Theoretical and experimental investigations are described of the linearized wave equation of supersonic flow with a single relaxation process. Firing-range experiments using a known model gas mixture with a single relaxation process are discussed. Qualitatively, it is shown that weak conical and spherical waves decay as predicted by theory. In addition, this decay can be determined quantitatively for conical disturbances; and, satisfactory agreement with theory is found. For application to unknown relaxation processes, it is suggested that observation of the damping of weak waves provides an additional tool for the study of fast rate processes.

Preston's method of measuring skin friction in the turbulent boundary layer makes use of a circular Pitot tube resting on the wall. On the assumption of a velocity distribution in the wall region common to boundary layer and pipe flows the calibration curve for the Pitot tube can be obtained in fully developed pipe flow. Earlier experiments suggested that Preston's original calibration was in error, and a revised calibration curve has been obtained and is presented here.

From experiments in strong favourable and adverse pressure gradients, limits are assigned to the pressure-gradient conditions within which the calibration can be used with prescribed accuracy. It is shown that in sufficiently strong favourable gradients the ‘inner-law’ velocity distribution breaks down completely, and it is suggested that this breakdown is associated with reversion to laminar flow.

As an incidental result, values have been obtained for the constants occurring in the logarithmic expression for the inner-law velocity distribution.

The inviscid stability of the laminar mixing of two parallel streams of a compressible fluid is investigated with respect to three-dimensional wavy disturbances. The flow is more unstable as the angle between the disturbance-wave-number vector and the principal-flow direction exist even at very high Mach number, and the flow is still unstable. However, it is also found that increasing the Mach number of the flow tends to stabilize the flow.

The classical potential solution for the flow about a thin airfoil in either steady or oscillatory motion requires application of the condition, postulated by Kutta, that the fluid velocity be finite at the trailing edge of the airfoil. The Kutta condition derives from the argument that viscous stresses will not allow a flow to turn about a sharp edge. Analytic verification of the validity of this condition, of particular interest in the unsteady case, has not previously been obtained. The problem is treated here by utilizing the Oseen formulation for viscous flow. The solution thus obtained approaches small-perturbation potential flow at a large distance from the airfoil and retains a qualitatively correct representation of the rotational flow near the airfoil. By simply assuming that the resultant force on the airfoil is finite, it is shown that the Kutta condition must apply in the limit of vanishing viscosity.

The first-order corrections, for large Reynolds number, to the lift and moment on an oscillating airfoil are explicitly determined. The effect of the Oseen approximation on the applicability of the numerical results remains to be established.

An accurate measurement of low-Reynolds-number sphere drag has been made. Some of the inaccuracies of previous measurements are revealed. Comparison with the theoretical studies shows that the Oseen formula is as accurate as any in predicting sphere drag below a Reynolds number of 0·4.

The first in a new series of European research conferences in mechanics was held in Berlin on 5 and 6 April 1965. The subject was the Coanda effect, or boundary layers and jets on highly curved walls. Participation was restricted to about 40 people, invited on the basis of their active interest in the subject. These Colloquia are intended to have an informal, workshop-like, character, and formal papers are not normally available, nor will any full proceedings be published. The first author was the chairman of the Colloquium. The following account of the scientific developments of the Colloquium has been prepared to make them widely available. The references quoted give further details of the work discussed at the Colloquium and of related previous work.

Viscous, incompressible, axially symmetric flow about an impulsively started rotating sphere is studied in terms of non-steady, partially linearized Navier-Stokes equations. The non-linear centripetal acceleration is included in full, but the other non-linear terms are neglected because of the restriction in interest to the case of large (but subcritical) Reynolds or Taylor numbers, a2Ω/v. Approximate closed-form solutions for u(r,θ,t), v(r,θ,t), w(r,θ,t) are found which satisfy all relevant boundary and initial conditions. The linearization approximation is checked for consistency and a restriction on Ωt is found. The velocity profiles, in the range of validity, are shown to be approximately similar in time, so their shapes may be qualitatively correct for larger values of Ωt. Some comparison with existing steady-state theories is given and the boundary-layer displacement thickness and viscous torque on the sphere are calculated.

The drag of a sphere has been measured as it moves along the axis of a rotating, viscous fluid. Rotation has been found to modify the classical low-Reynolds-number flow so that the drag is increased and the effects of finite Reynolds number, R, and of wall proximity are reduced as the rotation parameter, the Taylor number T, increases. The results confirm the theory of Childress (1963, 1964) when both Reynolds number and Taylor number are small. The rate at which the sphere rotates with respect to the rotating fluid frame has also been measured and was found to be less than the values calculated by Childress (1964) for small T and R, but to approach the theoretical values in a reasonable way.

The forced motion of a liquid heated non-uniformly from below and subject to a non-constant basic temperature profile is examined. The problem is formulated as a two-point boundary-value problem which is solved by a numerical method. In agreement with previous work, the presence of a positive vertical lapse rate of basic temperature tends to decrease the forced motion. It is found that constant heat generation within the fluid produces a parabolic basic temperature profile, and this tends to increase the forced velocity components.

Theoretical and experimental results are presented for the reflexion and transmission of water waves, passing over a step bottom between regions of finite and infinite depth. Two-dimensional motion is assumed, with the wave crests parallel to the step, and in the theory linearized irrotational flow is assumed. By matching ‘wavemaker’ solutions for the two regions at the cut above the step, an integral equation is derived for the horizontal velocity component on the cut. This integral equation is solved numerically and the reflexion and transmission coefficients and associated phase shifts are obtained. These results are compared with the long-wave theory and significant frequency effects are found, even for quite long waves. Experimental results are presented, which are in fair agreement with the theory.