An investigation was conducted in a hypersonic shock tunnel to study the laminar boundary-layer transition on a highly cooled 10° cone of 4 ft. length over the Mach-number range of 8·5 to 10·5 with a stagnation temperature of 1400 °K. The effects on transition of tip surface roughness, tip bluntness, and ± 2° angle of attack were investigated. With fast-response, thin film surface heat-transfer gauges, it was possible to detect the passage of turbulent bursts which appeared at the beginning of transition. Pitot-tube surveys and schlieren photographs of the boundary layer were obtained to verify the interpretation of the heat-transfer data. It was found that the surface roughness greatly promoted transition in the proper Reynolds-number range. The Reynolds numbers for the beginning and end of transition at the 8·5 Mach-number location were 3·8 × 106−9·6 × 106 and 2·2 × 106−4·2 × 106 for the smooth sharp tip and rough sharp tip respectively. The local skin-friction data, determined from the Pitot-tube survey, agreed with the heat-transfer data obtained through the modified Reynolds analogy. The tip-bluntness data showed a strong delay in the beginning of transition for a cone base-to-tip diameter ratio of 20, approximately a 35% increase in Reynolds number over that of the smooth sharp-tip case. The angle-of-attack data indicated the cross flow to have a strong influence on transition by promoting it on the sheltered side of the cone and delaying it on the windward side.

This paper describes an experimental study of the starting process in a reflected-shock tunnel, and compares the results with numerical calculations reported previously (Smith 1962). It is shown that an unsteady expansion wave dominates the transient flow, and the shock-wave system plays a minor role. The effects of initial pressure in the nozzle were investigated, and the behaviour of the secondary shock wave was noted. It was found that initial pressures larger even than the steady-flow static pressure can be tolerated without prolonging the starting process, despite the presence of a strong secondary shock wave. Other analyses, based on the ‘steady-state’ model of the starting process, are discussed and shown to give an unrealistic description of the flow field.

Pressure distribution and the effect of air injection in the separated flow over a spiked-hemisphere were investigated at a Mach number of 3·3, and Reynolds number around the transitional value. Pressure distribution along the spike as well as over the body was measured in the absence of injection. Air was injected into the separated flow at the spike tip and base and reattachment region through one or more orifices drilled normal to the surface, and the resulting flow patterns were observed using the schlieren technique. The results show that (i) the pressure variation along the spike is similar to a two-dimensional separated flow in the transition régime; and (ii) the mass injection at the spike tip has a strong destabilizing effect regardless of injection rate, while the injection from spike base and reattachment region can be either slightly stabilizing or destabilizing depending on the flow condition.

A real fluid is contained between two horizontal infinite disks which rotate about a common vertical axis with the same angular velocity. On the upper disk there is an axisymmetric non-uniform temperature distribution with a minimum at the point of intersection of the disk and the axis of rotation. The lower disk is insulated. It is assumed that inertial accelerations are negligible in comparison with Coriolis accelerations and that viscous effects are confined to Ekman layers at the disks. Outside the Ekman layers, therefore, since the motion is axisymmetric, the buoyancy forces, by the geostrophic approximation, drive only an azimuthal component of the velocity field which cannot alter the temperature field. Thus heat is convected only by the secondary circulation which is driven by the viscous forces of the Ekman layers. It is possible then for the secondary flow to be so small that heat is transferred by conduction processes.

This paper analyses the conditions necessary for either conduction or convection processes to predominate and the structure of the velocity and temperature fields in these different situations. In addition the separate effects of a temperature maximum on the upper disk and of replacing the upper disk by a stress-free surface are considered.

This is a study of the propagation of gravity waves over a basin in which the propagation distance is large compared with the scale of the bottom topography, which, in turn, is large compared with the depth. Special emphasis is given to the low-frequency part of the spectrum and to geometries containing a beach (see figure 1) because of their importance in tidal wave phenomena. Both reflexion phenomena and the dispersive character of the propagation are accounted for and the non-linear aspects of the large amplification associated with the beach climbing are also included. However, the analysis of problems in which the waves break is valid only up to the inception of breaking; post-breaking phenomena are not treated.

Two-dimensional flow of a second-order fluid near a stagnation point occurring on a flat plate which is performing harmonic oscillations in its own plane is considered. The equations have been integrated by the Kármán-Pohlhausen method for small values of ω, the frequency of the oscillation of the plate, and the W.B.K. method is applied to solve the equations for high values of ω. The velocity profile within the boundary-layer region and the shearing stress on the plate have been obtained in both the cases. The oscillation of the shearing stress has a phase lead over the oscillation of the plate. This phase lead decreases with increase of the second-order effect for small values of ω.

Empirical information is extracted from constant-pressure flows and, on this basis alone, the equations of motion are solved for flows where the pressure gradient parameter, β = δ*(dp/dx)/τ0 is held constant. The experimental defect profiles of Clauser and the near-separating profile of Stratford are predicted quite well.

The present work is an extension of the work of Clauser and Townsend in that a particular form for an effective or eddy viscosity is hypothesized. Here, however, a continuous, and analytically precise family of defect profiles are calculated for the entire range, −0·5 ≤ β ≤ ∞. The solutions span the whole profile with the exception of the viscous sublayer.

A detailed consideration of the viscous sublayer and a comparative examination of various eddy viscosity hypotheses are included in a companion paper.

Precise data are presented on the Rayleigh-Jeffreys instability in air, argon and carbon dioxide at pressures between 0·6 and 6·0 atm in layers of depths 1/8, 1/4, and 3/4in. A new method yields better resolution and repeatability than the methods employed in the past. Here the gas layer is brought through the state of marginal stability by increasing the pressure while both the temperature and the temperature difference are held constant. The onset of convection is detected by means of a type of heat flow meter ascribed to Prof. L. M. K. Boelter. The equipment and procedure are described and analysed in detail.

The experimentally-determined value of the critical Rayleigh number is 1793, repeatable within a probable deviation of 1% due to random errors. Considering in addition the systematic errors of the instrumentation but not the uncertainties of property values, we place the absolute value within 1793 ± 80. The corresponding theoretical value is 1708.

Finite rates of pressure rise inhibit the development of convection. The results achieved at the least rates of pressure rise are in agreement with steady-state determinations.

The approach employed in this investigation shows great promise as a method for measuring the transport properties of gaseous mixtures or of gases at combined high temperature and high pressure.

A dimensional argument is presented leading to a functional form for the effective viscosity which embraces the hypothesis of a previous paper (Mellor & Gibson 1966; hereafter referred to as paper A) in the defect portion of a turbulent boundary layer. The new argument also suggests a way of determining the effective viscosity in the viscous sublayer when the flow is subjected to mainstream pressure gradients.

It will be shown that the large wall-velocity profiles and the defect-velocity profiles automatically overlap, even in the absence of a logarithmic portion. It will be shown further that equilibrium flows are uniquely determined by β and R.

The principle of exchange of stabilities (exchange principle) for the thermal stability problem has been proved by Pellew & Southwell (1940) for fluids bounded by two infinite, horizontal parallel planes. Chandrasekhar (1952) discussed the establishment of the exchange principle for the same geometry when the fluid is an electrical conductor and when an arbitrary oriented, uniform, external magnetic field is applied in the vertical direction.

In this paper, the exchange principle is examined for fluids completely confined in an arbitrary region with rigid bounding surfaces that are good electrical conductors with respect to the fluid. The uniform magnetic field is applied in an arbitrary direction. A generalized thermal boundary condition is imposed which includes the fixed temperature and prescribed heat-flux conditions as special cases.

If no magnetic field is applied to the fluid, the present work reduces to a generalization (for completely confined fluids) of the Pellew & Southwell proof of the exchange principle. In the magnetohydrodynamic (MHD) thermal stability problem, the exchange principle is found to be valid if the total kinetic energy associated with an arbitrary disturbance is greater than or equal to its total magnetic energy. In a special case it is demonstrated that a sufficient condition which will establish the exchange principle is k ≤ η, where k is the fluid thermal diffusivity and η is the fluid electrical resistivity.

Laminar hypersonic flow past a sphere is examined on the basis of the constant-density approximation. The Navier-Stokes equations governing the flow are reduced to a nearly parabolic form so that backward influence is essentially eliminated. Two methods of solution are then used on the resulting equations. The first method is the so-called series-truncation method (local similarity), and the second method is an implicit finite-difference method. The solutions from the two methods are compared for various values of the shock Reynolds number. These solutions are also compared with Lighthill's inviscid constant-density solution for high-shock Reynolds number.

The interaction was observed between a supersonic free jet of partially ionized argon and the magnetic field of a coil concentric with the jet. Nominal values of the parameters were: Mach number, 3; Reynolds number, 1000; magnetic Reynolds number, 0·2; magnetic interaction parameter, 1; Hall parameter, 1. The jet was strongly channelled. Axial and radial electric fields were observed in the jet with a net rise in potential across the interaction.

These observations were consistent with predictions based on the single fluid, macroscopic equations, and a simple slug flow model. The current equation was solved to second order in the Hall parameter giving a closed form expression for the Hall potential which agreed with the experiments for weak fields. Flow perturbations were calculated for Mach numbers of 3.11, 6.08, and 10.05, neglecting Hall currents; the calculations are in qualitative agreement with the experiments and show Joule heating to be the main factor in perturbing the flow at high Mach numbers.

The Orr-Sommerfeld equation is solved for large Reynolds number by use of inner and outer expansion theory. The method is shown to have distinct computational advantages over the method of solution due to Sommerfeld and Lin and to be applicable to a wider class of boundary conditions. The method can be simply extended to other characteristic problems in fluids involving viscous effects concentrated in narrow regions.

Plumpton & Ferraro (1955) considered the torsional oscillations of an infinitely conducting sphere in a uniform magnetic field. They showed that if the fluid and magnetic viscosity were assumed to be zero in the governing differential equations, then a continuous spectrum of eigenvalues could be obtained. This novel feature was clarified by Stewartson (1957) when he obtained the exact solution and showed that in the correct limit of a perfect conductor the eigen-values are discrete. Furthermore, in the limit of infinite conductivity the oscillations occur only on the axis of symmetry (figure 1).

This paper is concerned with unsteady laminar boundary layers on solid bodies in the presence of a fluctuating external flow of small amplitude. Any containing enclosures are assumed to be at infinity. Compressibility is ignored and conditions are given under which this and other approximations are valid. Special attention is focussed on the phenomenon of the formation of a steady-streaming flow, induced by the Reynolds stresses in the oscillatory boundary layer: it is shown that, if the characteristic Reynolds number of the steady streaming is large, there is an outer boundary layer within which the steady-streaming velocity decays to zero. The thickness of this outer layer is large compared with that of the inner (oscillatory) layer, but small compared with a typical dimension of the body.

The partial differential equation for the flow in the outer layer is solved in a typical case by a generalization of a series-expansion method due to Fettis. Similarity solutions of the equation are also described.

The theory is applied specifically to the case of flow generated by a circular cylinder oscillating along a diameter in an infinite fluid. Qualitative agreement is obtained with experiments performed by Schlichting.

Non-equilibrium inviscid flows behind a spherical-segment shock wave are investigated with the method of series truncation. This semi-analytical technique developed at Stanford is based on a systematic co-ordinate-perturbation scheme. The flow variables are expanded in series in powers of the longitudinal curvilinear co-ordinate leading away from the stagnation point. The problem is thus reduced to one of numerical integration of ordinary differential equations for functions of the normal co-ordinate. Unlike the similar situation of the Blasius series in boundary-layer theory, the present scheme–having to deal with elliptic equations–must resort to series truncation. As a consequence, a truncation error is introduced. The present paper shows a simple way of reducing this error.

The simplified air chemistry adopted is based on non-equilibrium dissociation and recombination of oxygen diluted in inert nitrogen. A wide spectrum of non-equilibrium régimes is investigated for a fixed set of flight conditions. In particular, near-frozen flows are followed to the vicinity of the stagnation point through a region of large temperature and concentration gradients located near the body. This equilibrium-drive region, arising from the singular nature of the frozen limit, is studied in some detail.

An integral-equation approach is used to calculate the first-order effect of the proximity of a boundary on the Stokes resistance of a body. It is shown, that this approach gives both a simple derivation of the modified Stokes resistance and a method of investigating the accuracy of the final result. The problem of two settling particles is also considered briefly.

The large-eddy energy equilibrium hypothesis states that the largest eddies of a turbulent shear flow are in approximate energy equilibrium throughout a significant part of their lives. This hypothesis leads to a relationship between the mean rate of shear strain and the Reynolds shear stress which involves the scale of the large eddies. By assuming that the large-eddy scale is proportional to the standard deviation of the free turbulent boundary, or laminar superlayer, the validity of this hypothesis may be checked experimentally. Intermittency and mean velocity measurements made in five different two-dimensional shear flows are presented and these results, together with values calculated from Townsend's measurements in a two-dimensional wake, support the form of relationship suggested by the energy equilibrium hypothesis.

Heat-transfer coefficients are calculated for forced convection from a heated flat plate, of finite breadth and infinite span, at zero incidence to a steady stream of viscous, incompressible fluid. The complete range of the Reynolds number R is considered and the results for large R are compared with the Pohlhausen boundary-layer solution for a plate of infinite breadth with the Blasius velocity field.

It is found that the heat transfer from the trailing edge of the plate is important for small Reynolds numbers but steadily diminishes as R increases. The limiting value of the heat-transfer coefficient at the leading edge agrees to good accuracy with Pohlhausen's result and the corresponding overall heat-transfer coefficient is within 3% of Pohlhausen's value for an equal length of the infinite plate measured from the leading edge. The results over the whole Reynolds-number range are probably correct to this order of accuracy.

The Reynolds analogy between skin friction and heat transfer, exactly true at large Reynolds numbers, is found to be inadequate at small values of R, as may then be expected, due to the existence of a pressure gradient parallel to the plate.

A solution is obtained for the boundary of the magnetic field of two arbitrary line currents immersed in a plasma at uniform pressure. The linear dimensions of the boundary, which are determined for several sets of data, are proportional to the intensity of the line currents (assuming that their ratio is constant) and inversely proportional to the square root of the plasma pressure. The cusps over the boundary, which when the two line currents are equal and opposite are symmetrical with respect to the line currents, move towards the weaker current until they eventually disappear on the line joining the two currents. When the distance between the currents is such that when the cusps disappear the two line currents lie in the same cavity, some plasma gets trapped inside the cavity. When the cavities of two line currents of the same sign touch we get an abrupt instability; the plasma is suddenly pushed out by the surface currents and this results in the formation of a larger field cavity.