This paper discusses two infinite length models (planar and cylindrical) for ciliary propulsion of microscopic organisms. Through the concept of an extensible envelope (instantaneous surface covering the numerous cilia) over the organism, we consider a small amplitude analysis for the velocity of propulsion. A comparison of the velocities of propulsion for the infinite models reveals that they are just over twice that obtained for the finite spherical model (Blake 1971). This indicates that planeness is more important than finiteness, as the solution for typical micro-organisms (e.g. disk-shaped) should occur somewhere between these two models. The maximum velocity of propulsion obtained is one quarter of the wave velocity; that inferred for Opalina, the organism modelled, is nearly one fifth of the wave velocity. Associated shapes of the surface and paths of movement of the tips of the cilia are illustrated.

This paper is intended to evaluate the wall effects in the pure-drag case of plane cavity flow past an arbitrary body held in a closed tunnel, and to establish an accurate correction rule. The three theoretical models in common use, namely, the open-wake, Riabouchinsky and re-entrant-jet models, are employed to provide solutions in the form of some functional equations. From these theoretical solutions several different rules for the correction of wall effects are derived for symmetric wedges. These simple correction rules are found to be accurate, as compared with their corresponding exact numerical solutions, for all wedge angles and for small to moderate ‘tunnel-spacing ratio’ (the ratio of body frontal width to tunnel spacing). According to these correction rules, conversion of a drag coefficient, measured experimentally in a closed tunnel, to the corresponding unbounded flow case requires only the data of the conventional cavitation number and the tunnel-spacing ratio if based on the open-wake model, though using the Riabouchinsky model it requires an additional measurement of the minimum pressure along the tunnel wall.

The numerical results for symmetric wedges show that the wall effects in-variably result in a lower drag coefficient than in an unbounded flow at the same cavitation number, and that this percentage drag reduction increases with decreasing wedge angle and/or with decreasing tunnel spacing relative to the body frontal width. This indicates that the wall effects axe generally more significant for thinner bodies in cavity flows, and they become exceedingly small for sufficiently blunt bodies. Physical explanations for these remarkable features of cavity-flow wall effects are sought; they are supported by the present experimental investigation of the pressure distribution on the wetted body surface as the flow parameters are varied. It is also found that the theoretical drag coefficient based on the Riabouchinsky model is smaller than that predicted by the open-wake model, all the flow parameters being equal, except when the flow approaches the choked state (with the cavity becoming infinitely long in a closed tunnel), which is the limiting case common to all theoretical models. This difference between the two flow models becomes especially pronounced for smaller wedge angles, shorter cavities, and with tunnel walls farther apart.

In order to gauge the degree of accuracy of these theoretical models in approximating the real flows, and t o ascertain the validity of the correction rules, a series of definitive experiments was carefully designed to complement the theory, and then carried out in a high-speed water tunnel. The measurements on a series of fully cavitating wedges at zero incidence suggest that, of the theoretical models, that due to Riabouchinsky is superior throughout the range tested. The accuracy of the correction rule based on that model has also been firmly established. Although the experimental investigation has been limited to symmetric wedges only, this correction rule (equations (85), (86) of the text) is expected to possess a general validity, at least for symmetric bodies without too large curvatures, since the geometry of the body profile is only implicitly involved in the correction formula. This experimental study is perhaps one of a very few with the particular objective of scrutinizing various theoretical cavity-flow models.

The velocity fields in and around a deformed drop suspended in an arbitrary (albeit Stokesian) unbounded flow field are solved. The usefulness of the solution is demonstrated by solving the drag force and lateral migration of a drop suspended in an unbounded Poiseuillian field.

It is demonstrated that, due to the deformation of the drop, there exists a radial component of the settling velocity. The direction of the radial migration depends primarily on the product UHR (the Hadamard-Rybczynski terminal settling velocity) by U0 (the maximum Poiseuillian velocity). A positive product results in a lateral migration away from the location of maximum velocity; the converse also holds.

We consider the stability of the motion generated in a differentially heated vertical slot filled with a linearly stratified salt solution. The theoretical mean motion field between infinite plates is a function of the Rayleigh number Rs, = gβ(∂S0/∂z) D4/k8ν. If Rs is zero the salinity does not enter the problem and one finds instability in the form of stationary rolls which obtain most of their energy from the basic velocity field. Even at very small Rs of order -1000 these shear instabilities are replaced by diffusively destabilized convective rolls which appear at a thermal Rayleigh number Ra = gαΔTD3/kTν which is two orders of magnitude less than that required for the shear generated modes. The present calculations, which take proper account of both the mean fields and the boundary conditions, give results which compare somewhat more favourably with the experimental results of Thorpe, Hutt & Soulsby (1969) than the theory put forward by these authors. It is shown why their theory, which deals with different boundary conditions from those in the experiment, gives adequate results as Rs tends to negative infinity.

The steady motion of a viscous fluid contained between two concentric spheres which rotate about a common axis with different angular velocities is considered. A high-order analytic perturbation solution, through terms of order Re7, is obtained for low Reynolds numbers. For larger Reynolds numbers an approximate Legendre polynomial series representation is used to reduce the governing system of equations to a non-linear ordinary differential equation boundary-value problem which is solved numerically. The resulting flow pattern and the torque required to rotate the spheres are presented for various cases considered.

The energy theory of hydrodynamic stability is applied to the viscous incompressible flow of a fluid contained between two concentric spheres which rotate about a common axis with prescribed angular velocities. The critical Reynolds number is calculated for various radius and angular velocity ratios such that it is certain the basic laminar motion is stable to any disturbances. The stability problem is solved by means of a toroidal–poloidal representation of the disturbance flow and numerical integration of the resulting eigenvalue problem.

In problems where a viscous fluid flows past a porous solid it has frequently been assumed that the tangential component of surface velocity is zero. When the porous solid has an open structure with large pores the external surface stress may produce a tangential flow below the surface. Recently, Beavers & Joseph (1967) have assumed that the surface velocity UB depends on the mean tangential stress $[\mu(d\overline{u}/dy)]_{y=0}$ in the fluid outside the porous solid through the relation \[ \left[\mu\frac{d\overline{u}}{dy}\right]_{y=0} = \frac{\mu\alpha}{k^{\frac{1}{2}}}(U_B-Q), \] where Q is the volume flow rate per unit cross-section within the porous material due to the pressure gradient, k is the Darcy constant and α is a constant which depends only on the nature of the porosity. An artificial mathematical model of a porous medium is proposed for which the flow can be calculated both inside and outside the surface. This conceptual model was materialized and the experimental results agree with the calculations. The calculated values of α so found are not quite independent of the external means of producing the external tangential stress.

The present paper contains an analysis of the model of a porous material proposed in part 1, and carries out calculations which allow comparison between theory and the experiments described therein. The relevant boundary conditions to be applied at an interface between a fluid and such a material are considered.

The variation of the translational temperature, rotational temperature, and density through shock waves in oxygen and nitrogen was studied using classical laws of mechanics and a Monte Carlo scheme. The collision dynamics were calculated using an intermolecular potential by Parker with both a two-dimensional approximation and the full three-dimensional calculations. The rotational velocity frequency distributions were also calculated. The average number of collisions a molecule will experience a t various stages passing through a shock wave were found and plotted with the temperature and density profiles. The nitrogen results were compared with experimental results and good agreement was found. This also provided a method for giving a first approximation to the three-dimensional intermolecular potential.

Waves generated at the stern of a ship must travel through the ship's wake. The effect of the mean flow in the wake refracting the waves is calculated by using a much simplified model. It is found that the waves diverging from the stern of a ship may differ considerably from the bow waves, in qualitative agreement with observation.

Drops formed from the breakup of charged cylindrical liquid jets have been shown to be smaller than those formed in the unelectrified case. This change has been related to electrically induced instabilities on the jet. Small-perturbation analysis was used to formulate the Lagrangian and write the differential equation for the jet. Non-dimensionalized plots of the solutions exhibit the stabilizing or destabilizing influences of surface tension and electric effects, and allow these influences to be related back to liquid physical properties. Drop diameter to be expected from breakup of the electrified jet was calculated as a function of jet diameter, physical properties of the liquid, jet electrification, and the mode of instability dominating the breakup process.

Benjamin (1970) has calculated the upstream influence in open-channel flow, and has argued that a similar effect occurs when a body is moved along the axis of a tube of uniformly rotating fluid. In the present paper Benjamin's work is extended to the case of interfacial waves in a two-fluid system. It is shown that there are certain special flows for which the upstream influence vanishes.

The discussion concerns free wave motions generated from rest in a finite region of an ocean of heavy liquid lying on a horizontal plane. It is shown that the horizontal fist moment of the free-surface displacement varies linearly with time. Hence, if the total volume displaced is not zero and therefore the centroid of the displacement is definable, the centroid travels with a constant horizontal velocity as the wave motion evolves. This conclusion holds exactly for waves of any amplitude and even remains applicable subsequent to the breaking of waves.

The 23rd EUROMECH colloquium on finite-amplitude and diffusive effects in acoustics was held in Rapperswil (Switzerland), 5–7 April 1971. There were 41 participants from 7 countries, and the authors were the chairmen of the meeting organization. References quoted in this report give the titles of the talks and sources for further details of the work described at the meeting; there will be no other publication of the proceedings. The subject matter of this meeting was more strongly restricted than is indicated by its title, inasmuch as papers motivated solely by sonic-boom research problems were not included. Included in particular were problems of acoustic damping by relaxation, dust, moisture, etc.; damping in ducts; effects of turbulence; acoustic streaming; and thermo-acoustic effects.

Upon review of past experimental results and theoretical efforts it is apparent that the mechanism by which combustion noise is generated is not well understood. A theory of combustion noise is developed in this paper which follows rigorously from the principles of fluid mechanics. Lighthill's approach, used in his studies of aerodynamic noise, is closely followed in the present work. The sound radiated from open, turbulent flames is found to depend strongly upon the structure of such flames; at present their structure is not well known. However, meaningful bounds and scaling rules for the sound power output and spectral content are derived based upon the present limited knowledge. A framework is developed which explains past experimental work and the origin of combustion noise.