This paper is primarily concerned with the turbulence generated by the interaction of random entropy fluctuations with non-uniform mean flows. The results are obtained by using rapid distortion theory in conjunction with a high frequency solution of a previously developed wave equation that governs the small amplitude unsteady vortical and entropic motion on steady potential flows (Goldstein 1978). The analysis is applied to symmetric contractions or expansions (or combinations of the two) and comparisons are made with a corresponding theory of Batchelor & Proudman (1954) for the rapid distortion of upstream turbulence by a contraction of this type. It is shown that the energy of the entropy-generated turbulence increases much more rapidly with contraction ratio than that of the imposed upstream turbulence. Turbulence of the former type can therefore dominate the latter even when the upstream entropy fluctuations are weak relative to the imposed turbulent intensities. Moreover the structure of the entropy-generated turbulence is found to be quite different from that of the contracted upstream turbulence.

A secondary purpose of the paper is to discuss some effects of compressibility on rapid distortion theory.

By establishing that the length scale governing the detachment of a shock wave from a wedge is the distance from the leading edge to the sonic line, and by considering the view of observers with different length scales, it is predicted that the detachment distance increases gradually with wedge angle for relaxing flow and more rapidly in a perfect gas. Both of these features are confirmed by experiments in the free-piston shock tunnel. The influence of other length scales is discussed. The phenomenon is related to a relaxation effect in which a subsonic layer grows from the translational-rotational shock as the wedge inclination is increased beyond the frozen sonic point.

A time similarity formulation of the flow equations for unsteady plumes is shown to exist only when the buoyancy flux at the source varies as a power function of time. The time similarity equations for unsteady plumes are solved numerically. It is shown that the velocity of the leading edge of the plume is less (at most the 0·42 fraction) than the velocity inside the plume behind its leading edge; this observation is consistent with Turner's (1962) results on the behaviour of a starting plume with constant buoyancy flux at the source. Finally, experimental results of axial temperature histories in the buoyant plume generated by a fast-growing fire are compared with the theoretical predictions.

This paper investigates a class of bead–rod and bead–spring models which have been proposed to describe the dynamics of an isolated macromolecule in a flowing solution. Hassager (1974a) has pointed out a surprising result in regard to these models: the statistical conformation of a molecule (and hence its influence on the flow) apparently depends upon whether a very stiff-springed model structure or a rigid one is used. This paradox is examined and resolved. It is shown that a unique answer is obtained by regarding the system as the classical limit of a quantum-mechanical one. The extent of the quantum influence can be characterized by a dimensionless group Q. For a ‘hot’ or ‘large’ system (for which Q → 0) the classical (stiff spring) results are recovered. The effects of the parameter Q on the size of the molecules and the rheology of the solution are calculated in detail for a simple model, and the gross features are identified for a more realistic Rouse chain model, each in both weak and strong flows.

A final section considers weak, rapidly varying flows. It is shown that, within the context of classical (non-quantum) physics, for sufficiently rapid changes any model structure will tend to move with the applied flow, and therefore exert no stresses on the fluid. This explains the theoretical observation of Fixman & Evans (1976) that, in regard to the particle stress, the limits of rigidity and infinitely high frequency do not commute.

The initial development of turbulence in the shear layer of a circular jet is observed to show disturbances of increasing scale at discrete frequencies in an approximate 4:2:1 sequence. These are completely confined within the laminar shear layer and convect at 0·59 of the jet velocity. Such relatively regular behaviour was not observed once the disturbances became larger in transverse dimension than the laminar shear layer.

In the development of the subsequent turbulent shear layer it was found that the fluctuating turbulent shear did not scale with local mean shear, but rather scaled more closely with the minus half power of distance from the apparent origin of the laminar shear layer emanating from the nozzle. The scale of the shear fluctuations departed from growth in proportion to shear layer thickness, remaining almost constant. In these aspects it appears that the turbulent shear layer is not well described by a similar growth with axial distance.

The shear fluctuations convected at a speed closer to the local mean velocity than do velocity fluctuations and showed a relatively more patchy distribution with a distinct rotational sense and no reversal of skewness across the layer. Velocity fluctuations showed phase lags approaching $\frac{1}{3}\pi$ relative to shear fluctuations suggesting that dominant velocity disturbances are those associated with entrainment behind concentrations of rotation.

The effect of viscosity on the inner free surface of a rotating imploding cylindrical liquid shell compressing an ideal gas or magnetic flux load is analysed in the limit of high Reynolds number Re. The condition of vanishing tangential stress on the free surface leads to the formation of a boundary layer of thickness ∼ Re−½. Within this layer the zonal velocity v is reduced by an amount Δv such that Δ v/vRe−½. This results in a requirement of slightly increased rotation in order to satisfy the criterion for suppression of the Rayleigh-Taylor instability on the free surface. Calculations are presented for a model implosion trajectory.

For steady laminar flow with closed streamlines Batchelor (1956) has shown how an integral condition arising from the effect of viscosity can be used with the inviscid flow equations to determine the vorticity distribution when the Reynolds number is large. Here a condition analogous to that used by Batchelor is derived for a class of flows with helical streamlines. An exact integral condition relating the constant axial pressure gradient and the viscous terms is obtained, which when combined with the inviscid flow equations leads to the result that the axial velocity is proportional to the stream function for the motion in the plane normal to the axial velocity.

Strong external disturbances were introduced into a mixing layer in order to test the formation of the quasi two-dimensional coherent eddies and their survival under less than ideal conditions. Velocity and temperature correlation measurements, flow visualization, and the simultaneous use of a large number of sensors suggest that these eddies are very stable in the range of Reynolds numbers considered and they persevere in spite of the external buffeting imposed. Some measurements were carried out in a mixing layer between two parallel streams and some in a mixing layer entraining quiescent surrounding fluid. In both cases the large eddies could be described. as vortex rolls spanning the test section; these rolls may be contorted and sometimes skewed, but they are basically two-dimensional.

The asymptotic properties of Burgers turbulence at extremely large Reynolds numbers and times are investigated by analysing the exact solution of the Burgers equation, which takes the form of a series of triangular shocks in this situation. The initial probability distribution for the velocity u is assumed to decrease exponentially as u → ∞. The probability distribution functions for the strength and the advance velocity of shocks and the distance between two shocks are obtained and the velocity correlation and the energy spectrum function are derived from these distribution functions. It is proved that the asymptotic properties of turbulence change qualitatively according as the value of the integral scale of the velocity correlation function J, which is invariant in time, is zero, finite or infinite. The turbulent energy per unit length is shown to decay in time t as t−1 (with possible logarithmic corrections) or $t^{-\frac{2}{3}}$ according as J = 0 or J ≠ 0.

The evolution of an eddy in a two-layer shear flow and the radiation field generated by the eddy are investigated by solving the initial value problem. The solution indicates that two wave regimes with different characteristics exist in the x/t plane, where t is the time and x is the distance from the initial disturbance. The near-field (small x/t) behaviour depends critically on the stability of the shear. In a baroclinically stable shear flow, the radiation field of the baroclinic waves is confined to a region the boundary of which expands linearly with time. If the shear flow is baroclinically unstable, the eddy gradually evolves from an isotropic structure into a wave packet that grows exponentially and expands as the square root of time. The far field (large x/t) consists mainly of long barotropic Rossby waves. As x/t increases, the effect of the mean currents becomes weaker and the motion becomes increasingly barotropic in character. If we consider the strong boundary current as a source of baroclinic energy in the ocean, the far-field results show that the mid-ocean eddies can reach large amplitudes independent of the mean currents. The transient motion (small x and t) of the eddy is examined by numerically computing the stream function from the solution. The results show that the combined actions of baroclinic instability and wave dispersion cause an initially isotropic eddy to remain roughly isotropic for a relatively long period of time. This suggests that the initial development of unstable eddies cannot be neglected in studying the meridional scale of the eddy field in the atmosphere. Application of the model to study the dispersion of wind-generated Rossby waves is discussed.