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.

The motion induced in a layer of Boussinesq fluid by a moving thermal wave is studied in the case where the mean velocity could exceed the wave speed. A nonlinear boundary-layer theory shows that strong streaming is possible for small viscosity. Velocity fluctuations are limited in magnitude by their short time scale, while viscosity alone, assumed to be relatively weak, limits the mean flow.

We consider the propagation of sound in a two-dimensional shear layer in a duct. Initially plane sound waves propagate in a subsonic flow whose steady velocity U(y) is in the axial direction and is a function of the normal co-ordinate alone. The initial-value problem in time and space is solved within the framework of a perturbation scheme. Far from the wave front and for large time the refractive effects are considerable. However, the present results indicate that standing wave type patterns lead to a strong dependence on axial location in the duct. The paper also points out the Weakness inherent in theories which attempt to treat the refraction problem without considering the source conditions.

The flow in a two-dimensional laminar separation bubble is analyzed by means of finite-difference solutions to the Navier-Stokes equations for incompressible flow. The study was motivated by the need to analyze high-Reynolds-number flow fields having viscous regions in which the boundary-layer assumptions are questionable. The approach adopted in the present study is to analyze the flow in the immediate vicinity of the separation bubble using the Navier-Stokes equations. It is assumed that the resulting solutions can then be patched to the remainder of the flow field, which is analyzed using boundary-layer theory and inviscid-flow analysis. Some of the difficulties associated with patching the numerical solutions to the remainder of the flow field are discussed, and a suggestion for treating boundary conditions is made which would permit a separation bubble to be computed from the Navier-Stokes equations using boundary conditions from inviscid and boundary-layer solutions without accounting for interaction between individual flow regions. Numerical solutions are presented for separation bubbles having Reynolds numbers (based on momentum thickness) of the order of 50. In these numerical solutions, separation was found to occur without any evidence of the singular behaviour at separation found in solutions to the boundary-layer equations. The numerical solutions indicate that predictions of separation by boundary-layer theory are not reliable for this range of Reynolds number. The accuracy and validity of the numerical solutions are briefly examined. Included in this examination are comparisons between the Howarth solution of the boundary-layer equations for a linearly retarded freestream velocity and the corresponding numerical solutions of the Navier-Stokes equations for various Reynolds numbers.

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.

Various theoretical aspects of peristaltic motion have attracted considerable attention in the recent literature. There also exists a difference of opinion concerning the definition of peristaltic reflux. Thus far, there has been no completely satisfactory experimental verification of any of the theoretical analyses. The present article describes some details of an experimental work which was carried out to verify the theoretical analysis of peristaltic transport in a two-dimensional channel with one fixed wall and one flexible wall on which a travelling sine wave is imposed. An approximate correction for finite width was introduced. Comparison of the theoretical and experimental results shows a good agreement and gives verification to the theoretical analysis. In the light of the experimental results, a discussion of the different definitions of peristaltic reflux is presented.

An experimental investigation was conducted in a circular pipe to examine the influence of a transverse magnetic field on the structure of turbulent shear flow of a conducting fluid (mercury). In the present paper, part 1, mean velocity profiles, turbulence intensity profiles, velocity fluctuation spectra, axial pressure drop profiles, and skin friction data are presented which quantitatively exhibit the Hartmann effect and damping of the velocity fluctuations over a broad range of Reynolds numbers and magnetic fields. The results of heat transfer experiments will be reported by the authors in the following paper, part 2.

An experiment on the stability of convection rolls with varying wave-number is described in extension of the earlier work by Chen & Whitehead (1968). The results agree with the theoretical predictions by Busse (1967a) and show two distinct types of instability in the form of non-oscillatory disturbances. The ‘zigzag instability’ corresponds to a bending of the original rolls; in the ‘cross-roll instability’ rolls emerge at right angles to the original rolls. At Rayleigh numbers above 23,000 rolls are unstable for all wave-numbers and are replaced by a three-dimensional form of stationary convection for which the name ‘bimodal convection’ is proposed.

The truncated Burgers models have a unique equilibrium state which is defined continuously for all the Reynolds numbers and attainable from a realizable class of initial disturbances. Hence, they represent a sequence of convergent approximations to the original (untruncated) Burgers problem. We have pointed out that consideration of certain degenerate equilibrium states can lead to the successive turbulence-turbulence transitions and finite-jump transitions that were suggested by Case & Chiu. As a prototype of the Navier–Stokes equations, Burgers model can simulate the initial-value type of numerical integration of the Fourier amplitude equations for a turbulent channel flow. Thus, the Burgers model dynamics display certain idiosyncrasies of the actual channel flow problem described by a truncated set of Fourier amplitude equations, which includes only a modest number of modes due to the limited capability of the computer at hand.

The conventional hot-wire static calibration procedure for the measurement of absolute turbulence intensities with constant-temperature hot-wire anemometers is investigated and serious errors are found. An alternative calibration procedure is developed which involves shaking the wire at low frequencies in a uniform flow. A series of tests indicate that this dynamic calibration method is more accurate and consistent than the conventional procedure.

A method for verifying various calibration procedures is demonstrated. This method involves the measurement of velocity perturbations in a series of Karman vortex streets. The velocity perturbation amplitude is held fixed, but the frequency varies from one vortex street to another. This method also acts as a direct check of the hot-wire system frequency response.

The influence of large variations of viscosity on convection in a layer of fluid heated from below has been investigated. Solutions for the flow and temperature fields were obtained numerically assuming infinite Prandtl number, free-surface boundary conditions, and two-dimensional motion of fixed horizontal wavelength. The effects of a temperature-dependent and a depth-dependent viscosity were each studied; calculations were also carried out using a temperature- and depth-dependent viscosity model appropriate to the earth's mantle.

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).

Based on a set of modulation equations derived in a previous paper, the nonlinear evolution of wave envelope in deep water is studied numerically. It is found that the wave envelope tends to disintegrate to multiple groups of waves each of which approaches a stable permanent envelope representing dynamical equilibrium between the amplitude dispersion and the frequency dispersion. Qualitative agreement with the experimental measurements of Feir (1967) is also observed.

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 linear hydrodynamic stability analysis of liquid pools heated from below combining surface tension and buoyancy effects as presented by Nield (1964) is confirmed by experiment for a series of silicone oils. The experimental method used is an adaptation of the Schmidt–Milverton technique, in which the stability limit is located by the change of slope in the plot of heat flux versus temperature drop across the liquid pool.

A quasi-one-dimensional non-linear model is developed for the axisymmetric dynamics. Streaming is coaxial with a cylindrical ‘wall’ supporting a potential having a linear axial dependence. In addition to a tangential field due to an axial current, the stream surface supports charges in proportion to the stream-wall potential difference; hence it is driven by normal and shear electric stresses. Free charge and polarization waves compete with the destabilizing effect of capillarity. With supercritical steady flow (the local jet velocity exceeds the wave velocity), it is found that the stream accelerates or decelerates in accordance with whether an equivalent longitudinal force density is respectively positive or negative. With subcritical flow, the effect of the force is reversed. Experiments demonstrate accelerating and decelerating flow régimes. Model and experiment are in agreement with regard to choking at a critical radius, and the dependence of radius and potential on position. Hysteretic switching between flow régimes is obtained by adjustment of stream and wall potentials, and is explained in terms of the model.

A schematic picture of the structure of a mature hurricane is hypothesized. The heat and moisture transfer, the boundary-layer dynamics and the overall dynamic and thermodynamic balances are analysed crudely, but sufficiently accurately to provide support for the hypothesis.

The effect of blowing through a porous rotating disk on the flow induced by this disk is studied. For strong blowing the flow is almost wholly inviscid. First-order viscous effects are encountered only in a thin layer at some distance from the disk. The results of an asymptotic analysis are compared with numerical integrations of the full equations and complete agreement is found.

A direct numerical integration of the time-dependent, incompressible Navier-Stokes equations is used to treat the nonlinear evolution of perturbed, linearly unstable, nearly parallel shear flow profiles in two dimensions. Calculations have been made for infinite (inviscid) and finite Reynolds numbers. The latter results are compared with laboratory measurements of Sato & Kuriki for wakes behind thin flat plates, and many of the detailed features are in excellent agreement, including mean flow profiles with ‘overshoot’ development, first harmonic energy profiles with off-axis nulls, and first harmonic phase profiles. The linear instability saturates by forming a vortex street consisting of elliptical vortex pairs. The solutions are followed for times up to eleven linear exponentiation times of the unstable disturbance. A new low-frequency non-linear oscillation is found, which explains the features of the above experiment, including the nearly periodic phase inversions in the first harmonic component of the longitudinal velocity. It results from a nutation of the elliptical vortices with respect to the mean flow direction. Inertial range spectral energy properties are also examined. Inviscid solutions have large wave-number spectral energies obeying the approximate power law, Ek ∼ k−μ, where μ lies between 3 and 4.

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.