This paper deals with the study of the response of a cold wire used as a thermal sensor in a turbulent flow for different types of probes and for several gases (air, argon and helium). It is now well known that in the case of air flows the transfer function of the probe shows a typical step at low frequencies, as pointed out by Perry, Smits & Chong (1979).

In this plateau region the wire temperature may be influenced by the prong temperature through two different paths. The first is conduction between prong and wire, as already discussed by Maye (1970) using the ‘cold length’ lc, introduced by Betchov (1948). As suggested by Hojstrup, Rasmussen & Larsen (1975) the second is the result of the thermal boundary layer on the prong being very large at low velocities in gases of large thermal diffusivity; this region of influence (by the prong) extends over a length of the wire characterized by the thickness lb, of the thermal boundary layer on the prong.

In this paper a simple analysis of the behaviour of the transfer function of cold wires taking these two effects into account is presented by introducing the parameter η = lb/lc. An experimental investigation of these phenomena has been undertaken using a procedure which allows temperature fluctuations to be produced over a larger range of frequencies than has been usually made up to now.

Good agreement is obtained between experimental results and predictions using this analysis for several types of prong in different gaseous flows (air, argon and helium). An important step in the frequency response is found in the latter case because of the large thermal diffusivity of helium. Furthermore an example of the thermal prong–wire interaction is presented in the ease of intermittent temperature measurements.

The stability characteristics of some fluid flows at high Taylor or Gortler numbers are determined using perturbation methods. In particular, the stability characteristics of some fully developed flows between concentric cylinders driven either by a pressure gradient or the motion of the inner cylinder are investigated. The asymptotic structure of short-wavelength disturbances to these flows is obtained and used as a basis for a formal perturbation solution to the corresponding stability problem appropriate to a developing boundary layer. The non-parallel effect of the basic flow on the condition for neutral stability is discussed. The results obtained suggest that the disturbances are concentrated in internal viscous or critical layers well away from the wall and the free stream. The stability of a boundary layer on a concave wall to Görtler vortices that propagate downstream is also considered. These modes are found to be more stable than the usual time-independent modes and they propagate downstream with the speed of the basic flow in the critical layer. Some comparison with previous experimental and theoretical work is given.

Analytical formulae or the effect of interaction between pairs of rigid spherical particles on the mean velocity of each species in a statistically homogeneous dilute polydisperse system were given in Part 1 (Batchelor 1982), and are here evaluated numerically. We have calculated the pair-distribution function and the associated value of the sedimentation coefficient for a wide variety of conditions of the two interacting species, including different values of the ratio of the radii of the spheres (λ), different values of the ratio of their (reduced) densities (γ), small and large values of the Péclet number of the interaction, and different forms of the potential of the mutual force exerted directly between the two spheres. Values of λ and γ such that some of the trajectories of one sphere centre moving under gravity alone relative to another are of finite length lie outside the scope of the calculations at large Péclet number, and the change of behaviour across the boundary of this excluded set of values leads to a complicated dependence of the sedimentation coefficient on λ and γ. At small Péclet number the behaviour is simpler, and a formula which represents the calculated values of the sedimentation coefficient over the whole range of values of λ and γ (on which the dependence is known to be linear) with fair accuracy in the absence of interparticle forces is devised. Our calculations of the effect of an interparticle force were based on the assumption of a high Coulomb barrier at a certain sphere separation which could be varied, and a van der Waals attractive force at larger separations. It appears that the direct contribution to the sedimentation coefficient made by gravity is always appreciably larger than that made either by relative Brownian diffusion of the two interacting spheres or by the interparticle force. However, all three of these (effective) forces normally have a significant influence on the pair-distribution function and thereby also affect the sedimentation coefficient indirectly. Some published observations of the mean particle velocity in monodisperse systems are interpreted in the light of the present calculations of the effect of interparticle forces.