Earlier models of fire plumes based on simple entrainment laws and neglecting dynamic pressure have failed to produce the relatively shallow inflow over the fire perimeter known as fire wind. This inflow is of prime importance in fire modelling as it normally provides much of the air required for combustion; for this reason we have carried out a very simple numerical experiment on two-dimensional natural convection above a strip heat source with the intention of simulating those aspects of fire behaviour involved in the generation of fire wind without attempting the formidably difficult task of detailed fire modelling. Our results show clearly that fire wind is driven by the dynamic pressure field which is generated by and intimately related to the region of strong buoyant acceleration close above the ground boundary. Throughout our parametric range there is a concentrated region of large horizontal pressure gradient in a neighbourhood above the perimeter of the fire, and elsewhere the pressure gradients play a lesser role.

We have investigated also the dependence of our solution on the boundary conditions, particularly those at the lateral boundary, where we have imposed as little constraint as possible on flow into and out of the computational region. Considerable effects even of such weak side-boundary constraints persist throughout the solution region at moderate values of the pseudo-Rayleigh number (based on eddy diffusivities), but these can be limited by an appropriate choice of the thermal conditions and kept within acceptable bounds at large pseudo-Rayleigh numbers. Similar effects of boundary conditions are likely to appear in other mesoscale convectively driven atmospheric models, including sea breezes, katabatic winds and locally concentrated convective columns.

A nonlinear exact solution to the problem of two-dimensional gravity-free incompressible potential flow around an arbitrarily shaped supercavitating hydrofoil near a free surface is obtained. A combination of Newton's method with a functional iterative procedure is used to solve the nonlinear integral and algebraic equations of this problem. Fast and stable convergence results by starting the iteration with a readily chosen initial solution. Some representative numerical computations are made for practical hydrofoils having both generally shaped camber and leading-edge thickness distributions. The force coefficients, pressure distribution and free-streamline shapes of the cavity are calculated for each case with an execution time on an IBM 370-158 of 200–530 s depending upon the initial trial solution.

It has been found that the periodic boundary layer formed on a vertically oscil-lating vertical wall bounding a stratified fluid is liable to two distinct modes of wavelike instability. In the first, which arises when the oscillation frequency ω is lower than 0·7 times the buoyancy frequency N, the phase lines are aligned horizontally. The second mode, in which the phase lines are aligned at 45° or more to the horizontal, becomes dominant as ω is increased above 0·9 N.

In distinction from the unstratified periodic Stokes layer, there appears to be, for ω in the vicinity of N, a definite low threshold to the boundary-layer Stokes-Reynolds number (defined as Wo/(2ων)½, where Wo is the maximum vertical wall velocity and v is the kinematic viscosity) above which the instability is sustained a t a detectable level.

Systematic measurements of drift currents below and of airflows above an air-water interface have been made under various wind conditions. The current near but not immediately below the water surface is found to follow a Kármán-Prandtl (logarithmic) velocity distribution. The current immediately below the water surface varies linearly with depth. The transitions of the current boundary layer to various regimes appear to lag behind, or to occur a t a higher wind velocity than, those of the airflow. The fraction of the wind stress supported by the wave drag seems to vary with the wind and wave conditions: a large fraction is obtained at low wind velocities with shorter waves and a small fraction is obtained a t high wind velocities with longer waves. At the air-water interface, the wind-induced current is found to be proportional to the friction velocity of the wind. The Stokes mass transport, related to wave characteristics, is only a small component of the surface drift in laboratory tanks. However, in terms of the fraction of the wind velocity, the mass transport increases, while the wind drift decreases, as the fetch increases. The ratio between the total surface drift and the wind velocity decreases gradually as the fetch increases and approaches a constant value of about 3·5% at very long fetches.

The effect of variable Coriolis parameter on the formation of inertial Taylor columns is determined for the case of a two-layer fluid with moderate stratification. Analytic solutions of the inertial, quasi-geostrophic, β-plane equations are obtained. As a special case, sohtions corresponding to a single-layer, homo-geneous fluid are also obtained. When both layer velocities are retrograde (westward), the effect of β is to limit the horizontal extent of the disturbance due to the bump. When both layer velocities are prograde (eastward), an extensive meandering wake is found downstream of the bump. Associated with this wake can be large stationary cyclonic and anti-cyclonic eddies. The meander amplitudes in the two layers are typically nearly the same. I n both the retrograde and prograde cases, the strength of the disturbance to the flow above the bump is less in the upper layer compared with the lower, indicating an attenuation in the vertical due to stratification. For a counter-flow situation, the solutions are complicated by the possibility of a stationary baroclinic wave, one that would exist even for β = 0. In all the situations in which a meandering wake is formed, there is a wave-drag force on the bump. Some laboratory experiments corres- ponding to the single-layer solutions are described.

The stability of perturbed normal shock waves is considered. Shock perturbations depend directly upon the disturbances in the flow adjacent to the shock. In the present paper an initially stationary shock is assumed to be perturbed by acoustic waves reaching it from the downstream side. This case corresponds to the situation occurring in shock diffraction or reflexion. Two-dimensional problems of this type have been investigated previously, both analytically and experimentally. These previous analytic results have, in all cases, indicated that the perturbations of the shock decay with time as $t^{\frac{3}{2}}$, while experimentally both t½ and $t^{\frac{3}{2}}$ decays have been observed. It is demonstrated in the present investigation that, when waves are continuously generated at a point or points behind the shock, a t½ decay of the shock perturbations will occur, corresponding to the decay of the incident waves. However, when the source of waves is located only at the shock, as in a diffraction problem, $t^{-\frac{3}{2}}$ decay occurs owing to the cancellation, to lowest order, of the incident wave by its reflexion from the shock. These results explain the divergence between theory and experiment in this area, since the experiments giving the slower decay contained a source of waves behind the shock.

It is concluded that shock stability can only be considered in the context of the type of disturbances incident upon the shock.

A potential flow model of two-dimensional vortex shedding behind an inclined plate is developed. The free shear layers which emanate from the sides of the plate are represented by discrete vortices through the use of the appropriate complex-velocity potential, the Kutta condition and the Joukowsky transformation between a circle and the plate cross-section. The analysis is then applied to predict the kinematic and dynamic characteristics of the flow for various angles of attack. The results compare favourably with the available experimental data as far as the form of vortex shedding and the Strouhal number are concerned. The calculated normal-force coefficients are 20−25% yo larger than those measured by Fage & Johansen (1927).

Euromech 52, on drag reduction in turbulent flows due to additives, was held from 27-30 August 1974in Stockholm, Sweden, under the chairmanship of M. T. Landahl, and was intended to bring together specialists in the various aspects of the drag-reduction phenomenon to discuss current experimental and theoretical work, and to identify promising directions for future research. There were forty-seven participants from eleven countries and twenty-two papers were presented, with ample time for discussion. These papers, which are briefly summarized in this report, could be grouped roughly under the headings of §§ 2-6 below.

Detailed experimental data are presented on the transition between regular and Mach reflexion. Data have been obtained for steady, pseudo-steady and un-steady flows, and include a study of the continuous and discontinuous transitions predicted by previous researchers. It is found that the criterion often used to calculate the transition condition is wrong in every case that we have investigated. In its place we propose an alternative criterion which has the property that the system remains always in mechanical equilibrium during transition.

A linear stability analysis is used to investigate the stability of rotational Couette flow of sbratified fluids. The linearized time-dependent perturbation equations are solved using explicit finite-difference approximations. Small random axisymmetric perturbations of a given wavelength are initially distributed in the flow field, and their development in time is obtained by numerical integration. It is found that the kinetic energy of the perturbations oscillates in time owing to the periodic transformation of the disturbance flow field from a one-vortex system to a two-vortex system and vice versa. The neutral condition is defined as the state in which the maxima of the perturbation kinetic energy curve no longer change in time. A neutral-stability curve is obtained using the experimentally observed critical wavelengths. It is in general agreement with the experimental data, and it confirms the experimental result that stable density stratification enhances stability.

The linear stability of non-planar shear flow of a stably stratified fluid is investigated. Howard's (1961) semicircle theorem, which places bounds on the range of the complex phase speed c, is derived, although sufficient conditions for stability of the (x-directed) basic flow $\overline{u}(y, z)$ have not been established. The stability properties of some particular shear-layer and jet flows for long-wave disturbances are examined. Much of the effort is directed to delineation of unstable properties of the flow $\overline{u}(y, z) = \tan h\,y \tan h\,z$ in terms of c, the wavenumber α and a local form J0, of the Richardson number. Limiting cases are inflexion-point instability (J0 = ∞) and two-dimensional instability of a vertically stratified shear flow ($J_0 < \frac{1}{4}$). The present numerical computations reveal that at least two modes of instability are present for each pair of values of α and J0 for α [les ] 0·2 and $J_0 < \frac{1}{4}$. The source of instability for each mode is examined by means of computed energy transformations. However, numerical difficulties prevent a detailed examination of these unstable modes for α > 0·2.

The method of energy is used to study the stability of uniformly accelerated flows, i.e. those flows characterized by an impulsive change in boundary temperature or velocity. Two stability criteria are considered: strong stability, in which there is exponential decay of the disturbance energy, and marginal stability, in which the disturbance energy is less than or equal to its initial value. For the important case in which the critical stability parameter (measured by the Marangoni, Rayleigh or Reynolds number) decreases with time, it is proved that an onset time exists. Furthermore, it is shown that the experimental onset time is bounded below by the marginal stability limit, which in turn is bounded below by the strong stability limit.

The method is then applied to the problem of an impulsively cooled liquid layer susceptible to instabilities driven by interfacial-tension gradients. The strong stability and marginal stability boundaries are calculated and bounds on the onset time are given. These results represent the first rigorous bounds for convective instability problems of this class. Comparison with the limited available experimental data shows the calculated results to be lower bounds on the experimental onset times, and hence the theory is in agreement with available experimental results.