ALBERT

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: Liquid-into-liquid jets in short cylindrical vessels have been investigated under conditions of uniform flow by using an aqueous blue tracer solution in conjunction with tránsparent cylindrical tanks. The vessels had diameters D of 3, 6, 12 and 24in., length-to-diameter ratios L/D of 1, 2 and 3 and inlet diameters d between ¼ and 1 in. Reynolds numbers in the inlet tube, Rei, ranged between 100 and 28,000. Four main types of jet were observed: [formula omitted] The laminar length a of sub-turbulent jets was investigated and correlated with Rei and the geometric parameters by the equation [formula omitted]. © 1966, Cambridge University Press. All rights reserved.

Description: A correlation scheme for velocity and temperature profiles is derived for turbulent boundary layers in adverse pressure gradients. The resulting analytical expressions are obtained by what could be referred to as ‘regional similarity’ arguments. This avoids the need to make use of the Reynolds analogy (explicitly, at least) or the usual local gradient-type diffusion expressions for momentum and thermal transport (‘the local similarity’ and Boussinesq concept). The expressions agree well with experimental data for the velocity profiles and encouraging correlation is shown for the temperature profiles. The expressions cover a wider part of the profile than given by the logarithmic law of the wall. Surface roughness and Prandtl-number effects are included in the analysis. © 1966, Cambridge University Press. All rights reserved.

Description: The turbulent flow of a weakly conducting liquid between parallel plates in the presence of a transverse magnetic field is investigated. The form of the mean velocity profile is determined by a series of constraints resulting from the boundary conditions and the Navier–Stokes equations and by the Malkus postulates on the spectrum of the mean vorticity gradient. The width of the transition regions near the walls is derived in terms of the governing dimensionless numbers and this expression is checked, in the asymptotic laminar case, against the well-known Hartmann result. A graphical method, exploiting the relation between the boundary region thickness and the smallest scale of motion defined by the Malkus theory is proposed to determine the scale of the velocity profile, i.e. the flow rate in terms of the pressure gradient and the magnetic field strength. © 1966, Cambridge University Press. All rights reserved.

Description: Numerical methods are used to investigate the steady two-dimensional motion of a viscous incompressible fluid past a flat plate of finite breadth at zero incidence to a uniform stream. Before application of numerical techniques, the governing partial differential equations for the stream function and vorticity are reduced to ordinary differential equations by an adaptation of methods normally used to solve Oseen's linearized equations. The complete range of the Reynolds number R is considered, from indefinitely small to indefinitely large. All the results are intended to represent solutions of the full Navier-Stokes equations of motion, although in practice approximations are inevitable. These are mainly brought about by the necessity of limiting the size of the calculations. At the lower end of the Reynolds-number range, the calculated frictional drag coefficient agrees well with the results of Tomotika & Aoi (1953) based on Oseen's equations. At intermediate and higher Reynolds numbers there is good agreement with the experimental results of Janour (1951) and with the improvement of the Blasius solution given by Kuo (1953). Finally a limiting solution is obtained as R → ∞. This shows that the drag coefficient is proportional to R−½, in accordance with boundary-layer theory. The actual calculated value of the coefficient is about 4% higher than the Blasius value. Although the present results tend generally to confirm the trend of the recently published results at R = 0·1, 1 and 10 of Janssen (1957), there are substantial discrepancies in the detailed results in a number of instances. In particular, the drag values obtained at R = 1 and 10 are some 20% higher than Janssen's although there is reasonable agreement at R = 0·1. It seems possible that Janssen's analogue is a little crude at the higher Reynolds numbers. © 1966, Cambridge University Press. All rights reserved.

Description: A critical scrutiny of the nature of the three-dimensional characteristics of the vortex wake of a circular cylinder serves to suggest lines for further investigation and furnishes some ideas on the nature of the growth and development of these non-uniformities. It is suggested that the basic occurrence in the growth of three-dimensionality is the continuation of vortex lines, oriented more or less parallel to the body, into the direction of the free stream. The causes of this vary, as do the details of the development with the particular situation considered. Experiments were performed in a wind tunnel at Reynolds numbers based on cylinder diameter of 85, 235 and 2 × 104, at which stable, transitional and turbulent vortices were investigated. © 1966, Cambridge University Press. All rights reserved.

Description: Non-equilibrium inviscid flows behind a spherical-segment shock wave are investigated with the method of series truncation. This semi-analytical technique developed at Stanford is based on a systematic co-ordinate-perturbation scheme. The flow variables are expanded in series in powers of the longitudinal curvilinear co-ordinate leading away from the stagnation point. The problem is thus reduced to one of numerical integration of ordinary differential equations for functions of the normal co-ordinate. Unlike the similar situation of the Blasius series in boundary-layer theory, the present scheme–having to deal with elliptic equations–must resort to series truncation. As a consequence, a truncation error is introduced. The present paper shows a simple way of reducing this error. The simplified air chemistry adopted is based on non-equilibrium dissociation and recombination of oxygen diluted in inert nitrogen. A wide spectrum of non-equilibrium régimes is investigated for a fixed set of flight conditions. In particular, near-frozen flows are followed to the vicinity of the stagnation point through a region of large temperature and concentration gradients located near the body. This equilibrium-drive region, arising from the singular nature of the frozen limit, is studied in some detail. © 1966, Cambridge University Press. All rights reserved.

Description: A solution is offered for the relative phase relationship of bed, depth and surface waves observed in alluvial channels, and is found to be in good agreement with observation in laboratory flumes. The solution does not depend on an assumption of a phase lag between the velocity and sediment movement. The emphasis of the paper is on the mechanics of bed-wave formation. © 1966, Cambridge University Press. All rights reserved.