The utility of piston theory as a means of solving insentropic two-dimensional aerodynamic problems has been aptly demonstrated by many writers in recent years. The present treatment removes the restriction of isentropic flows, extending the applicability of piston theory to flows with strong shocks. Sample calculations for a thin biconvex airfoil are carried out in which the local flow is assumed to be isentropic and non-isentropic. Comparison of the result is made with that of the shock expansion theory of Cole, Gazley & Williams (1956).

Consider a wing-jet combination placed in a wind tunnel; the measured thrust on the wing due to a high speed jet emerging from it will require to be corrected to give the infinite stream value. This paper provides a theory of these wind tunnel corrections, and incidently establishes that the ideal thrust is almost independent of the jet exit angle.

A model equation is derived to study trapped nonlinear waves with a turning effect, occurring in disturbances induced on a two-dimensional steady flow. Only unimodal disturbances under the short wave assumption are considered, when the wave front of the induced disturbance is plane. In the neighbourhood of certain special points of sonic-type singularity, the disturbances are governed by a single first-order partial differential equation in two independent variables. The equation depends on the steady flow through three parameters, which are determined by the variations of velocity and depth, for example (in the case of long surface water waves), along and perpendicular to the wave front. These parameters help us to examine various relative effects. The presence of shocks in a continuously accelerating or decelerating flow has been studied in detail.

Supersonic boundary-layer flow on a flat plate near a point of injection cut-off is considered. The goal is to develop a non-singular solution in the limit of large Reynolds number in the vicinity of the boundary-condition change. An application of Goldstein-type singular solutions shows that an interaction-type theory is required even for transverse velocity jumps on the boundary O(R− ½). The interaction analysis is developed in terms of the linearized triple-deck theory described by Smith & Stewartson (1973a). The analytically derived solution provides a continuous pressure and wall-shear distribution.

The flow of a Boussinesq density-stratified fluid of large depth past the algebraic mountain (‘Witch of Agnesi’) is studied in the hydrostatic limit using the asymptotic theory of Kantzios & Akylas (1993). The upstream conditions are those of constant velocity and Brunt–Väisälä frequency. On the further assumptions that the flow is steady and there is no permanent alteration of the upstream flow conditions (no upstream influence), Long's model (Long 1953) predicts a critical amplitude of the mountain (ε = 0.85) above which local density inversions occur, leading to convective overturning. Linear stability analysis demonstrates that Long's steady flow is in fact unstable to infinitesimal modulations at topography amplitudes below this critical value, 0.65 [lsim ] ε < 0.85. This instability grows at the expense of the mean flow and may be attributed to a discrete spectrum of modes that become trapped over the mountain in the streamwise direction. The transient problem is also solved numerically, mimicking impulsive startup conditions. In the absence of instability, Long's steady flow is reached. For topography amplitudes in the unstable range 0.65 [lsim ] ε < 0.85, however, the flow fluctuates about Long's steady state over a long timescale; there is no significant upstream influence and no evidence of transient wave breaking is found for ε [les ] 0.75.

The effects of the surface density field on wind-driven subtropical gyre circulation are examined within the content of a continuously stratified, potential vorticity conserving model. It is found that the ventilated fluid downwelled from the mixed layer is confined to a relatively thin layer in subtropical regions; the maximum depths of the ventilated region occur in the eastern and southern regions of the gyre. As a consequence of the relative thinness of the ventilated region in the wind-driven gyre, the transport associated with the surface density field is a small part of the total transport in subtropical regions. Thus the surface density field and the potential vorticity associated with ventilated fluid play a minor role in subtropical gyre dynamics and the potential vorticity of unventilated recirculating fluid is found to play the major role in subtropical gyre dynamics. A method of calculating the flow in the relatively large recirculating region is developed and the results of a specific example are discussed.

The paper examines the influence of a piston motion on the gaseous motion set up by an explosion. This is a problem of relevance not only to explosions in which the remnants of the original explosive are present, but also by the application of the hypersonic similarity law, to the steady flow at high Mach number past a blunt-nosed object with increasing thickness. In the vicinity of the piston perturbation theory breaks down and matching techniques have to be employed. A solution is given in terms of a small parameter which essentially depends on the ratio of the speed of the piston to that of the shock. Some particular cases are discussed in which the piston motion plays a similar role to the counter pressure of the undisturbed gas.

Rotational flow through narrow axial channels is considered in connection with a proposed technique to sort and separate particles according to sedimentation velocities. Nonlinear and linear axisymmetric flow through two channels connected by a slot in the vertical wall is studied numerically. A linearized formulation for the three-dimensional flow through a circumferentially blocked channel, with arbitrary positioning of the inlets and outlets, is examined analytically. Both approaches indicate that to have a sharp criteria for fractionation, the vertical shear layers on the channel walls must overlap. Otherwise, Coriolis effects, accompanying a strong azimuthal motion, make the sorting less precise. Results of an exploratory experiment with a simple two-stage machine demonstrate the feasibility of the basic process for simultaneous and continuous separation and fractionation.

Instead of considering just the vertically averaged current and the vertically averaged concentration, a multi-mode model is derived in which more of the vertical structure can be computed directly rather than being lumped into a dispersion coefficient. Test cases, of laminar flows, are used to quantify the accuracy of the lowest non-trivial truncation (two modes) in replicating both the flow and the dispersion process.

A general one-dimensional model for the steady adiabatic motion of gas-particle mixtures in arbitrarily oriented ducts with gradually varying cross-section and wall friction is presented. The particles are assumed to be incompressible and in thermomechanical equilibrium with a perfect gas phase, and the effects of their finite volume and of gravity are also taken into account.

The equations of motion are written in a form that allows a theoretical analysis of the behaviour of the solutions to be carried out. In particular, the results of the application to the model of a procedure that permits the identification and the topological classification of the singular points of the trajectories representing, in a suitable phase space, the solutions of the set of equations defining the problem are described. This characterization of the singular points is useful in order to overcome difficulties in the numerical integration of the equations.

Subsequently, a geometrical analysis is carried out which allows a study of the signs of the local variations of the flow quantities, and shows that some unusual behaviour may occur if certain geometrical and fluid dynamic conditions are fulfilled. For instance, in an upward motion it is possible to have a simultaneous decrease of velocity, pressure and temperature, while in a downward flow an increase of all these quantities may be found. It is also shown that conditions exist in which expansion and heating of the mixture may take place simultaneously, both in accelerating and decelerating flows.

The model is applied to the study of upward motion in particular ducts, having converging-diverging and constant-diverging cross-sections; to this end the equations are integrated numerically by using the Mach number as the independent variable. The results show that even limited variations of the duct diameter may give rise to significant qualitative and quantitative variations in the flow conditions inside the duct and in the mass flow rate. Finally, an example is given of a subsonic downward flow in which a simultaneous increase of pressure, temperature and velocity occurs even in the case of a pure perfect gas.

We extend the results of a previous paper to fluids of finite depth. We consider the Hamiltonian theory of waves on the free surface of an incompressible fluid, and derive the canonical transformation that eliminates the leading order of nonlinearity for finite depth. As in the previous paper we propose using the Lie transformation method since it seems to include a nearly correct implementation of short waves interacting with long waves. We show how to use the Eikonal method for slowly varying currents and/or depths in combination with the nonlinear transformation. We note that nonlinear effects are more important in water of finite depth. We note that a nonlinear action conservation law can be derived.