An investigation of the structure of jets in rotating systems is presented. The fluid is assumed to be homogeneous and the flow laminar and quasi-geostrophic. When the rate of rotation is small, the dynamics is shown to be identical to that of jets in non-rotating systems, being a balance between inertial terms and lateral dissipation. As the rate of rotation increases the Ekman layers become important and in the strongly rotating case the friction in the Ekman layers dominates lateral dissipation. The jet in a non-rotating system entrains fluid at its edges and the downstream momentum flux is independent of the distance downstream. In the strongly rotating case, however, the jet ejects fluid at its edges and the downstream momentum flux decreases with downstream distance due to dissipation in the Ekman layers. A similarity solution for the general case with both types of friction is obtained and the transition from a jet in which lateral dissipation dominates to one in which Ekman friction is more important is discussed. General features of jets in strongly rotating systems are studied and implications for the Gulf Stream are mentioned.

Robins showed in 1742 that a transverse aerodynamic force on a rotating sphere could be detected by suspending it as a pendulum. Differences of periodic time in conical pendulum motion with spin and orbit parallel and opposed have been found to give a reasonably accurate measure of the lift coefficient, and the results shown extend knowledge of the effect down to a Reynolds number of 2 × 103 and up to a ratio of 12 between the peripheral and translational velocities.

The response characteristics of a hot wire operated at constant temperature and exposed to a mean-velocity gradient along its length are examined both analytically and experimentally. The shear sensitivity of local wire temperature distributions, as measured with an infrared microscope, are compared with predicted temperature distributions in order to select a convective heat transfer correlation which can be applied locally along a wire in shear flow. On the basis of this correlation, the steady-state and dynamic response behaviour of platinum and tungsten wires in shear flow are examined by means of computer-generated data. Response curves of general applicability are presented which can be used to correct local mean-velocity and turbulence intensity measurements whenever a mean-velocity gradient exists along a wire.

Forced axial flow in an annular gap of a cylindrical rotor is investigated analytically and experimentally. At small rotation rates and narrow gap widths, the axial flow is a simple Poiseuille flow over most of the rotor. The distance required for this Poiseuille flow to get established is estimated. An instability is observed at large rotation rates with certain input geometries.

A primarily experimental investigation was undertaken to determine the internal structure of steady, quasi-uniform, non-separated, axisymmetric flows in circular pipes with sinusoidal wall profiles. The quantities measured include radial and longitudinal distributions of mean velocity, pressure, and total head; the Reynolds shear stress and all three components of turbulence velocity; and boundary shear stress and pressure. Two different wall-wave steepnesses were investigated, and a constant Reynolds number of 1·13 × 105 (based on the average pipe diameter) was maintained in most experiments. The boundary shear stress was found to be shifted upstream relative to the boundary wave, whereas the wall pressure is shifted slightly downstream. The turbulence measurements revealed that there is a central core extending over some 60% of the pipe radius in which the turbulence quantities are constant along the pipe. Near the boundary, however, the turbulence velocities and stress vary periodically along the boundary waves. The longitudinal component of mean velocity was found to be distributed radially according to the power law, but with an exponent that varies along each wave; a simple analytical model is constructed to predict the variation of the exponent. It was not found possible to relate the local boundary shear stress to just the local flow characteristics, since the convective or ‘history’ effects play a significant role in its determination. An empirical formula is derived relating the local boundary shear stress to the local velocity distribution and the first two derivatives of the boundary profile.

Experiments were conducted in an ascending laminar flow through a vertical pipe under combined free and forced convection at constant heat flux through the wall.

Mean velocity and temperature profiles were measured with a hot-wire probe. This velocity profile which is deformed by the buoyancy forces, enabled us to compute the reduced acceleration parameter. The profiles obtained showed that the value of the parameter at which reverse transition takes place is approximately the same as that found in isothermal boundary-layer flow. By measuring the autocorrelation function of the velocity after the reverse transition it was shown that the flow in the boundary layer becomes laminar as well as fluctuating and that it oscillates with a predominating period.

A model equation of Langevin type for the turbulent velocity field is constructed, in which the non-linear terms of the Navier–Stokes equation are replaced by a dynamical damping term and a random forcing term, with strength parameters determined by the past history of the energy spectrum. The model leads to a closed set of first-order differential equations in time for the evolution of two functions: the energy spectrum and the effective memory times for the interaction of mode triads. Invariance of the energy transfer to random Galilean transformation is achieved by using the interaction between solenoidal and compressive parts of a convected test field to determine the memory–time functions. The model equation is developed from the direct-interaction approximation as starting-point. At an intermediate stage, before the Galilean invariance is introduced, a model representation of Edwards's (1964) theory is obtained which extends the latter to statistically non-stationary states.

A simple dynamical argument suggests that the k−3 enstrophy-transfer range in two-dimensional turbulence should be corrected to the form \[ E(k) = C^{\prime} \beta^{\frac{21}{3}}k^{-3}[\ln (k/k_1)]^{-\frac{1}{3}}\quad (k \gg k_1), \] where E(k) is the usual energy-spectrum function, β is the rate of enstrophy transfer per unit mass, C′ is a dimensionless constant, and k1 marks the bottom of the range, where enstrophy is pumped in. Transfer in the energy and enstrophy inertial ranges is computed according to an almost-Markovian Galilean-in variant turbulence model. Transfer in the two-dimensional energy inertial range, \[ E(k) = C\epsilon^{\frac{2}{3}}k^{-\frac{5}{3}}, \] is found to be much less local than in three dimensions, with 60 % of the transfer coming from wave-number triads where the smallest wave-number is less than one-fifth the middle wave-number. The turbulence model yields the estimates C′ = 2·626, C = 6·69 (two dimensions), C = 1·40 (three dimensions).

The time-mean heat transfer of the incompressible laminar boundary layer on a flat plate under the influence of oscillation is studied analytically. Flow oscillation amplitude outside the boundary layer is assumed constant along the surface and the viscous dissipation effect is considered. First, the small velocity–amplitude case is treated and the approximate formulae are obtained in the extreme cases when the frequency is low and high. Next, the finite velocity–amplitude case is treated under the condition of high frequency and it is found that the formulae obtained for the small amplitude and high frequency case are also valid. These results show that, when the oscillation is of high frequency, the time-mean heat flux to the wall can be several times as large as that without oscillation. This is due wholly to the viscous dissipation effect combined with oscillation.

The effect of sloping boundaries on thermal convection is studied theoretically and in the laboratory in the context of a model in which fluid is contained in a differentially heated rectangular box of small aspect ratio (depth/length), inclined at an angle δ to the vertical. Like its two limiting cases, Bénard convection and convection in the vertical slot, a basic state which exists for low Rayleigh numbers becomes unstable as this parameter is increased. The types of instability and indeed the manner in which the motions become turbulent depend crucially on δ. In our work with water the following general picture of the primary instabilities applies:

1. For 90° > δ > 10° with the bottom plate hotter, the instabilities are stationary longitudinal convectively driven rolls with axes oriented up the slope. Near δ = 10° there is an upper and lower Rayleigh number cut off. If the Rayleigh number is too small diffusion damps the instabilities, but if it is too large they are damped by the development of a stable upslope temperature gradient in the mean flow.

2. For 10° > δ > −10° (negative angles imply a hotter upper plate), transverse travelling waves oriented across the slope are the first instabilities of the mean flow. They obtain their kinetic energy via the working of the upslope buoyancy force.

3. For - 10° > δ > −85° longitudinal modes are again observed. These are rather curious in that they may exist when the stratification $-\hat{g}\cdot\nabla T $ is everywhere positive. The necessary energy for these modes comes out of the mean velocity field and out of the mean available potential energy.

Agreement between the stability theory and the experiments is generally quite good over the whole range of δ, considering the approximations involved in finding a suitable basic flow solution.

For Rayleigh numbers less than ∼ 106 turbulence is only possible for positive angles. For 85° > δ > 20° the development of unsteadiness involves the occurrence and the breaking of wavy longitudinal vortices in a manner reminiscent of the development of turbulence in cylindrical Couette flow.

The conventional ‘bridge-feedback amplifier’ constant-temperature hot-wire anemometer is analysed to determine its static and dynamic response. The effects of moderate feedback amplifier gain, bridge imbalance, stray bridge reactance, amplifier offset voltage, lack of common mode rejection, amplifier frequency response and departure from constant transconducture are included. The root loci of the system are mapped out and the consequences of the analysis are discussed from the viewpoint of both the operator and the designer.

Repeated observations of dye plumes on Lake Huron are interpreted according to the theoretical proposals of Richardson (1926) and Batchelor (1952) about the characteristics of a dispersing cloud of marked fluid within a field of homogeneous turbulence. The results show the average of several instantaneous concentration distributions about their centre of gravity to be approximately Gaussian and the distance-neighbour function to be of approximately Gaussian form. The data are consistent with the theoretical description given by Batchelor, namely, \[ q(y,t) = (2\pi\overline{y^2})^{-\frac{1}{2}}\exp (-y^2/2\overline{y^2}),\quad (\overline{y^2} = (\frac{2}{3}\alpha t)^3), \] where q(y, t) is the distance-neighbour function and α is the constant of the ‘4/3-power law’. The average value of α is estimated to be 0·12 cm2/3 sec−1. The rate of turbulent energy dissipation in the near-surface currents of Lake Huron is estimated as ε ∼ 2·1 × 10−3 cm2sec−3.

A theoretical and experimental study is made of the failure of electrical insulation in a layer of dielectric fluid filling a circular hole in a horizontal solid dielectric sheet. A potential difference is applied between conducting fluids which bound the fluid and solid dielectric layer above and below. It is observed that a critical potential difference is reached at which the fluid dielectric becomes statically unstable under the action of surface tension and normal electrical stresses at its interfaces. When this potential is reached the dielectric fluid insulation fails.

The critical potential difference is calculated by both an approximate and an exact theory. The approximate theory ignores the changes in the electrostatic field within the solid dielectric by allowing a charge distribution at the curved surface of the hole. Comparison with the results of an exact theory shows that such an approximation introduces only small errors in the calculated points of transition to instability.

It is shown that failure may take the form of a symmetric (sausage) mode of displacement, or an antisymmetric (kink) mode, depending on whether the radius of the hole is greater or less than approximately the depth of the layer respectively. The two forms of failure were indicated in the experiments, and the observed critical voltages are in good agreement with those predicted by the theory.