ALBERT

Description: Various observations of layering and intrusions in the ocean strongly suggest that such structures and motions are produced and driven by horizontal and vertical gradients of temperature and salinity, i.e. by double-diffusive processes. Much of the laboratory work in this field has concentrated on one-dimensional problems, with the neglect of two-dimensional phenomena. The latter are addressed explicitly in the present paper, using the salt-sugar analogue system in a simple geometry, but with the aim of establishing some more widely applicable general principles. Two sources of salt or sugar solution were fed in at opposite ends of a 750 mm long tank, with an overflow tube drawing fluid from a point at the centre of the tank. With two salt sources of different concentrations and densities, a stratification built up through the 'filling box' process, and the total density range lay within that of the input solutions. For one salt and one sugar source, a much larger density gradient could be set up, with the range lying outside that of the inputs. The flows were monitored using various experimental techniques: photographs of dye streaks with still and video cameras; a polarimeter to monitor sugar concentration; and the withdrawal of samples for the measurement of density and refractive index, from which the separate contributions of salt and sugar to the density could be calculated. Three related experiments with simple input conditions were particularly instructive, and these will be described first. Both inputs and the withdrawal tube were located at mid-depth, and the tank fluid and the salt and sugar supplies had the same density. The only difference between runs was the initial composition of the solution in the tank: pure salt, pure sugar, and a 50:50 mixture of the two. Following an initial transient response which was different in the three experiments, they all tended to the same asymptotic distributions of salt, sugar and density after about 100 h, with a sharp central interface and weakly stratified upper and lower layers. This state corresponded approximately to the one-dimensional 'rundown' of a layer of salt solution above sugar solution, with a slightly higher, unstable concentration of salt in the top layer compared to the bottom and a very stable sugar distribution, with a much larger concentration in the bottom layer than in the top one. This distribution cannot be produced by 'finger' rundown, and it corresponds to the maximum release of potential energy. It was, however, achieved through the action of many intrusions, which remained active in the dynamic final state, and maintained a strong communication between the two ends of the tank. A comparable experiment was carried out using a tank 1820 mm long. With this larger aspect ratio there was a predominantly local influence of the sources at each end of the tank. Other runs have explored a variety of geometries of the sources and sinks, and the final state has been shown to be sensitive to these boundary conditions.

Description: Double-diffusive plumes, injected into surroundings of nearly the same density, are observed to separate near the source and to produce both upward and downward convection, which is enhanced as layers form at the top and bottom of the experimental tank. This process has been quantified in this paper for both sugar plumes in homogeneous salt solution and salt plumes in sugar solution, over a range of small density differences on either side of zero. The tank was fitted with a partition at mid-depth, which could be closed at the end of a known period of input, so that the concentration changes above and below the source could be deduced. The density of the input and tank fluids, and that of the upper and lower layers, was measured in each case, as well as a second property, conductivity for the salt and optical rotation for the sugar inputs. These measurements were motivated by, and shed light on, the experimental results of Turner & Veronis (2000). There are large differences between the upward and downward transports produced by the two types of plume, because of the different rates of diffusion of salt and sugar in and out of the plumes and the subsequent transports through the interfaces that form as the plumes spread out along the top and bottom boundaries. One result is that at a density ratio close to 1 a salt plume produces equal upward and downward transports of salt, whereas at the same density ratio a sugar plume leads to a much larger downward flux of sugar. This is consistent with the 'diffusive' final state observed by Turner & Veronis (2000), and this conclusion is supported by a more detailed analysis of the redistribution of the tank fluid.

Description: This paper proposes a theory of collisions between small drops in a turbulent fluid which takes into account collisions between equal drops. The drops considered are much smaller than the small eddies of the turbulence and so the collision rates depend only on the dimensions of the drops, the rate of energy dissipation ε and the kinematic viscosity v. Reasons are given for believing that the collision rate due to the spatial variations of turbulent velocity is shown to be [formula omitted], valid for [formula omitted] between one and two. A numerical integration has been performed using this expression to show how an initially uniform distribution will change because of collisions. An approximate calculation is then made to take account also of collisions which occur between drops of different inertia because of the action of gravity and the turbulent accelerations. The results are applied to the case of small drops in atmospheric clouds to test the importance of turbulence in initiating rainfall. Estimates of ε are made for typical conditions and these are used to calculate the initial rates of collision, the change in mean properties and the rate of production of large drops. It is concluded that the effects of turbulence in clouds of the layer type should be small, but that moderate amounts of turbulence in cumulus clouds could be effective in broadening the drop size distribution in nearly uniform clouds where only the spatial variations of velocity are important. In heterogeneous clouds the collision rates are increased, and the effects due to the inertia of the drop soon become predominant. The effect of turbulence in causing collisions between unequal drops becomes comparable with that of gravity when ε is about 2000 cm2 sec−3. © 1956, Cambridge University Press. All rights reserved.

Description: This paper continues an investigation into the mixing of a dense layer of salt solution in a turbulent pipe flow in order to obtain a more detailed understanding of the underlying physical processes. The effect of the density difference on the velocity profile in a sloping pipe is calculated using a simplified model, and the results compared with direct measurements obtained by timing streaks of dye at various levels in the pipe. These velocity profiles are also used in conjunction with density profiles to estimate the dependence of the transfer coefficients for salt and momentum K S and K M , on stability. It is found that K S is much more greatly affected by the density gradient than K M , and that the ratio K S /K M may be represented, to the accuracy of the experiments, as a function of the local Richardson Number Ri. The results agree with what is known of K S /K M in neutral and very stable conditions, and they confirm an earlier prediction by Ellison that the critical flux Richardson number, at which K S becomes zero, is much less than unity. Finally, a crude semi-empirical method is outlined which indicates how the new measurements of the transfer coefficients may be related to the overall properties of the flow discussed in the first part of the paper. © 1960, Cambridge University Press. All rights reserved.

Description: A laboratory model of a tornado vortex has been produced, incorporating two features which are believed to be important to the understanding of the atmospheric phenomenon, but which have been largely ignored in previous studies. First, it has been shown that a vortex can be driven from above by a mechanism analogous to convection in a cloud, and that density differences within the funnel itself are not essential. Associated with this mechanism of formation is a circulation in the vertical, with an upflow in the centre surrounded by a compensating annular downflow. Secondly, the bottom boundary is seen to have a strong influence on the vortex, since the down and up flows are linked there by a rapid radial inflow in a thin boundary layer. In the present paper an approximate theoretical description of such a vortex is proposed. The interior and boundary layer flows are first examined separately, and then a condition is sought which makes the two solutions consistent. The starting-point of the theory is the assumption of a form of stream function which describes a circulation in the vertical having the essential features of that observed. The result of the matching procedure is to fix both the form of the tangential velocity profile, and the relative magnitudes of the three components of velocity. These deductions are not critically dependent on the assumed form of the motion in the vertical, and are in good agreement with the first measurements in the laboratory vortices, though the quantitative experimental results are not emphasized here. © 1966, Cambridge University Press. All rights reserved.

Description: It has been suggested on theoretical grounds that a vortex could be initiated in a cylindrical region of fluid, originally in solid rotation, by the horizontal mixing of angular momentum produced by external stirring. In this paper various arguments for and against the mechanism are examined and their difficulties exposed. No firm conclusion is reached. A series of mathematical models of the mixing motions has been used, to bring out the differences between mechanical stirring and the agitation of a gas by random molecular motions. They suggest the introduction of a diffusion coefficient for angular momentum, to be determined empirically. These theoretical ideas are then applied to the interpretation of the results of a laboratory experiment which has been designed to test the proposed mechanism directly.A wide, flat tank of liquid was set up on a rotating table and stirred with a vertically oscillated grid, whose elements were much smaller than the width of the tank. A neutrally buoyant particle was used as a tracer of fluid motions, to measure relative circulation velocities and the properties of the turbulence. The motion observed was dominated by the loss of angular momentum to the walls and the grid, an effect which has not been taken into account in previous theoretical assessments of the effects of mixing of angular momentum. The relative circulation present was not significantly different from zero, and the limits of error of the measurements imply that the rate of diffusion of angular momentum is less than 5% of that for fluid particles, with 95% probability.

Description: In this paper we present a rather personal view of the important developments in double-diffusive convection, a subject whose evolution has been the result of a close interaction between theoreticians, laboratory experimenters and sea-going oceanographers. More recently, applications in astrophysics, engineering and geology have become apparent. In the final section we attempt to draw some general conclusions and suggest that further progress will again depend on a close collaboration between fluid dynamicists and other scientists. © 1981, Cambridge University Press. All rights reserved.

Description: The entrainment assumption, relating the inflow velocity to the local mean velocity of a turbulent flow, has been used successfully to describe natural phenomena over a wide range of scales. Its first application was to plumes rising in stably stratified surroundings, and it has been extended to inclined plumes (gravity currents) and related problems by adding the effect of buoyancy forces, which inhibit mixing across a density interface. More recently, the influence of viscosity differences between a turbulent flow and its surroundings has been studied. This paper surveys the background theory and the laboratory experiments that have been used to understand and quantify each of these phenomena, and discusses their applications in the atmosphere, the ocean and various geological contexts. © 1986, Cambridge University Press. All rights reserved.