The stability of the Stewartson layer in a rotating incompressible fluid is investigated within the framework of a linear theory. The boundary-layer structure of the shear layer is correctly taken into account and the effect of viscous dissipation on the disturbance is included in the governing equations. The growth rate ωi of the disturbance is given as a function of the unified parameter mRo/(γ½), where m, an integer, is the azimuthal component of the wavenumber vector, γ the radius of the layer, Ro the Rossby number and E the Ekman number. Instability occurs when m Ro/(γ½) > 9·5. The time evolution of a growing disturbance is given schematically. Comparison of our results with the experiments by Hide & Titman shows good agreement.

The stress relaxation effect in an incompressible elastico-viscous fluid is investigated for the case of the lubrication of line-contact rollers. Two extreme cases are considered: that of low pressures with rigid surfaces and constant viscosity and that of heavily loaded elasto-hydrodynamic lubrication. In order to solve this problem, a new invariant material time derivative is suggested. This derivative is referred to a co-ordinate system attached to the principal axes of the strain-rate tensor, while the former derivatives have been referred to the fluid particle. It is shown that, unlike the previous derivatives, the new one enables a separate parametric description of the stress relaxation process and the first normal-stress difference. The results show that a significant increase in the load capacity is obtained, owing to the relaxation time of the fluid. The investigation is for fluids with a relaxation time small compared with the transit time of the lubricant through the bearing.

Results corresponding to those of Newman (1975) for wholly or partially immersed cylinders are obtained, namely relations between the phase angles of the cylindrical outgoing surface waves generated either by the forced oscillations of an immersed axisymmetric body or by the scattering effect of the body on a plane wave.

This paper discusses the theory of the generation of sound which occurs when a frozen turbulent eddy is convected in a mean flow past an airfoil or a semi-infinite plate, with and without the application of a Kutta condition and with and without the presence of a mean vortex sheet in the wake. A sequence of two-dimensional mathematical problems involving a prototype eddy in the form of a line vortex is examined, it being argued that this constitutes the simplest realistic model. Important effects of convection are deduced which hitherto have not been revealed by analyses which assume quadrupole sources to be at rest relative to the plate or airfoil. It is concluded that, to the order of approximation to which the sound from convected turbulence near a scattering body is usually estimated, the imposition of a Kutta condition at the trailing edge leads to a complete cancellation of the sound generated when frozen turbulence convects past a semi-infinite plate, and to the cancellation of the diffraction field produced by the trailing edge in the case of an airfoil of compact chord.

This paper reports an experimental investigation into the impingement of underexpanded axisymmetric jets on each of three wedges arranged symmetrically in the jets. Three jets were used; two were produced by a convergent-divergent nozzle of exit Mach number 2.2 which was operated at underexpansion ratios of 1·2 and 2, while the third jet was produced by a convergent nozzle operated at an underexpansion ratio of 4. The base widths of the wedges equalled the exit diameter of the convergent-divergent nozzle, their apex angles were 90°, 60° and 45° and they were situated within or just downstream of the first cell of each jet.

Detailed front-face pressure distributions were obtained for 15 different configurations. Shadowgraph photographs were taken of these and other cases. The results show a variety of possible flow patterns. The major factors determining which flow pattern occurs are the combination of the centre-line Mach number and wedge apex angle and the jet shock strength and position. It was found that observed shock intersections can be reconstructed by means of shock polars, but that a four-shock confluence will not always occur when it is possible according to the shock polars. In one case there is evidence of the existence of a β triple-shock confluence. An interesting and unusual flow involving a stagnation bubble was obtained when the wedges were situated downstream of the free-jet Mach disk.

This paper experimentally investigates the heat transport and structure of convection in a high Prandtl number fluid layer whose viscosity varies by up to a factor of 300 between the boundary temperatures. An appropriate definition of the Rayleigh number R uses the viscosity at the average of the top and bottom boundary temperatures. With rigid boundaries and heating from below, the Nusselt number N normalized with the Nusselt number N0 of a constant-viscosity fluid decreases slightly as the viscosity ratio increases. The drop is 12% at a variation of 300. A slight dependence of N/N0 on R is consistent with a decrease in the exponent in the relation N ∝ Rβ from its constant-viscosity value of 0·281 to 0·25 for R [lsim ] 5 × 104. This may be correlated with a transition from three- to two-dimensional flow. At R ∼ 105 and viscosity variation of 150, the cell structure is still dominated by the horizontal wavelength of the marginally stable state. This is true with both free and rigid upper boundaries. The flow is strongly three-dimensional with a free upper boundary, while it is nearly two-dimensional with a rigid upper boundary.

This paper reports an experimental investigation of pressure and force distributions on a sharp-nosed circular cylinder inclined to a uniform low-speed air flow under conditions of laminar separation of the boundary layer. The main concern is with the out-of-plane force (i.e. the side force if the body is at incidence). The experimental model consisted of an extensively pressure-tapped cylinder to which four different noses were fitted. The results show that there is an oscillatory distribution of out-of-plane force along the cylinder for most of the inclination range 0-90°. The amplitude of this distribution is strongly affected by nose shape in conditions where the out-of-plane force extends onto the nose. At very high angles of inclination the oscillatory distribution disappears and is replaced by a vortex pattern like that found on an infinite yawed cylinder. The general nature of the out-of-plane force is found to be consistent with the impulsively started flow analogy. Unsteadiness in the flow was found to cause a serious reduction in many of the time-averaged values. The unsteadiness is ascribed to the switching of the flow pattern due to free-stream turbulence. Measurements of the time histories of certain pressures enabled values of the force in the unswitched state to be calculated. The Reynolds number was found to have an important influence at inclinations above 55°. However, it was also found that the range of Reynolds numbers over which this effect occurs can depend on the scale of the model.

The wall structure of the turbulent boundary layer was examined using hot-wire rakes and conditional sampling techniques. Instantaneous velocity measurements indicate a high degree of coherence over a considerable area in the direction normal to the wall. At y+ = 15, there is some evidence of large-scale correlation in the spanwise direction, but almost no indication of the streamwise streaks that exist in the lower regions of the boundary layer. Conditional sampling showed that the normal velocity is directed outwards in regions of strong stream-wise-momentum deficit, and inwards when the streamwise velocity exceeds its mean value. The conditionally averaged Reynolds shear stress was approximately an order of magnitude greater than its conventionally averaged value and decayed slowly downstream.

The return to isotropy of homogeneous axisymmetric turbulence at Reλ ≈ 28 is studied by means of the direct spectral simulation (DSS) technique of Orszag & Patterson (1972) and the direct-interaction approximation (DIA) of Kraichnan (1959) as implemented by Herring (1974). The results of the two methods are compared for different initial degrees of anisotropy. The general agreement between the methods is good. Most of the discrepancies can be attributed to present technical limitations in implementing both schemes. The DSS has been found to be superior for strong anisotropies, because the numerical method used for solving the DIA equations is limited in its angular resolution. For small anisotropies the angular anisotropy becomes less important and the DIA results are accurate; in this case the DIA seems to be superior as it is free from the statistical uncertainties inherent in the DSS method. With respect to a return-to-isotropy study these statistical errors are large, in particular for small anisotropies. The physical interpretation of the angular energy distribution is discussed also. The numerical results and theoretical considerations for the DIA equations show that one should retain angular moments at least up to the fourth in order to obtain accurate values of the Rotta constant at moderate anisotropies.

Steady two-dimensional flow of Newtonian liquid in a layer around the inside of a rotating horizontal cylinder is analysed as a regular perturbation from rigid-body motion. The equations governing the first perturbation are solved in closed form. Parameter limits are taken in order to elucidate the flow structure and to provide simpler working formulae. The limiting cases are for small Reynolds numbers, which resembles viscous film flow down a curved wall; for large Reynolds numbers, which involves a periodic boundary layer; and for small ratios of average film thickness to cylinder radius. In every case the maximum film thickness occurs in the upper quadrant on the rising side of the cylinder and the minimum thickness is diametrically opposite.

The study of natural convection in a saturated porous medium bounded by two concentric, horizontal, isothermal cylinders reveals different types of evolution according to the experimental conditions and the geometrical configuration of the model. At small Rayleigh numbers the state of the system corresponds to a regime of pseudo-conduction. The isotherms are coaxial with the cylinders. At larger Rayleigh numbers a regime of steady two-dimensional convection sets in between the two cylinders. Finally, for Rayleigh numbers above the critical Rayleigh number Ra*c the phenomena become three-dimensional and fluctuating. The appearance of these different regimes depends, moreover, on the geometry considered and, in particular, on two numbers: R, the ratio of the radii of the cylinders, and A, the ratio of the length of the cylinders to the radius of the inner one. In order to approach these experimental observations and to obtain realistic theoretical models, several methods of solving the equations have been used.

The perturbation method yields information about the thermal field and the heat transfer between the cylinders under conditions close to the equilibrium state.

A numerical two-dimensional model enables us to extend the range of investigation and to represent properly the phenomena when steady convection appreciably modifies the temperature distribution and the velocities within the porous layer.

Neither of these models allows account to be taken of the instabilities observed experimentally above a critical Rayleigh number Ra*c. For this reason, a study of stability has been carried out using a Galerkin method based on equations corresponding to an initial state of steady convection. The results obtained show the importance of three-dimensional effects for the onset of fluctuating convection. The critical transition Rayleigh number Ra*c is thus determined in terms of the ratio of the radii R by solving an eigenvalue problem.

A numerical three-dimensional model based on the method of finite elements has thus been developed in order to point out the different types of evolution with time. Steady two-dimensional convection and fluctuating three-dimensional convection have been actually found by calculation. The solution of the system of equations by the method of finite elements is briefly described.

The experimental and theoretical results are then compared and a general physical interpretation is given.

Large coherent eddies have been observed in turbulent shear layers and seem to play an important role in their growth, mixing and noise production. Winant & Browand (1974) have observed that the pairing of large eddies is central to the question of shear-layer development, and they model the pairing process with discrete line vortices. It is shown here that the growth of the layer and amalgamation of large eddies are not adequately treated by isolated-line-vortex models, which are proved to be essentially non-evolutionary. A more detailed model of the shear layer, itself consisting of vortex elements, is shown to provide the definition required to observe the evolution and coalescence of the large eddies. The observed development of this model shear layer is consistent with many features of experimentally observed flows.

A new experimental technique is described for the study of the interactions between the large-scale vortical features in the two-dimensional mixing layer. Detector probes above and below the mixing layer are used to monitor the large-scale structure. Conditional sampling is performed in a moderate Reynolds number developing flow, by using phase and amplitude information from these detector probes. It is shown that significant Reynolds-stress production is associated with the pairing interaction in which two vortical structures combine to form a single, larger vortical structure.

The lateral migration of a neutrally buoyant rigid sphere suspended in a second-order fluid is studied theoretically for unidirectional two-dimensional flows. The results demonstrate the existence of migration induced by normal stresses whenever there is a lateral variation of the shear rate in the undisturbed flow. The migration occurs in the direction of decreasing absolute shear rate, which is towards the centre-line for a plane Poiseuille flow and towards the outer cylinder wall for Couette flow. The direction of migration agrees with existing experimental data for a viscoelastic suspending fluid, and qualitative agreement is found between the theoretically predicted and experimentally measured sphere trajectories.

The problem of uniform flow past a flat plate whose surface has a constant velocity λU opposite in direction to that of the mainstream is considered for large values of the Reynolds number R. In a previous communication (Klemp & Acrivos 1972) it was shown that, if the region of reverse flow which is established next to the plate as a consequence of its motion is O(R−1/2) in thickness, the appropriate laminar boundary-layer equations have a solution provided λ ≤ 0·3541. Here the analysis is extended to the range λ > 0·3541, which cannot be treated using a conventional boundary-layer approach. Specifically, it is found that for λ > 0·3541 the flow consists of three overlapping domains: (a) the external uniform flow; (b) a conventional boundary layer with reverse flow for xs < x < 1, where xs, refers to the point of detachment of the ψ = 0 streamline and x = 1 is the trailing edge of the plate; and (c) an inviscid collision region in the neighbourhood of xs, having dimensions O(R−1/2) in both the streamwise and the normal direction, within which the reverse moving stream collides with the uniform flow, turns around and then proceeds downstream. It is established furthermore that xs = 0 for 0 ≤ λ ≤ 1 and that xs < 0 for λ > 1.

Also, detailed streamline patterns were obtained numerically for various λ's in the range of 0 ≤ λ ≤ 2 using a novel computational scheme which was found to be more efficient than that previously reported. Interestingly enough, the drag first decreased with λ, reached a minimum at λ = 0.3541, and then increased monotonically until, at λ = 2, it was found to have attained essentially the value predicted from the asymptotic λ → ∞ similarity solution available in the literature. Thus it is felt that the present numerical results plus the two similarity solutions for λ = 0 and for λ → ∞ fully describe the high-R steady flow for all non-negative values of λ.

Supersonic nozzle flows of a condensable vapour are considered in the high activation limit for homogeneous nucleation. Conditions are determined under which the final collapse of the supersaturated state is described by a condensation shock. It is shown that the shock zone is associated with droplet growth: droplet production occurs in a thin layer upstream of the growth region. Some new scaling laws are obtained for the structure of the production layer.

The properties of a turbulent boundary layer were investigated as they relate to the form drag on a two-dimensional fence. Detailed measurements were performed at zero pressure gradient of velocity profiles along smooth, rough and transitional flat plates. Upon comparison with other published data, these measurements resulted in simple formulae for the displacement thickness and the local shear coefficient and in a modification to the universal velocity defect law for equilibrium boundary layers.

With these boundary layers, experiments were performed to determine the drag on a two-dimensional fence. These data were analysed along with data from previous investigations. It was found that after suitable blockage corrections all form-drag coefficients for two-dimensional fences collapsed on a single curve if they were calculated with the shear velocity as the reference velocity and plotted against the ratio of the fence height to the characteristic roughness parameter of the approaching flow.

When an interface between two fluids moves in contact with a solid boundary, the Navier-Stokes equations and the no-slip boundary condition provide an unsatisfactory theoretical model, because they predict an undefined velocity at the contact line and a non-integrable stress on the solid boundary. If the surface irregularities are included in the model, the flow on a length scale large compared with their size can be calculated, using a slip coefficient and treating the surface as smooth.

A simple type of corrugated surface is examined, and the effective slip coefficient calculated, for grooves of finite and infinite depth. The slip coefficient when the grooves are filled with one fluid and another fluid flows over them is also calculated. It is suggested that, when a fluid displaces another on a rough surface, the displaced fluid remains in the hollows on the surface, thus providing a partly fluid boundary for the displacing fluid and leading to a slip coefficient for the flow.

Fluid contained between two vertical plates and rising between them provides a simple example of a flow for which the solution can be found with and without a slip coefficient. With slip present, the force on the plates is finite and its value is calculated.

This note describes a comparative investigation of static and dynamic calibration procedures for standard hot-wire probes. It is demonstrated that nearly the same sensitivity dE/dV can be obtained by both procedures. The discrepancy reported by Perry & Morrison (1971) is shown to be due mainly to a poor approximation of static calibration data over a large velocity range by a constant-exponent power-law function.