This study deals with the mass-transport velocity within the bottom boundary layer of cnoidal waves progressing over a smooth horizontal bed. Mass-transport velocity distributions through the boundary layer are derived and compared with that predicted by Longuet-Higgins (1953) for sinusoidal waves. The mass transport at the outer edge of the boundary layer is compared with various theoretical results for an inviscid fluid based on cnoidal wave theory and also with previous experimental results. The effect of the viscous boundary layer is to establish uniquely the bottom mass transport and this is appreciably greater than the somewhat arbitrary prediction for an inviscid fluid.

The free-convective flow induced when a semi-infinite horizontal fuel surface burns in a quiescent oxidizing atmosphere is considered. For high values of the Grashof number the dominant feature of the flow is a boundary layer close to the surface within which there is a flame or intense reaction zone. An outer flow or fire-wind is induced by entrainment into this boundary layer. A simple experiment supports this overall picture of the flow.

Free-streamline theory is employed to construct an exact steady solution for a linear array of hollow, or stagnant cored, vortices in an inviscid incompressible fluid. If each vortex has area A and the separation is L, there are two possible shapes if A½/L is less than a critical value 0.38 and none if it is larger. The stability of the shapes to two-dimensional, periodic and symmetric disturbances is considered for hollow vortices. The more deformed of the two possible shapes is found to be unstable while the less deformed shape is stable.

The oxygen vibrational and dissociation relaxation behind regular reflected shocks has been calculated and measured. Numerical calculations using published rate coefficients supplied the relaxation-zone data needed to estimate the range of most useful experimental conditions. Then photographs of the shock reflexion were taken using a complementary double-exposure interferometer. The density profiles in the relaxation zones behind the reflected shocks were measured by means of a multibeam laser-differential interferometer. The results of these experiments confirmed the theoretical model adopted for the calculations within a certain range of experimental conditions, but clearly revealed the need for revising the rate coefficients. New calculations with different vibrational relaxation times and dissociation rate coefficients then had the result that the best fit of calculated to measured profiles was obtained when the following values were inserted.

Vibration\begin{eqnarray*} & p\tau_v = A_v\exp(B_vT^{-\frac{1}{3}}),\\ & A_v = (2.1\pm 0.2)\times 10^{-5}\,{\rm kg/ms},\quad B_v = 129\,{}^{\circ}{\rm K}^{\frac{1}{3}}. \end{eqnarray*}

Dissociation: O2 + O_2[rlarr ] 2O + O_2 \begin{eqnarray*} & {\mathop {k_1}\limits^{\rightharpoonup}} = A_1T^{-2.5}\exp (-\theta_D/T),\\ & A_1 = (6.2 \pm 0.5)\times 10^{18}\,{\rm m}^3\,{}^{\circ}{\rm K}^{2.5}/{\rm mol}\,{\rm s},\quad\theta_D = 59\,136\,{}^{\circ}{\rm K}. \end{eqnarray*}

Dissociation: O2 + O[rlarr ]3O \begin{eqnarray*} & {\mathop {k_1}\limits^{\rightharpoonup}} = A_2T^{-1.0}\exp (-\theta_D/T),\\ & A_2 = (4.0 \mp 0.5)\times 10^{-13}\,{\rm m}^3\,{}^{\circ}{\rm K}/{\rm mol}\,{\rm s}. \end{eqnarray*}

Accurate measurements of the density distribution in Ar and N2 shock waves have been made in a shock tube for the Mach number range from 1.55 to 9 and 10 respectively by the absorption of an electron beam. A modified absorption law has been used for data reduction. The density profiles were corrected for the influence of shock curvature and density rise behind the shock wave. The measurements in Ar agree to within 1% with those of Schmidt (1969) in the mean range of Ms but give a slightly smaller density gradient for Ms = 9. Comparison with various theories shows very good agreement with Bird's Monte Carlo simulation in the whole Mach number range for a simple repulsive intermolecular force law. Further, the agreement with the Mott-Smith density profile for the same interaction law is also good, and surprisingly is found to be better for lower than for higher Mach numbers. Qualitative agreement is obtained with the solutions of Hicks & Yen for hard-sphere and Maxwell molecules. The Navier-Stokes and BGK solutions are found to differ significantly from the present experiments even for the lowest measured Mach number (1·55), whereas the Burnett equation gives better agreement, especially with respect to the asymmetry of the profiles.

The measured N2 profiles agree on the whole with the shock-tube measurements of other investigators but show substantial deviations from the low density wind-tunnel experiments of Robben & Talbot (1966b) for higher Mach numbers. Bird's ‘energy sink model’ (1971) is in agreement with the measured density profiles for a realistic interaction law and a suitable rotational collision number. Rotational relaxation in nitrogen is found to be very fast for all Mach numbers. Consequently the coupling between rotational and translational relaxation is very strong.

Jets from notched nozzles are investigated by schlieren photography and pressure traverses. It is demonstrated that the dominant feature of the flow which determines the structure far downstream is the trailing vortices shed from the swept edges of the notches.

This paper examines the problem of a pulsating compact body moving with constant velocity. This problem is usually incorrectly treated as a convected monopole. The analysis here shows that the motion of such a ‘real’ source introduces additional coupled multipoles, whose combined effects generate previously unexpected convective features. The amplification obtained is not the monopole convective amplification (1 — Mr)−2. It is found to depend on the virtual mass tensor of the body, the minimum effect being (1 — Mr)−3. There is also amplification in the direction perpendicular to the flight path (unless the motion is parallel to a principal axis of the virtual mass tensor).

The field produced by oscillation of a convected compact body of constant geometry is also investigated. Again, this problem is often misrepresented as a moving dipole. Here it is shown that the effect of convection on such a real source is surprising and complicated. It cannot be described completely by Doppler factors, and there is amplification in the direction perpendicular to the source motion.

These two model problems serve as a warning that the effect of flight on real sources cannot be anticipated until such real sources are correctly modelled, and that also the influence of source motion is likely to be much greater than has so far been anticipated.

Preliminary measurements have been made of the debouching of homogeneous fluid from a broad source at its equilibrium depth into a linearly stratified tank of salt water. With c the velocity of the nose of the intrusion, h its half-thickness near the source, N the environmental buoyancy frequency and v the kinematic viscosity of the fluid, it is shown for 100 [lsim ] Re ≡ 2ch/ν [lsim ] 500 that the intrusion becomes practically steady under an inertia-buoyancy balance. The internal Froude number Fr = c/Nh is shown to be of order unity. Forward-propagating disturbances and the ends of the tank are inferred to play an important part in the flow.

Numerical solutions for the flow field about cones with nose angles of up to 30° at angles of attack up to 50° for a range of Reynolds numbers and wall temperature ratios are presented. The solutions obtained permit interaction between the inviscid region and the boundary layer on the body through the displacement-thickness effect. The solutions are valid throughout the flow field except in the region adjacent to the leeward line of symmetry. Comparisons are made with experimental results and other numerical solutions. Detailed flow structure and the variation of surface conditions with cone angle, incidence, Reynolds number and wall temperature are indicated. The numerical methods used for the inviscid flow equations are Telenin's method and the method of characteristics, while a modified form of the method of integral relations is applied to the boundary-layer equations.