Measurements of sectional and total forces and the spanwise correlation of vortex shedding are presented for a circular cylinder in planar oscillatory flow at Keulegan-Carpenter numbers, KC, in the range from about 4 to 55. The viscous parameter β is in the range from around 100 to 1665. Circulation measurements around a circuit close to and enclosing the cylinder, are also presented. A mode-averaging technique was used for both sectional forces and circulation measurements and this gave, for typical modes of vortex shedding, time histories over an average cycle. The transverse force and the circulation tend to fluctuate in sympathy with each other, except around the instant of flow reversal when the force changes sign but the circulation remains high. Values of the strength of shed vortices, estimated from the measured circulation, are found to be comparable with steady-flow results. For KC [lsim ] 30, modes of vortex shedding occur over distinct ranges of KC with spanwise correlation high at the centre of a KC-range for a particular mode of shedding but low at the boundaries. Above KC ≈ 30 the correlation is no longer very sensitive to KC and the correlation length is estimated to be equal to 4.65 cylinder diameters. In the transverse vortex-street regime (8 [lsim ] KC [lsim ] 15) the cylinder was found to experience a steady transverse force, the coefficient of which is estimated to be about 0.5 at KC = 14.

Two incompressible viscous fluids with different densities meet at a planar interface. The fluids are subject to an externally imposed oscillating acceleration directed normal to the interface. The resulting basic-state flow is motionless with an internal pressure oscillation. We discuss the linear evolution of perturbations to this basic state. General viscosities and densities for the two fluids are considered but a Boussinesq equal-viscosity approximation is discussed in particular detail. For this case we show that the linear evolution of a perturbation to the interface subject to an arbitrary oscillating acceleration is governed by a single integro-differential equation. We apply a Floquet analysis to the fluid system for the case of sinusoidal forcing. Parameter regions of subharmonic, harmonic, and untuned modes are delineated. The critical Stokes-Reynolds number is found as a function of the surface tension and the difference in density and viscosity between the two fluids. The most unstable perturbation wavelengths are determined. For zero surface tension these are found to be short, on the order of a small multiple of the Stokes viscous lengthscale. The critical Stokes-Reynolds number and the most unstable perturbation wavelengths are found to be insensitive to the degree of density and viscosity differences between the two fluids.

The propagation of weak shock waves (Ms = 1.007, 1.03 and 1.1) through a statistically uniform random medium has been investigated experimentally in a shock tube. The wave-from geometry, rise time and amplitude of initially plane shocks which have propagated through a random mixture of helium and refrigerant 12 are measured. The effect of shock propagation on the properties of the random medium is visualized with schlieren and shadow photography. The pressure histories of the distorted shock waves reflecting from a normal end wall are observed to be both peaked and rounded. In the rounded case the perturbed shock is found to be made up of a succession of weak, slightly curved fronts with a total effective rise time orders of magnitude greater than the classical Taylor thickness. The radius of curvature of the weakest shocks after propagating through the random medium is inferred from observations at two downstream stations to be about 7 times the integral scale of the gas inhomogeneities. It is concluded that the observed distortions of the wave fronts can best be explained in terms of random focusing and defocusing of the front by the inhomogeneities in the medium. A ray-tracing calculation has been used to interpret the experimental observations. It is found that geometrical considerations are sufficient to account for many of the effects observed on the shocks.

The problem of a turbulent boundary layer that evolves into a wake flow at the sharp trailing edge of a thin flat plate is considered; the formal structure of the near-wake flow is investigated using matched expansions in the limit of infinite Reynolds number. The symmetric turbulent near wake is shown to develop a two-layer structure which is independent of turbulence model. The general asymptotic analysis shows that a thin layer at the wake centreline grows linearly with distance from the trailing edge while the centreline velocity varies logarithmically in a manner that is supported strongly by experimental measurements. The relatively thick outer layer of the near-wake flow is undisturbed by the evolution of the inner layer to leading order. An additional region near the trailing edge is required to resolve a non-uniformity in transverse velocity. The general asymptotic results are used to guide the development of a zonal turbulence model for the near wake in the form of a simple eddy viscosity formula. Analytic profiles for velocity and Reynolds stress are obtained for the near-wake region; these profiles are shown to provide accurate representations of available near-wake experimental data.

Herein we show that the modal description of deep-water waves on the sea surface Watson & West 1975) is independent of any reference surface around which expansions of the velocity potential and the surface velocity are done. We demonstrate by direct construction that the interaction between long and short waves does not lead to divergent terms in the equations of motion when this formalism is used.