The measurement of the turbulent shear stresses and normal and bi-normal intensities with a hot-wire anemometer requires that the directional sensitivity of the hot-wire be known. Normal component or cosine law cooling is generally assumed, although for finite wire lengths the non-uniform wire temperature must cause a deviation from the cosine law.

Careful heat transfer measurements from wires inclined and normal to the flow were taken for several values of the Reynolds number, the length-to-diameter ratio of the wire, the overheat ratio and for several support configurations. All experiments were performed in air at low subsonic velocities, i.e. M < 0·1. The measurements indicate that the heat loss from an inclined wire is larger than that from a wire normal to the flow with the same normal component of velocity. The data were correlated by \[ U^2_E(\alpha) = U^2(0)(\cos^2\alpha + k^2\sin^2\alpha), \] where UE(α) is the effective cooling velocity at the angle α between the normal to the wire and the mean flow direction and U(0) is the velocity at α = 0. The value of k was found to depend primarily upon the length-to-diameter ratio ([lscr ]/d) of the wire. For platinum wires k is approximately 0·20 for [lscr ]/d = 200, decreases with increasing [lscr ]/d, and becomes effectively zero at [lscr ]/d = 600.

To aid in interpreting the heat transfer data, measurements of the temperature distribution along inclined and normal wires were made with a high sensitivity infra-red detector coupled to a high resolution microscrope with reflective optics. The measurements indicate that inclined wires and normal wires have nearly identical end conduction losses, although the temperature distribution on an inclined wire is slightly asymmetrical. Therefore, the deviation from the cosine law is caused by an increase in the convection heat loss, and this increase is attributed to the tangential component of velocity.

Laboratory measurements were made of the instabilities of the Ekman layer using hot wire anemometers. The apparatus consisted of two parallel circular rotating plates forming a spool; the air was admitted through screens at the outer edge and removed through a screen cage at the hub. In the Ekman layers formed on the inner surfaces of the plates, measurements were made of the mean velocities as functions of r and a; the velocity fluctuations were also measured.

It appears that the instability labelled type II by Faller always occurs first, and at zero Rossby number the critical Reynolds number is 56 ± 2. This instability originates in the boundary layer, but at slightly higher Reynolds number the fluctuations persist far into the geostrophic region, probably as inertial waves excited by the boundary-layer fluctuations.

At higher Reynolds number another instability appears of shorter wavelength and slower speed. This instability is confined to the boundary layer and is apparently the type I reported by Faller.

The phase speeds, frequencies, and wave-front orientations of both type instabilities have been measured.

A model of airflow over a mountain is treated mathematically in this paper. The fluid is inviscid, incompressible and of variable density. The flow is in a long channel, bounded above by a rigid horizontal lid and below by an obstacle. The variation with height of the horizontal velocity and of the density is specified far upstream. The details of flow are examined for particular conditions upstream which lead to a linear vorticity equation, although the non-linear inertial terms in the Euler equations of motion are exactly represented. In this case the flow is described by the superposition of solutions of some diffraction problems. Classical techniques of diffraction theory are then used to demonstrate the existence and some general properties of solutions for steady flow. Thus a steady solution is always possible if no restriction is placed on the amount of energy available to drive the flow, that is to say there is no critical internal Froude number (measuring the dynamical effect of buoyancy) for the existence of a steady flow. Finally the flows past a dipole and a vertical wall are computed.

Hot-wire response equations to include the effects of the tangential velocity component as well as the non-linearities caused by high intensity turbulence are derived for linearized constant temperature operation. For low intensity turbulence similar equations are derived for constant current operation. The equations are applied to an X-wire array to determine the errors in selected turbulence quantities which arise from the assumption of cosine law cooling. The error depends upon the quantity measured, the method of operation, and [lscr ]/d. For [lscr ]/d = 200 the error ranges from 0 to 17%.

A rigid cylinder is initially at relative rest in a uniformly rotating, inviscid, incompressible fluid, with its generators perpendicular to the axis of rotation. The fluid is accelerated suddenly to a small constant velocity parallel to the axis of rotation, which is maintained thereafter. The growth of the subsequent disturbance due to the cylinder is interpreted in terms of plane inertial waves, the disturbance energy propagating with the local group velocity, which is in the plane of the wave front and proportional to the wavelength. Taylor columns, in which the fluid moves with the cylinder rather than round it, grow indefinitely in both directions parallel to the rotation axis, the head of the column moving with finite speed.

In a slightly viscous fluid, an ultimate steady state is reached, in which the columns are of finite length.

If a cylinder is moved horizontally in a non-rotating uniformly stratified Boussinesq liquid, an identical analysis may be applied with a similar interpretation in terms of internal gravity waves rather than inertial waves.

Flow at high Hartmann number along the annular channel between two nonconducting cylinders of circular cross-section is examined. The core is divided and wakes appear at the boundaries of the various regions. In §§ 1-4 the case in which the cylinders are concentric is studied. In §5 the cylinders are eccentric, and it is shown that in this case there is a net flow of current around the annulus.

An analysis has been made of a two-dimensional turbulent wake which was subjected to a homogeneous strain. This was applied in such a way that the rate of growth of the wake tended to be accelerated but the main stream convective velocity remained constant. An attempt to describe the flow by classical self-preservation techniques was made. However, the results suggested that a detrainment of wake fluid would result. In lieu of this a more realistic approach was sought and it was found that in certain situations where the flow has had an opportunity to develop before the strain is applied, the growth of the wake in the strain field can be described successfully by a simple geometric distortion. It appears likely that in these cases the interaction between the external strain and the turbulent structure within the wake is negligible, the wake remaining essentially passive. Suggestions as to the mechanism of the turbulent mixing and transport under these conditions are made.

It is shown that a deformable body can move persistently from rest through a perfect fluid without having to produce vorticity in the fluid.

The suppression of initially isotropic turbulence by the sudden application of a uniform magnetic field is considered. The problem is characterized by three dimensionless numbers, a Reynolds number R, a magnetic Reynolds number Rm and a magnetic interaction parameter N (for definitions, see equations (1.2) and (1.4)). It is supposed that R [Gt ] 1, Rm [Lt ] 1 and N [Gt ] 1. There are two important time scales, ta a time characteristic of magnetic suppression, and t0 = Ntd, the ‘turn-over’ time of the turbulent energy-containing eddies. For 0 < t [Lt ] t0 the response of the energy-containing components of the turbulence to the applied field is linear and the time dependence of the kinetic energy density K(t) and magnetic energy density M(t) are analysed. There are essentially two distinct contributions to each from two domains of wave-number space D1 and D2 (defined in figure 2). In D1 the response is severely anisotropic, while in D2 it is nearly isotropic. The relative importance of the contributions K1(t) (from D1) and K2(t) (from D2) to K(t) depends on the value of the Lundquist number S = (NRm)½. If S [Lt ] 1, then K1(t) dominates for all t [lsim ] t0 and K(t) ∝ t−½ for td [Lt ] t [Lt ] t0. If 1 [Lt ] S [Lt ] R−2m, then a changeover in the dominant contribution occurs when t = O(S½Rm) t0. Analogous results are obtained for the magnetic energy density.

The turbulent energy equation is converted into a differential equation for the turbulent shear stress by defining three empirical functions relating the turbulent intensity, diffusion and dissipation to the shear stress profile. This equation, the mean momentum equation and the mean continuity equation form a hyperbolic system. Numerical integrations by the method of characteristics with preliminary choices of the three empirical functions compare favourably with the results of conventional calculation methods over a wide range of pressure gradients. Nearly all the empirical information required has been derived solely from the boundary layer in zero pressure gradient.

Experiments are described in which the velocity profiles of axisymmetric jets are measured in water and in dilute solutions of water-soluble polymers. The ambient fluid and that entering through the nozzle were homogeneous. The similarity characteristics of velocity profiles including a linear variation of centre-line velocity with the inverse of the distance from the nozzle were unaltered by these substances. On adding large polyethylene oxide molecules to the system the jet spread at an increased angle, possibly due to the entrainment rate being enhanced by an increase in turbulent elasticity for polyethylene oxide solutions. It is also postulated that additives which had no effect on the velocity were not large enough to influence the small microscale eddies in which the energy to activate an entrainment cycle is stored.

A general theory is given for the effect of solid walls on a translating and rotating particle in the limiting case of zero Reynolds number. Both the force and couple on the body are found as an expansion in terms of a parameter k = a/d, assumed small, where a is a characteristic particle size and d a characteristic distance of the particle from walls. It is shown how such expansions may be used in specific examples. The theory is then extended to include the general motion of a small particle in an arbitrary Stokes flow field in which solid or other boundaries are present. Finally the motion of two small bodies of arbitrary shape in an arbitrary Stokes flow field is considered.