shock theory is developed to treat inviscid motions, and the method of multiple scales is used to derive the nonlinear parabolic equation governing the evolution of weakly dissipative waves. The latter is used to compute the viscous shock structure. New phenomena of interest include shock waves having an entropy jump of the fourth order in the shock strength, shock waves having sonic conditions either upstream or downstream of the shock, and collisions between expansion and compression shocks. When the fundamental derivative of the undisturbed media is identically zero it is shown that the ultimate decay of a one-signed pulse is proportional to the negative 1/3-power of the propagation time.

An experiment conducted on the Oregon continental shelf has provided measurements of velocity fluctuations in the viscous sublayer and buffer layer of the boundary-layer flow. Spectra from the viscous sublayer collapse considerably when scaled as suggested by Bakewell & Lumley (1967), and buffer-layer spectra collapse reasonably well with laboratory spectra when the scaling customarily used in the logarithmic layer is applied. However, in spite of the usefulness of the spectral scaling, the scaled sublayer and buffer-layer spectra from the ocean floor fall below the scaled laboratory spectra in the energy-containing portion of the spectrum, perhaps because the sea floor is not perfectly planar.

Time-dependent flows occur naturally as in pulsatile blood flow and in tidal estuaries and comprise many of the man-made flows of practical importance. A knowledge of the rate of mixing of a contaminant substance in such time-dependent flows is of paramount interest in, for example, the injection of a chemical substance in blood flow, the discharge of outfalls in estuaries, and the mutual contamination length of two feed fluids when switching from one feed line to another as part of a manufacturing process. This paper presents a study of contaminant spread in two specific and well-defined flows and provides a basis for the interpretation of contaminant mixing in the more complex flow situations that normally prevail.

An extension of the probabilistic formulation of the streamwise dispersion of contaminant molecules given in Dewey & Sullivan (1982) is used to study time-dependent laminar flows between parallel plates and in tubes wherein the flows are homogeneous in the streamwise direction. The two flows considered in detail are oscillating flows and impulsively started flows. In impulsively started flows it is shown that, although the basic dispersive mechanism acts in much the same way as described by Taylor (1953), the start-up effects on the dispersion can be quite prolonged and very significantly reduce the streamwise spread of contaminant over that which is observed in the fully developed flow. In oscillatory flows, unlike the situation presented by Taylor (1953) in which a diminished value of molecular diffusivity κ increases the contaminant cloud axial growth rate in a tube of radius a, it is found that optimal streamwise contaminant spread results from a value of κ that depends upon kinematic viscosity v and frequency ω. The streamwise cloud-variance growth rate is explored over the full range of the two parameters γ2 = ωa2/κ and λ2 = ωa2/2v for all time, and it is shown that a global maximum results when γ ≈ 2π and λ ≈ 2.

Edge-wave solutions to the linearized shallow-water equations for water waves are well known for a variety of bottom topographies. The only explicit solution using the full linearized theory describes edge waves over a uniformly sloping beach, although the existence of such waves has been established for a wide class of bottom geometries. In this paper the full linearized theory is used to derive the properties of edge waves over a shelf. In particular, curves are presented showing the variation of frequency with wavenumber along the shelf, together with some mode shapes for a particular shelf geometry.

An annulus covered by a rotating screen (or surface) which imparts stress and turbulence to the upper of two fluid layers has been shown by Scranton & Lindberg (1983) and Jones & Mulhearn (1983) to produce mixed-layer entrainment that is dependent on annulus curvature and geometry. This general result is confirmed here, where photographs of the mixed-layer interface indicate that turbulent entrainment rapidly diminishes away from the outer wall. The problem is explained as a damping of the turbulence within the bulk of the mixed layer by inertial stability associated with angular momentum increasing rapidly with radius except very close to the outer wall. Through hot-film-anemometer measurements, a shallow turbulent Ekman layer is found to exist immediately underneath the rotating screen, having a depth of order $ 0.4u_{*}r/\overline{v}$, where u* is the friction velocity, $\overline{v}$ is the mean circumferential flow speed within the layer and r is the radius. For r of order 1 m, this depth is typically only a small fraction of the mixed-layer depth determined from the density profile.

When the stress input is placed near the inner wall, the mean-flow radial profile is much more nearly irrotational and the turbulence-damping problem becomes minimal. The entrainment is then much more uniform with radius, and local interfacial scaling can be used to relate the entrainment rate to one or more local Richardson numbers containing a turbulent velocity scale rather than u* or $\Delta\overline{v}$, where Δ signifies the change across the interface. Although u* and $\Delta\overline{v}$ are proper ‘external’ scales for entrainment in a horizontally homogeneous mixed layer that is turbulent throughout, a local internal turbulent velocity scale can alternatively be used. Entrainment rates thus scaled are presented and compared with Turner's (1973) locally scaled entrainment.

The small-scale structure of the streamwise velocity fluctuations in the wall region of a turbulent boundary layer is examined in a new wind-tunnel facility using hot-wires smaller than any previously constructed (typical dimensions: l = 25 μm, d = 0.5 μm). In the boundary layer in which the measurements were made, the ratio of the hot-wire length to the viscous length is 0.3. The turbulent intensity measured with the small hot wires is larger than that measured with longer wires owing to the better spatial resolution of the small wires. The velocity fluctuations measured by the small hot wires are also analysed to determine the burst frequency at two Reynolds numbers and at various distances from the wall. The dimensionless burst frequency does not depend on the Reynolds number when scaled with wall parameters. However, it increases with Reynolds number when scaled with outer variables. Velocity fluctuations measured by two hot wires, less than two viscous lengths apart, are analysed to reveal the small-scale features present during a burst and in the absence of a burst. The main conclusions are: (1) intermittent small-scale shear layers occur most frequently when bursts are present, less frequently just after a burst, and even less frequently just before a burst; and (2) on occasion the velocity gradient of the small-scale shear layers is as large as the mean-velocity gradient at the wall.

Clouds of bubbles are generated at the sea surface by breaking wind waves or by heavy rain. Rows of subsurface bubble clouds have been detected by a bottom-mounted side-scan sonar, and are possibly formed by the effects of Langmuir circulation. A simple equation is devised to describe the effects of the turbulent diffusion of bubbles from the free surface, bubble rise and dissolution, and advection by Langmuir circulation. The equation is solved analytically using a series expansion in which advection is supposed small in comparison with diffusion. The solution provides a quantitative measure of the principal effects produced by the circulation, in particular the distortion of the bubble field, and estimates of the advective flux.

A random-walk numerical model, in which changes occurring in individual bubbles are followed, is tested against the analytical model in the range for which the latter is valid. There is good agreement. The numerical model is useful in extending the solutions to more complex cases which include a broad distribution of bubble sizes, and to ranges in which the analytic solution is invalid. The model is used to quantify the effect of the circulation on the acoustic scattering cross-section of the bubble clouds and to explore differences between the conclusions of earlier models and observations by Johnson & Cooke (1979).

In the appendices an estimate is made of the depth to which bubbles can be carried by the vertical velocities observed below wind rows, and this is found to agree reasonably well with the maximum depth to which bubbles are observed to penetrate. Estimates of mean vertical diffusion coefficients based on observations of bubbles are compared with some calculated solely from the advective flux in Langmuir circulation. The latter are, as expected, smaller than those representing the sum of all the contributions to the flux, but are a significant fraction, of the order of 0.2–0.4. A method of deriving the vertical diffusion coefficient from observations of the vertical distribution of the acoustic scattering cross-section of bubbles appears not to be very sensitive to circulation and may provide estimates within about 25% of the actual values.

The linear stability equations for a round laminar thermal plume in a coflowing vertical stream have been solved numerically. Both symmetric and asymmetric disturbances have been considered for strengths of the forced flow varying between very weak and very strong. The parallel flow analysis confirms that the forced flow has a stabilizing effect. The upper branch of the neutral curve for sinuous disturbances is qualitatively like that of a round momentum jet. However, neither a critical Reynolds number nor a lower branch of the neutral curve was found. Non-parallel effects are discussed.

Noise spectra are measured at different distances downstream of a cavitating circular cylinder. The effects of velocity and cavitation number on noise spectra are presented. Together with flow observation the noise measurements allow the cavity development to be described and related to cavity-collapse intensity.

Euromech Colloquium 173 was held at Delphi from 13-16 September 1983. Thirty-six participants from eleven countries were present. Papers were presented on: (1) various approaches to calculating and computing air flow in rough terrain in the presence of changes in surface roughness, elevation and temperatures, including methods for interpolating, subject to certain physical constraints, the wind field from measurements at various fixed stations; (2) measurement and satellite photography of air flow in rough terrain near isolated mountains, near coastlines, over mountains, and over mountains near coastlines; (3) the applications of these studies to air-pollution dispersion and the exploitation of wind energy in rough terrain. The discussions led to agreement about how best to use and relate the various techniques for calculating air flows, the role of new techniques in remote sensing for improving understanding of flow in rough terrain, the factors determining air-pollution concentration that need particular study, and the special kinds of information about turbulence needed for estimating wind energy in rough terrain.

This paper aims to elucidate the structure of the turbulent mixing layers, especially, its dependence on initial disturbances. The mixing layers are produced by setting a woven-wire screen perpendicular to the freestream in the test section of a wind tunnel to obstruct part of the flow. Three kinds of model geometry are treated; these model screens produced mixing layers which may be regarded as the equivalents of the plane mixing layer and of two-dimensional and axisymmetric wakes issuing into ambient streams of higher velocity. The initial disturbances are imposed by installing thin rods of various sizes along the edge of the screen or at the origin of the mixing layer. Flow features are visualized by the smoke-wire method. Statistical quantities are measured by a laser-Doppler velocimeter. In all cases large-scale transverse vortices seem to persist, although comparatively small-scale vortices are superimposed on the flow field in the mixing layer. The mixing layers are in self-preserving state at least up to third-order moments, but the self-preserving state is different in each case. The growth rates of the mixing layer are shown to depend strongly on the initial disturbance imposed.

The effect of horizontally inhomogeneous flows on internal wave propagation in a stratified ocean with a constant Brunt-Väisälä frequency is analysed. Dispersion characteristics of internal waves in a moving fluid and kinematics of wave packets in smoothly inhomogeneous flows are considered using wave-normal surfaces. It is shown that internal-wave blocking and short-wave transformation may occur in longitudinally inhomogeneous flows. For parallel flows internal-wave trapping is possible in the vicinity of the limiting layer where the wave frequency in the locally comoving frame of reference coincides with the Brunt-Väisälä frequency. Internal-wave trapping also takes place in jet-type flows in the vicinity of the flow-velocity maximum. WKB solutions of the equation describing internal-wave propagation in a parallel horizontally inhomogeneous flow in the linear approximation are obtained. Singular points of this equation and the related effect of internal-wave amplification (overreflection) under the action of the flow are investigated. The spectrum and the growth rate of internal-wave localized modes in a jet-type flow are obtained.

The static pressure-hole problem is investigated both theoretically and experimentally. The influence of all significant dimensionless parameters is brought to light. These parameters represent the effects of the boundary layer, of the velocity gradient and of the wall curvature. A partial linearization makes it possible to propose a formula of correction containing three influence functions which cannot be determined by the theory. A limited number of experiments on appropriate models leads to the determination of these functions in case of practical requirements. So, a method of correction is obtained, but only in incompressible flow. The previous formula has been verified in two complex flows. The importance of the correction on the pressure drag of a slender body is brought to light and the difficulties in the application on the method are emphasized.

The effective viscosity of a suspension is defined to be the four-tensor that relates the average deviatoric stress to the average rate of strain. We determine the effective viscosity of an array of spheres centred on the points of a periodic lattice in an incompressible Newtonian fluid. The formulation involves the traction exerted on a single sphere by the fluid, and an integral equation for this traction is derived. For lattices with cubic symmetry the effective viscosity tensor involves just two parameters. They are computed numerically for simple, body-centred and face-centred cubic lattices of spheres with solute concentrations up to 90% of the close-packing concentration. Asymptotic results for high concentrations are obtained for arbitrary lattice geometries, and found to be in good agreement with the numerical results for cubic lattices. The low-concentration asymptotic expansions of Zuzovsky also agree well with the numerical results.

The behaviour of passive tracer particles in capillary Poiseuille flow is investigated with regard to the residence time in short axial sections of length z, in which z/a < Va/D, where a is the capillary radius, V is the mean velocity and D the coefficient of molecular diffusion. While methods exist for calculating moments of the cross-sectionally averaged axial concentration distribution as a function of time (e.g. Smith 1982b), much less is known about the distribution of residence time as a function of axial distance. An approximate theoretical solution for point sources in high-Péclet-number flows reveals that the mean residence time 〈t(z)〉, which is asymptotic to z/V0 near the source, will then rise faster than z/V0 before converging to z/V for large z, provided the source is not at the capillary wall. V0 is the advective velocity at the point of release. The variance 〈t2(z)〉 is found to increase initially in proportion to z3 provided the source is not at the capillary wall or on the axis. A Monte Carlo method based on the solution to the diffusion equation in the capillary-tube cross-section is developed to compute particle trajectories which are used to analyse both axial and residence-time distributions. The residence-time distribution is found to display significant changes in character as a function of axial position, for both point sources and a uniform flux of particles along the tube.

An analysis of the fluid flow and mass transfer induced by ventilation systems in containership holds was carried out. The result of the work was used to support the U.S. position before a committee of the International Convention on Safety to Life at Sea. The analysis consists of a detailed calculation of the forced motion through an interconnected set of narrow, stably stratified, vertical air passages, which represent an idealized containership hold. The results of this calculation were then used to predict the vapour concentration of spilled volatile material assumed to lie at the bottom of the vertical air passages. The result is a set of formulae which determine the rate of extraction of volatile material as a function of hold geometry, ventilation parameters, and ambient stratification. A variety of computed results are presented. The results indicate the crucial importance of locating the extractor as close to the hold bottom as technically possible.

A finite-difference Navier-Stokes model has been used to study rotating baroclinic flow for Richardson number [lsim ] 1, assuming no variations except in the vertical plane wholly containing the density-gradient vector. A section of a horizontally infinite channel has been studied, assuming periodic boundary conditions at the vertical computational boundaries and no-slip conducting horizontal boundaries. Two configurations were studied, both of which have an analytic basic solution with no horizontal variations in the velocities or density gradients. Symmetric baroclinic waves developed in the flows, as long as the Richardson number was not too large and the thermal Rossby number was large enough (for fixed diffusion parameters), consistent with linear theory. The structures and energetics of the fully developed waves were found to be especially dependent upon the Prandtl number Pr. Potential energy was the ultimate wave-energy source in all cases, and the average zonal flow was never much affected by the waves. For Pr > 1 the conversion from potential energy to wave kinetic energy was direct, via temperature and vertical-motion correlation. For Pr < 1 the conversion was from potential energy, to average kinetic energy by virtue of an induced meridional flow, to wave kinetic energy. For Pr = 1 the energy conversion was by either or both of the above, depending upon the other parameters.

The steady laminar natural convection of water in an inclined square cavity is investigated experimentally and analytically at temperatures in the neighbourhood of maximum density near 4°C. One hot wall of the square cavity is maintained at various uniform temperatures from 2 to 20°C and the opposing cold wall is kept at a uniform temperature of 0°C, while the other walls are thermally insulated. Photographs and analytical descriptions of the flow patterns, temperature profiles in the water layer and average heat-transfer coefficients are presented in this paper for various surface temperatures Th of the hot wall and inclination angles of the square cavity θ from 0° (heated from below) to 180° (heated from above) by 30° intervals. From this study it should be noted that the density inversion of water has a strong effect on the natural convection occurring in the inclined square cavity, and the average heat-transfer coefficient is a peculiar function of the surface temperature of the hot wall, unlike previous results for Boussinesq fluids without density inversion. Solutions of the governing equations for steady two-dimensional laminar natural convection are obtained numerically, and the results obtained agree reasonably well with the experimental ones in the ranges of 30° < θ ≤ 180° for Th > 8°C, 0° ≤ θ ≤ 120° for Th < 8°C, and 0° ≤ θ ≤ 180° for Th = 8°C.

Experimental evidence is presented which shows that both uniform and differential sedimentation are unstable flows for relatively concentrated fluid suspensions containing particles of two different densities or sizes. The instability takes the form of a new type of fingering phenomenon which develops as a result of the two kinds of particles segregating laterally from each other.