Search

Long has illustrated the increased power for fluid mechanics of a generalized type of dimensional analysis based on consideration of the known mathematical form of the governing equations and boundary conditions. It is shown that Long's method is mathematically equivalent to an analysis of the transformational properties of the governing equations and boundary conditions under a particular class of simple linear transformations of the variables of the problem, and that similarity results obtained by his method may also be derived directly by a purely mathematical technique that avoids reference to the concepts of dimensional analysis and the Buckingham II-theorem. Application of this transformation technique is illustrated by several examples. Consideration of a recent attempt by Bernstein to apply Long's procedure to the problem of the wind distribution in the turbulent planetary boundary layer indicates that this application is not valid.

The energy equation of eddying motion in a fluid of variable density is derived by methods based on a treatment by Ertel, with particular reference to conditions in the atmosphere. The general form of the criterion for the growth or decay of turbulence is then deduced. The limitations inherent in the Richardson criterion of turbulence are examined and it is shown that the latter neglects terms which are potentially large. These represent respectively, the rate of dissipation of eddying energy into heat by molecular viscosity, the rate of working of the fluctuating gradients of static pressure on the eddying motion, and the eddy diffusion of eddying kinetic energy. Richardson's criterion also involves the assumption of a special functional form for the vertical heat flux due to turbulence, which may not be generally valid. If it is, however, the critical value of the Richardson number above which turbulence is damped out is probably less than unity, in contradiction to Richardson's analysis, but in agreement with a theoretical analysis by Schlichting, which has been shown to be in satisfactory agreement with laboratory experiments.

Some simple transformation properties of the diffusion equation that has been classically used to describe turbulent transport in the atmosphere are briefly examined. The essential tensorial nature of the eddy diffusivity is emphasized and it is concluded that the standard form frequently adopted for the diffusion equation in the meteorological literature cannot be generally valid.

Concentrations produced by an extended near-ground line-source of vehicularly-generated highway air pollution are considered with special emphasis on the influence of the obliquity of the wind. A result previously quoted by Turner is clarified, and it is shown that over a wide range of wind directions the concentration distribution can be calculated by a simple approximate formula. Although the concentrations increase as the wind more closely parallels the direction of the highway, the increase is only slight and, for many practical purposes, could be disregarded.

It may readily be shown, from elementary arguments, that for steady fluid flow in circular tubes or between parallel plates, the shear stress in the direction of the mean motion varies linearly with the distance from the wall. This result is quite independent of the nature and origin of the fluid resistance and in particular is valid if the flow be turbulent. However, it has been proved by Ertel (1933) that in the lower layers of the atmosphere (1 ⩽ z ⩽ 30 m) the horizontal turbulent shearing stress defined by τ = η (z)∂v/∂z where η(z) is the vertical austausch coefficient and ∂v/∂z the vertical gradient of mean velocity, is to a high degree of approximation independent of the height. In view of the importance of this conclusion in atmospheric turbulence theory, and its obvious difference from the first, it has been thought worth while to examine Ertel's treatment in detail. The latter is based on the assumption of the isotropy of the coefficient of vertical turbulent momentum interchange and the final result depends on the relative smallness of the variation of wind direction with height in the surface layers. Complete neglect of this variation, however, requires a wind velocity constant with height, in which case Ertel's result would become trivial. The object of the present note is to show that the assumption of very small but plausible values for the wind direction change with height in the surface layers (of order 10-6 radians/cm.) suffices to account for the observed wind velocity increase in the lower layers. It may be concluded that Ertel's analysis is sound. Furthermore it appears on the basis of the theory that the mean wind direction change with height in the lower layers is too small to be observed practically.

A simple model is presented that incorporates the major features of atmospheric transport and diffusion of a NH3 plume together with aqueous absorption as the plume traverses a water surface. The model is based on the well-known concept of the deposition velocity, although empirical data concerning the latter is quite meager. A specific application is considered to the gas release from a NH3 stripper of a hypothetical sewage treatment plant, and it is concluded that NH3 absorption by adjacent water masses could be considerable.

This paper discusses the reference equilibrium atmosphere for the approximate equations of shallow layer thermal convection.

This paper discusses Bernstein's application of a generalized method of dimensional analysis, proposed by Huntley, to the Monin-Obukhov problem of the flux-gradient relationships in the thermally stratified air layer near the ground. It is concluded that the Huntley method is not a valid general procedure although, in disagreement with a conclusion of Bernstein, it is shown that the purely formal use of this technique leads to results that are actually valid under the very special conditions of free convection. This circumstance arises from the absence of any characteristic length scale under conditions of free convection in the surface layer.

Two autopsy-proved cases are presented of a rare form of congenital heart disease, anatomically corrected malposition (S, D, L). Anatomically corrected malposition means that despite the abnormal relationship between the great arteries, the aorta arises nonetheless above the anatomically left ventricle and the pulmonary artery originates above the anatomically right ventricle. (S, D. L) briefly indicates the segmental set or combination: situs solitus of viscera and atria (S), ventricular D-loop (D), AND L-MALPOSITION OF THE GREAT ARTERIES (L). These are the first cases of anatomically corrected malposition (ACM) in whom the presence of a subaortic muscular conus only has been documented pathologically. This established that ACM can occur with a subaortic conus, as well as with a bilateral conus. From the diagnostic standpoint, the distributions or epicardial courses of the coronary arteries are recommended as a helpful approach to ventricular identification. This diagnostic method has widespread angiocardiographic and surgical applications. Symbolic terminology, exemplified by anatomically corrected malposition (S, D. L) is brief and accurate. This approach may conveniently be applied to many other forms of comples congenital heart disease, and it considerably facilitates computer data processing.