The conditional sampling technique is used to measure ensemble averages of the longitudinal and normal velocity fluctuations u and v respectively and of the Reynolds shear stress fluctuations uv both within the turbulent and irrotational regions near the outer edge of a turbulent boundary layer. The measurements are made in both a smooth- and a rough-wall boundary layer under zero-pressure-gradient conditions. The smooth- and rough-wall results are qualitatively similar but the magnitude of the rough-wall averages is higher than that of the smooth- wall averages, corresponding with the higher value of wall shear stress on the rough surface. The maximum shear stress value encountered within a burst represents a significant proportion of the wall shear stress.

The statistical properties of the turbulence within the burst are close but not quite identical to the nearly Gaussian properties of the inner region of the boundary layer. During an attempt to distinguish between bursts of different ages or strengths at the time of measurement, it was found that bursts of relatively short duration travel at much the same longitudinal velocity as the local mean U and contribute little to the local shear stress. The longer and less frequent bursts have a mean velocity smaller than U and a maximum shear stress comparable to the shear stress at the wall.

The boundary layer that forms on the walls of a shock tube, after the diaphragm which initially separates two gases at different pressures is burst, is investigated. Both the driver and driven gases are assumed to have the same thermal properties and the shock tube wall is maintained at constant temperature. Crocco variables are used and a method is presented for solving the compressible boundary-layer equations within the tube in similarity variables. Three cases, corresponding to different initial pressure ratios of the driver and driven gases, are calculated which are representative of weak and medium-strength shock and expansion waves.

The problem considered is that of the steady motion of a series of neutrally buoyant, flat-faced, rigid, cylindrical capsules along the axis of a pipeline under the influence of a hydraulic pressure gradient. The Navier-Stokes equations are non-dimensionalized and expressed in central-difference form. Numerical solutions are found by the method of relaxation for Reynolds numbers up to 20 000 and a close agreement is obtained with readings from a laboratory apparatus for Reynolds numbers up to 2200.

The flow is examined in detail and the existence of toroidal vortices between successive capsules is demonstrated. Their shape is shown to be increasingly influenced by inertial forces as the Reynolds number increases, but the overall pressure gradient is not greatly dependent on the Reynolds number.

The flow of an incompressible viscous fluid past a deforming sphere is studied for small values of the Reynolds number. The deformation is assumed to be radial but is otherwise quite general. The case of S = O(l), where S is the Strouhal number, is investigated in detail. In particular, the drag is obtained up to O(R2 In R), where R is the Reynolds number.

Plane Poiseuille flow in which the pressure gradient has a small amplitude time-periodic component in addition to a constant component is considered. The velocity field close to the boundaries, arising from a small amplitude high frequency disturbance to the flow, is calculated to second order in the modulation amplitude. The energy-transfer integral for the disturbance is then calculated to the same order. It is found that, if the thickness of the disturbance shear wave relative to that of the modulation shear wave is greater than ½, the modulation inhibits energy transfer into the disturbance and so stabilizes the flow.

The structure and propagation rates of premixed flames are determined by singular perturbation in the limit where the activation temperature is large relative to other flow temperatures for several basic flows. Specifically, the simple kinetics of an exothermic first-order monomolecular decomposition under Arrhenius kinetics is studied for one-dimensional laminar flame propagation, spherically symmetric quasi-steady monopropellant droplet burning, and other simple geometries. Results elucidate Lewis-number effects, losses owing to fuel gasification processes, and conditions under which the thin-flame approximation is a limit of finite-rate Arrhenius kinetics.

This note intends to clarify the way in which the expansion of an initially uniform gas into an ambient atmosphere degenerates into an expansion into a perfect vacuum. The starting-point is a paper by Greenspan & Butler (1962) in which certain tentative remarks are made reprding this question. We show that the flow consists of an infinite-strength contact front coinciding with the gasvacuum interface of the perfect-vacuum expansion, driving an infinite-strength shock into the vacuum ahead of it. The ga,s-vacuum interface and the shock are separated a t all times even though the density of the gas through which the shock travels vanishes in the vacuum limit.

The radiation and scattering of time-periodic surface waves by partially immersed objects is investigated in the short-wave asymptotic limit ε → 0, where ε is a non-dimensional wavelength. Details are given for the prototype radiation and scattering problems in which the fluid has infinite depth and the body is a two-dimensional dock of finite width and zero thickness. The solutions are then generalized to deal with other two-dimensional geometries, with the restriction that the ends of the obstacle are horizontal for a distance of many wavelengths. The method of matched expansions is used. A first approximation ϕ0, presumed to be a good estimate for the potential throughout most of the fluid region, is obtained by replacing the free-surface condition by its formal limit ϕ0 = 0. In the vicinity of the ends of the obstacle, the correct surface condition is used but the geometry of the problem is simplified. The remaining surface layers are dealt with by superimposing on the function ϕ0 regular wave trains of the appropriate amplitude.

The general analysis developed in Parts 1 and 2 of three-dimensional duct flows subject to a strong transverse magnetic field is used to examine the flow in diverging ducts of rectangular cross-section, the walls of which are electrically non-conducting. A dramatically different flow is found in this case from that studied in Part 2, where the side walls parallel to the magnetic field were highly conducting. Now it is found that the core velocity normalized with respect to the mean velocity is of O(M−½) while the velocity in the side-wall boundary layers is of O(M½), so that these boundary layers carry most of the flow. The problem of entry is solved by analysing the change from fully developed Hartmann flow in a rectangular duct to the flow in the diverging duct. It is found that the disturbance in the upstream duct decays exponentially. The analysis of the side-wall boundary layers is more difficult than that in Part 1 on account of the different boundary conditions and requires the solution of two coupled integro-differential equations. Numerical solutions are obtained for a duct whose width increases linearly in the flow direction.

The 36th European Mechanics Colloquium (EUROMECH 36) which was held at Imperial College from 17 to 19 April 1972 was the first to be devoted to laser anemometry. It brought together European researchers whose primary interests included physics, electronics and fluid mechanics with the following purposes.

This paper examines the nature of the development of two-dimensional laminar flow of an incompressible fluid at the rear stagnation point on a cylinder which is started impulsively from rest. Proudman & Johnson (1962) first examined this type of flow, andobtainedasimilarity solution of the inviscid form of the equations of motion. This solution describes the nature of the flow at large distances from the surface, for large times after the start of the motion. Here, the flow at the rear stagnation point is examined in greater detail. The solution found by Proudman & Johnson constitutes the leading term in an asymptotic expansion, valid for large times. Further terms in this expansion are now calculated, and the method of matched asymptotic expansions is used to obtain an inner solution describing the flow near the surface. A numerical integration of the full initial-value problem gives good agreement with the analytical solution.

An accurate quasi-analytic method of solution is presented for the classical hydrodynamics problem of the constant-velocity entry of a prismatic wedge into a weightless incompressible inviscid fluid. The method uses the Wagner function W, which reduces the problem to the determination of a mapping function Λ = [Lscr ](W) for the hodograph. [Lscr ](W) is constructed by using the hodograph for an unsymmetric diamond together with a modifying or ‘preparatory’ trans-formation. A computer method of conformal mapping is developed and is used to obtain this latter transformation. Results are presented for the case of a 90° wedge and show that the solution is both more accurate than previous solutions, having an error of less than 1 %, and more complete, as it portrays the entire flow field and furnishes information about the functional dependence among the variables.