The interaction between convection in a horizontal fluid layer heated from below and an ambient vertical magnetic field is considered. The analysis is based on the Boussinesq equations for two-dimensional convection rolls and the assumption that the amplitude A of the convection and the Chandrasekhar number Q are small. It is found that the magnetic energy is amplified by a factor of order R½m, where Rm is the magnetic Reynolds number. The ratio between the magnetic and kinetic energies can reach values much larger than unity. Although the magnetic field always inhibits convection, this influence decreases with increasing amplitude of convection. Thus finite amplitude onset of steady convection becomes possible at Rayleigh numbers considerably below the values predicted by linear theory.

The creeping motion through a circular tube of neutrally buoyant Newtonian drops which have an undeformed radius comparable to that of the tube was studied experimentally. Both a Newtonian and a viscoelastic suspending fluid were used in order to determine the influence of viscoelasticity. The extra pressure drop owing to the presence of the suspended drops, the shape and velocity of the drops, and the streamlines of the flow are reported for various viscosity ratios, total flow rates and drop sizes.

Measurements have been made of the net force F acting on a bluff rigid body moving with velocity U (relative to a fluid rotating about a vertical axis with uniform angular velocity Ω) in a plane perpendicular to the axis of rotation. The force F is of magnitude 2ΩρVU, where ρ is the density of the fluid and V is a volume which depends on the size and shape of the body. The relative direction of F and U is found to depend on the quantity \[ {\cal S}\equiv \frac{2\Omega L}{U}\bigg(\frac{h}{D}\bigg), \] where L and h are horizontal and vertical lengths characterizing the object and D is the depth of the fluid in which the object is placed.

Euromech 60 is the third in a series of European Mechanics Colloquia dealing primarily with three-dimensional turbulent boundary layers. The Colloquium was held in Trondheim at the Technical University (NTH) from 14–16 April 1975 with forty-two participants from ten different countries, and was organized by L. N. Persen and T. K. Fanneløp. A total of 23 papers were presented, dealing with both experiments on and predictions of turbulent boundary-layer flows and related topics. Those concerned with the development of prediction methods were challenged by a set of boundary-layer flow problems defined well in advance in order to be calculated prior to the Colloquium. The results show close agreement for some calculated variables and surprisingly large discrepancies in others. A brief account of this exercise is included and it will also be the subject of a special report.

We consider the mixing between two miscible liquids of slightly different density (< 10%) when one of them (cargo) is injected into a tank partially filled with the other (inventory). The injection of the cargo is such that buoyancy and inertia act in concert on the plume produced by the cargo. The two basic processes that govern the mixing of the two liquids in the tank are the entrainment of tank liquid by the plume and the tank circulation set up by this entrainment and by the plume discharge. Unlike plumes in an environment of infinite extent, the plume in this case changes its environment continuously, which, in turn, has a continuously-varying effect on the plume. A mathematical model for the mixing of the two liquids is presented, from which one can compute the tank stratification that may result when given amounts of cargo and inventory are thus mixed. Plume entrainment theory is used for the plume dynamics and a ‘filling-box’ model is used for the tank circulation. The partial differential equations of the model are integrated by an original and unique numerical method. The problem was also treated experimentally. The tank stratification is expressed in terms of a normalized density-difference variable δ. Except for some very localized large discrepancies, due to certain local effects not included in the model, computed and experimental profiles of δ agree very well, their maximum and average deviations being within 4 and 2%, respectively. It is found that values of the empirical plume parameters α and λ that are used commonly for steady plumes in environments of infinite extent are approximately right for the time-dependent plumes under consideration too.

In this paper two aspects of the deepening of a mixed layer in a stratified fluid are examined in the laboratory. The first is the deepening of a layer into a region of constant density gradient. Turbulence is produced by an oscillating grid which generates a horizontally homogeneous field of motion with no significant mean flow. It is found that the rate at which the potential energy of the basic stratification is increased by the mixing does not bear a simple relationship to the rate of energy input by the grid. On the other hand, when allowance is made for the decay of turbulent energy away from the grid and only that portion to reach the bottom of the mixed layer is considered, the rate of potential energy increase is found to be proportional to this available energy. The second aspect to be discussed is the effect of energy radiation by internal waves in the region below the mixed layer. Estimates are made of the possible loss of energy to these waves, which reduces the amount available to deepen the layer. An experimental demonstration of up to 50 % reduction in the mixing rate due to the presence of internal waves is given. Finally, the implications of these results are discussed in the light of current theoretical models of the deepening process.

The influence of a mean uniform shear on the development of a partially mixed region in an unbounded stratified fluid is considered. Results are given for the very near field and the far field in the large-J (Richardson number) limit. A qualitative discussion for J [gsim ] 1 is also included. The near-field motion is modified on a time scale given by Rτ ∼ J−¼, where R = dU/dz is the mean shear strength. This modification is shown to be a consequence of the kinematic distortion of the wake profile by the mean shear. The radiation field is largely anticipated by the wave-packet discussion of an earlier paper.