Axisymmetric flow in a rotating annulus with differential heating is computed for a high-kinematic-viscosity fluid, such as silicone oil, by numerical integration of the Navier–Stokes equations. Linear stability analysis of the steady axisymmetric flow with respect to a wave perturbation gives a transition curve from the axisymmetric regime to the wave regime; the transition curve is similar to that obtained experimentally by Fein & Pfeffer (1976). However, if we neglect the centrifugal force term, the transition curve is not similar, but it resembles the curve for water (a familiar ‘anvil shape’ in the regime diagram). A dimensionless parameter v2(a + b)/8g(b – a)4 (where a and 6 are the radii of the inner and outer cylinders, d the depth of the fluid, ν the kinematic viscosity, g the acceleration due to gravity), which equals the ratio of the centrifugal force to the gravity force divided by the Taylor number, is more fundamental than the Prandtl number in determining the shape of the transition curve.

We present an experimental and numerical study of a novel variant of the Taylor–Couette problem. The ends of the annular region rotate with the inner cylinder producing a strong, symmetric forcing of the flow. One consequence of the imposed forcing is that asymmetric flows are more readily found than in the standard stationary-ends case. This has led to the discovery of several new and interesting bifurcation phenomena, including codimension-two points of a type normally associated with chaos in finite-dimensional dynamical systems.

The development of turbulent spots in plane Couette flow was studied by means of direct numerical simulation. The Reynolds number was varied between 300 and 1500 (based on half the velocity difference between the two surfaces and half the gap width) in order to determine the lowest possible Reynolds number for which localized turbulent regions can persist, i.e. a critical Reynolds number, and to determine basic characteristics of the spot in plane Couette flow. It was found that spots can be sustained for Reynolds numbers above approximately 375 and that the shape is elliptical with a streamwise elongation that is more accentuated for high Reynolds numbers. At large times though there appears to be a slow approach towards a circular spot shape. Various other features of this spot suggest that it may be classified as an interesting intermediate case between the Poiseuille and boundary-layer spots. In the absence of experiments for this case the present results represent a true prediction of the physical situation.

Longitudinal rolls represent the preferred form of convection in a horizontal fluid layer heated from below in the presence of parallel shear flows for sufficiently low Reynolds numbers and for a finite range of the Rayleigh number above the critical value Rac. In this paper properties of the longitudinal rolls and their stability with respect to three-dimensional disturbances are investigated in the case of Poiseuille flow. While the convective heat transport is independent of the Reynolds number, the mass flux through the channel at a given Reynolds number decreases with increasing Rayleigh number. A wavy instability is found to set in at a finite Reynolds number and relatively low Rayleigh numbers, depending on the Prandtl number P. In particular, the stability region for longitudinal rolls is analysed for P = 0.025, 0.1, 0.71, 2.5, and 7. For sufficiently small Reynolds number the oscillatory, the skewed varicose or the knot instability can precede the wavy instability. For P = 7 the wavy instability is preceded by a modified knot instability throughout the Reynolds-number range that has been investigated. In spite of the difference hi symmetry, the results for Poiseuille flow resemble those obtained earlier hi the case of plane Couette flow.

The paper is devoted to a theoretical analysis of nonlinear two-dimensional waves on the surface of a liquid film freely falling down a vertical plate. Using a model system of equations, steady-state travelling periodical wave regimes have been found numerically. It is shown that some of them agree quantitatively with experimental results. The question of the stability of various wave regimes with respect to two-dimensional infinitesimal disturbances is examined. The most-amplified disturbances are evaluated.

Monodisperse latex microspheres ranging in size from submicrometer to several micrometers in diameter can be prepared in the laboratory. The uniformity of diameter is important for instrument calibration and other applications. However it has proved very difficult to manufacture commercial quantities of mondisperse latex microspheres with diameters larger than about 3 micrometers owing to buoyancy and sedimentation effects. In an attempt to eliminate these effects NASA sponsored a Space Shuttle experiment called the Monodisperse Latex Reactor (MLR) to produce these monodisperse microspheres in larger sizes in microgravity. Results have been highly successful.

Using technology gained from this space experiment, a ground-based rotating latex reactor has been fabricated in an attempt to minimize sedimentation without using microgravity. The entire reactor cylinder is rotated about a horizontal axis to keep the particles in suspension.

In this paper we determine the motion of small spherical particles under gravity, in a viscous fluid rotating uniformly about a horizontal axis. The particle orbits are approximately circles, with centres displaced horizontally from the axis of rotation. Owing to net centrifugal buoyancy, the radius of the circles increases (for heavy particles) or decreases (for light particles) with time, so that the particles gradually spiral inward or outward.

For a large rotation rate, the particles spiral outwards or inwards too fast, while for a small rotation rate, the displacement of the orbit centre from the rotation axis is excessive in relation to the reactor radius. We determine the rotation rate that maximizes the fraction of the reactor cross-section area that contains particles that will not spiral out to the wall in the experimental time (for heavy particles), or that have spiralled in without hitting the wall (for light particles). Typically, the rate is close to 1 r.p.m., and design rotation rate ranges should span this value.

A brief description is given, with a new geometrical derivation, of the changes in velocity, vorticity and helicity of fluid elements and fluid volumes in inviscid flow. When a compact material volume Vb moves with a velocity νb in a flow which at infinity has a velocity U∞ and uniform vorticity Ω, it is shown that in general there is a net change δHE in the integral of helicity HE in the external region VEoutside the volume, i.e. HE = ∫νEu·Ωdν changes by δHE, where u and Ω are the velocity and vorticity fields. When the vorticity at infinity is weak (i.e. $|{\boldmath \Omega}|V^{\frac{1}{3}}_{\rm b}\ll |U_{\infty} - v_{\rm b}|)$ and when Ω is parallel to vb and U∞, the change in the external helicity integral, δHE is proportional to the dipole strength of νb. For the case of volumes with reflectional symmetry about an axis parallel to their direction of motion (e.g. axisymmetric volumes), δHE = -((νb−U∞)·Ω) νbCH, where $C_H = \frac{1}{3}(1+C_M)$, and CM is the added mass coefficient. So for a sphere moving along the axis of a pure rotating flow, δHE = −½νb (νb·Ω), which is negative. Larger values of the local helicity (u·Ω) are generated by the flow around a volume when (νb−U∞) Λ Ω ≠ 0, but for symmetric volumes there is no net contribution to δHE if (νb−U∞) Λ Ω = 0. These results are used to develop some new physical concepts about helicity in turbulent flow, in particular concerning the helicity associated with eddy motions in rotating flows and the relative speed Eb of the boundary defining a region of turbulent flow moving into an adjacent region of weak or non-existent turbulence.

The linearized initial-value problem for the generation of straight-crested waves in a deep, inviscid liquid in response to the prescribed motion of a piston wavemaker of finite depth is solved through integral transforms. The indicial admittance (the surface-wave response to a step-function velocity of the wavemaker) is cast in similarity form and expressed in terms of confluent hypergeometric functions for pure (no surface tension) gravity waves. This gravity-wave result, due essentially to Roberts (1987), provides an outer approximation for x [Gt ] l and gt2 [Gt ] l (x = horizontal distance from wavemaker and l = capillary length) but implies an infinite wave slope at the contact line (x = 0) in consequence of the neglect of surface tension. The corresponding similarity solution for capillary waves (no gravity) with either fixed contact angle or fixed contact line is constructed and is found to be analytic in x for t > 0 if the contact angle is fixed or singular like x4 log x if the contact line is fixed. An inner approximation for gravity waves with either fixed contact angle or fixed contact line is constructed for x = O(l) and gt2 [Gt ] l. The Laplace transform of the general solution is expressed in terms of confluent hypergeometric functions, which permits a compact discussion of its analytical properties.

The forced Korteweg-de Vries equation is now established as the canonical equation to describe resonant, or critical, flow over topography. However, when the fluid is uniformly and weakly stratified, this equation degenerates in that the quadratic nonlinear term is absent. This anomalous, but important, case requires an alternative theory which is the purpose of this paper. We derive a new evolution equation to describe this case which, while having some similarities to the forced Korteweg-de Vries equation, contains two important differences. First, a topography of amplitude α now produces a finite-amplitude response, whereas in the canonical forced Korteweg-de Vries equation, the response scales with α½. Secondly, the maximum amplitude the fluid flow response can achieve is limited by wave breaking, whose onset is characterized by an incipient flow reversal. Various numerical solutions of the new evolution equation are presented spanning a parameter space defined by a resonance detuning parameter, the topographic amplitude and a parameter measuring the strength of the stratification.

The flow structure associated with a line bubble plume in shallow water is investigated. G. I. Taylor has proposed the use of such plumes as wavebreakers. To be effective the surface current generated should be stable for a distance of the order of the wavelength, which in turn could be several times the depth. It appears that the formation of recirculating cells can affect the wavebreaking potential of line bubble plumes. The paper presents observations and measurements of the cell structure associated with line bubble plumes as obtained in a model towing basin of dimensions 1 × 1 × 40 m. A recirculating region was found on both sides of the plume, but the secondary (and higher-order) cell structures proposed by other investigators were not observed. The primary cells were found to be appreciably longer than those reported in the literature for vertical plane jets. The difference can in part be attributed to different definitions of cell length. The definitions used herein are based on observables, both on the water surface and in the interior of the flow, and they lead to consistent measures of length. Bubble-plume parameters (such as entrainment coefficient) are known to depend on gas flow rate, and it was found that the length of the primary cell is a weak function of this variable as well. Additional experiments with a vertical plane jet were conducted for comparison. Longer cells than those previously reported were again observed. The paper contains a complete theory for line bubble plumes, including the effects of compressibility, bubble slip and finite release volume, as well as a simplified similarity analysis useful in estimating plume properties and horizontal-current depth and velocity.

We extend existing measurements of bubble rise velocity or, equivalently, drag in the spherical-cap regime to include the effects of rise under an inclined plate which both changes the bubble shape and the effective buoyancy force in the direction of bubble motion. As found previously for rise in inclined tubes for example (Zukoski 1966) there is an angle of inclination for which the rise velocity is a maximum. We propose, also, an inviscid model that appears to describe the results adequately, as is the case for the spherical-cap regime in an extended fluid (Davies & Taylor 1950).

A workshop reviewing the current research on long-wave run-up was held in the Marine Science Center of the University of Southern California at Catalina Island, California, in August 1990. The workshop covered theoretical, experimental, and field studies of run-up phenomena. The primary application of the research results discussed was in tsunami run-up and flooding and in tsunami run-up hazard mitigation. Certain other applications of long-wave run-up related to wind waves were also discussed. This report summarizes the twenty-six papers presented and it provides one particular view of the current understanding of this run-up process.