Measurements of time-mean velocity have been made in a flat channel (aspect ratio 12 to 28), one of whose walls consists of a belt which can be moved in the direction of air blown through the channel or in the opposite direction. The wall layers generated in twenty-six turbulent flows, including plane Poiseuille and plane Couette cases, are compared with analytical results obtained by Kader & Yaglom and by Townsend. Empirical descriptions are developed for the viscous, logarithmic and gradient portions of these wall layers. The core regions of both Couette-type and Poiseuille-type flows are also described empirically. Parallels are drawn with developing boundary layers, and phenomena are identified that relate to the relaminarization of boundary layers.

An exact solution of the nonlinear magnetohydrodynamic equations for a viscous incompressible fluid of finite conductivity is obtained, which represents a circularly polarized structure with time dependent amplitude in a uniform magnetic field. There is a phase difference of ½π between the spatial structures of the velocity and the magnetic field of the disturbance. In the inviscid perfectly conducting limit, this solution represents a standing helical oscillation which is a circularly polarized standing Alfvén wave of arbitrary amplitude, and the sum of the kinetic and magnetic energy densities of the oscillation are constant in the absence of any input of energy.

A variational expression is constructed for the drag on a sphere of radius a that moves with speed U [Lt ] Ωa along the axis of a container of rotational speed Ω and length h [Gt ] a with E = v/Ωa2 [Lt ] 1. Two complementary approximations, based on the asymptotic solutions in the limits δ = Eh/2a ↑ ∞ and δ ↓ 0, and a variational interpolation between these approximations are compared with the numerical results of Hocking, Moore & Walton (1979). The limit δ ↓ 0 is singular, and the variational principle fails in that limit in the sense that the error in the drag is of the same order as the error in the trial function rather than of second order therein; nevertheless, the variational interpolation is in error by less than 0·1% for δ > 0·003 and by less than 1% for all δ. The variational formulation may be of interest in other contexts.

In laboratory experiments of simulated atmospheric mixed layers the entrainment zone is investigated from measurements of horizontally averaged temperature and buoyancy flux, and from visual observations of penetrating thermals using a spread laser beam. The region of negative buoyancy flux of entrainment is found to be confined between the outermost height reached by the few most vigorous penetrating parcels, and by the lesser height where mixed-layer fluid occupies, usually, some 90 to 95% of the total area. The height of most negative buoyancy flux of entrainment is found to agree roughly with the level at which mixed-layer fluid occupies half the area.

The thickness of the entrainment zone, relative to the depth of the well-mixed layer just beneath, is found to be quite substantial (0·2 to 0·4), and apparently decreases only asymptotically with increasing ‘overall’ Richardson number, Ri*. The thickness is not well predicted by parcel theory.

Extensive detrainment is found to occur within the entrainment zone, and adds to the difficulty in defining the position of the local interface between mixed-layer fluid and unmodified fluid.

For typical Ri* values occurring in the atmosphere, the dimensionless entrainment rate is found to be given satisfactorily by 0·25(Ri*)−1, although an $(Ri^{*})^{\frac{3}{2}}$ dependence cannot be ruled out by the present data. Entrainment into a neutral layer in the absence of a capping inversion is found to proceed at the expected rate.

The problem of transient natural convection in a cavity of aspect ratio A [les ] 1 with differentially heated end walls is considered. Scale analysis is used to show that a number of initial flow types are possible, collapsing ultimately onto two basic types of steady flow, determined by the relative value of the non-dimensional parameters describing the flow. A number of numerical solutions which encompass both flow types are obtained, and their relationship to the scale analysis is discussed.

Burgers’ equation, a one-dimensional analogue of the Navier–Stokes equation, has been solved numerically in full detail at high (equivalent) Reynolds numbers. These fine-mesh solutions have been used to study the dynamics of the Burgers’ equation analogue of three-dimensional turbulence and in particular the drain of energy from the large to the small structures.

The equation has also been solved on a coarse mesh, using various forms of subgrid model. The solutions so derived have been compared with filtered solutions of the same problem on a fine mesh. In this way it has been possible to test directly the performance of subgrid models at high Reynolds numbers, a test which cannot be made on the Navier–Stokes equations themselves.

With proper choice of the parameters, the performance of the subgrid models is very satisfactory.

The mechanism of the creation of secondary vortices behind an impulsively started circular cylinder is analysed in this paper by a higher order of accuracy numerical method. This is a combination of second-order and fourth-order compact finite difference schemes to resolve complete unsteady Navier–Stokes equations. The fourth-order compact scheme is used to calculate the Poisson equation of the stream function and the second-order alternating direction implicit scheme to resolve the vorticity transport equation.

In particular, the growth of primary and secondary vortices with time is analysed for Reynolds numbers equal to 300, 550 and 1000. A single secondary vortex first appears at a Reynolds number equal to 300 on the surface of the cylinder. At R = 550, this creation is found numerically at dimensionless time t about 2·85, and this single secondary vortex is transformed into a pair of secondary vortices at t about 5. For R = 1000, two single vortices can be observed at t about 2·5, one near the separation point and another more important, easily identified in flow structure. These secondary vortices are transformed into a pair of secondary vortices at t about 4·5.

A numerical analysis of the influence of the grid systems and the time step is also given. All numerical results presented here are compared with experimental visualizations. The comparison is found satisfactory.

This paper discusses experiments and a theoretical model for the convective circulation driven by a surface buoyancy flux in a horizontal layer of fluid. The layer is closed at one end and, at the other end, the buoyancy has a fixed value over a given depth. Such circulation occurs in side arms of cooling lakes used for waste-heat disposal from power generation. Some geophysical circulations, such as in the Red Sea, are also of the above type.

The experiments were done in a 35 ft long flume using heat transfer between the heated water and the atmosphere to generate the surface buoyancy flux. The observed circulation was characterized by two distinct layers flowing in opposite directions and separated by a density interface. For upper-layer depths less than about half the total depth at the open end, the downflow was observed to be concentrated near the closed end. Circulation flowrates and vertical temperature profiles were measured.

The theoretical model uses a ‘two-layer’ approach. The mass, momentum, and buoyancy conservation equations are integrated vertically on each side of the interface. Mass and buoyancy transfer across the interface are neglected. The interfacial shear stress is proportional to the square of the difference of the average layer velocities. For small layer densimetric Froude numbers, the free surface is shown to be approximately horizontal and the problem reduces to one ordinary differential equation for the thickness of the upper layer. General solutions of this interface equation are presented for horizontal and sloping bottoms. Different configurations are possible depending on the nature of the singular points which occur in the phase plan.

For the convective circulation, the interface is shown to go through a singular point. This condition leads to a simple analytical solution for the circulation flowrate in the case of constant surface buoyancy flux and horizontal bottom. This solution compares well with the experimental data and with measurements on the Red Sea circulation.

An experimental investigation on the IHSM 4 × 8 cm Shock Tube has confirmed the hypothesis of Ben-Dor (1978) and Ben-Dor & Glass (1979) that in truly non-stationary flows the transitions from regular to Mach reflexion (RR → MR) and from Mach to regular reflexion (MR → RR) are different. Consequently it is shown that a hysteresis loop exists in the ${\rm RR}\rightleftarrows {\rm MR}$ transition phenomenon.

Rapid distortion theory is used to calculate surface pressure fluctuations beneath a turbulent flow incident on a two-dimensional bluff body. These pressures depend on the ratio, L∞/a, of integral scale to body dimension: we give results in the two asymptotic limits L∞/a [Gt ] 1 and L∞/a [Lt ] 1. The large-scale limit is described by ‘quasi-steady’ theory – which we review here; and for the small-scale limit we introduce a ‘quasi-homogeneous’, or ‘slowly-varying’, approximation. The theory is compared with field and laboratory measurements and it is found that most measurements lie between the theoretical asymptotes, following the predicted trends.

A number of general conclusions have been obtained for which there are new physical explanations – and which laboratory and field experiments appear to confirm.

1. The r.m.s. pressure fluctuations, p′, caused by upwind turbulence, decrease in strength with distance from the stagnation point when L∞/a [Lt ] 1; but p′ increases with distance from the stagnation point when L∞/a [Gt ] 1.

2. For a given dimension of an obstacle, a, transverse to the flow field, p′ increases as the dimension, b, parallel to the flow field increases. At the stagnation point of an elliptical cylinder, when L∞/a [Lt ] 1, \[ p^{\prime} = {\textstyle\frac{1}{2}}\rho u^{\prime}_{\infty} U_{\infty}(1+b/a)(L_{\infty}/a)^{\frac{1}{2}} \] where u′∞, U∞ are the upwind r.m.s. turbulent and mean velocities and ρ is the density.

3. The fluctuating pressure has a cross-correlation length in the flow direction a factor of a/L∞ higher when L∞/a [Lt ] 1 than when L∞/a [Gt ] 1. In the axial direction the correlation length is again greater (though this time of the same order in L∞/a) when the incident turbulence is of small scale than when it is of large scale.

The response of a subsonic round jet to internal excitation by an acoustic wave has been examined using flow visualization and noise measurements. The jet was subjected to pulse excitation and to harmonic excitation. In both cases large-scale vortex ring structures were observed in the jet mixing layer. With pulse excitation, interactions between the vortex rings were observed, but no associated noise emission could be detected.

Equations for the instantaneous velocity and temperature fluctuations in a turbulent flow are used to assess the effect of a fluctuating convection velocity on Taylor's hypothesis when certain simplifying assumptions are made. The probability density function of the velocity or temperature derivative is calculated, with an assumed Gaussian probability density function of the spatial derivative, for two cases of the fluctuating convection velocity. In the first case, the convection velocity is the instantaneous longitudinal velocity, assumed to be Gaussian. In the second, the magnitude of the convection velocity is equal to that of the total velocity vector whose components are Gaussian. The calculated probability density function shows a significant departure, in both cases, from the Gaussian distribution for relatively large amplitudes of the derivative, at only moderate values of the turbulence intensity level. The fluctuating convection velocity affects normalized moments of measured velocity and temperature derivatives in the atmospheric surface layer. The effect increases with increasing order of the moment and is more significant for odd-order moments than even-order moments.

Fink & Soh (1978) reported a technique to calculate numerically the motion of vortex sheets. They claim it gives reliable results. This paper re-examines the error in the calculation of the velocity of mesh points representing the sheet and shows that the test case used by Fink & Soh is not an adequate one. Instead the roll-up of a vortex sheet shed by a ring wing is studied. The results obtained proved unreliable. (Although several possibilities are discussed) the reason for the breakdown in results remains unknown.