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Joanne Starr Malkus

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Joanne Starr Malkus

Abstract

Cross sections through two trade-cumulus clouds are presented, showing the temperatures, turbulence, and water-vapor content of the clouds and their nearby environment, the cloud slope, and the external wind profile. The two clouds were studied over the Caribbean Sea on the same afternoon in June, 1952, and were in widely differing phases of their life cycles. The measurements were made from a slow-flying aircraft, equipped with sensing instruments and whose behavior as a meteorological tool had been previously studied. Numerous calculations are made from the cross sections, including total and dynamic entrainment, drafts, slopes, and liquid-water content. These are, where possible, checked against the corresponding observations. In addition to testing previously evolved theoretical models, and the usefulness of the steady-state hypothesis, the data provide some evidence concerning the formation and growth of larger tradecumulus clouds from several smaller ones and by successive stages.

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Joanne Starr Malkus

Abstract

With use of the model of the steady-state entraining cumulus draft, it is possible to describe the formation and structure of the downdraft observed at the down-shear edge of an oceanic trade-cumulus cloud. The observations are airplane traverses made at several levels giving the temperature, humidity, and vertical draft structure in cloud and environment, and a nearby pilot-balloon run.

It is found that this downdraft must be mixing primarily with the updraft; that it gains its negative buoyancy mainly from evaporation; and that it is permitted to go through a life cycle of formation, strengthening, and decay which is closely dependent upon that of the updraft.

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Joanne Starr Malkus

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Joanne Starr Malkus
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Joanne Starr Malkus
and
Melvin E. Stern

Abstract

The effect upon a stable atmosphere of a heat source (5–10 km width), which is a specified function of the coordinates, is investigated theoretically. A two-dimensional problem is chosen, with the x-coordinate in the direction of the mean undisturbed surface wind U, and the z-direction vertical. The heat source, a finite-width pulse in x, has maximum amplitude at the ground (z = 0) and decays with height. A steady state, in which the heat supplied by the source is continuously carried away downstream, is assumed, and the equations of motion are linearized by the method of perturbations. By Fourier analysis of the pulse function, the perturbation equations are made separable, and solutions for the streamline flow are obtained. It is shown that “lee waves,” i.e., extended downstream oscillations in the streamlines, occur only if the undisturbed wind or stability undergoes a change in the vertical. The results of the analysis are compared with observations made over Nantucket Island, a flat sandy strip about 5 km in width.

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Melvin E. Stern
and
Joanne Starr Malkus

Abstract

In Part I, the convective motions produced by the flow of a stable air stream over a small flat island were studied when the distribution of heating as a function of the coordinates was assumed. In Part II, the mechanism of the heating is examined. It is found that the heat source obeys an eddy-conduction equation and is established by turbulent eddying in the mixed ground layer. The streamline displacement may be divided into two components, one obeying the equation for air flow over a mountain ridge and the other obeying a heat-conduction equation, the latter component being important only in the near vicinity of the island. An “equivalent mountain” corresponding to the heated island may be specified analytically; it depends only upon the temperature distribution along the surface, the wind speed, the eddy conductivity in the ground layer, and the undisturbed stability. Its amplitude is related to the maximum streamline displacement. The “equivalent mountain” for Nantucket Island is calculated for two extreme observational cases. The complete streamline picture is constructed for several examples of an air stream whose properties remain unaltered to great heights. The basic current possessing a change in stability or wind speed at an upper level is also discussed, and the forecasting of lee waves is related to the development of the mixed ground layer via the height of the “equivalent mountain.” An expression for the sea breeze is also derived.

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Joanne Starr Malkus
and
R. S. Scorer

Abstract

A differential equation is formulated for the rate of rise of isolated buoyant elements in the atmosphere, based in part on analogy with the work of Davies and Taylor (1950) who studied the ascent of air bubbles in liquid. The equation involves a drag force which is proportional to the ascent velocity squared and which depends upon a linear dimension of the buoyant element, such as the radius of curvature of its upper surface. To eliminate this dimension from the differential equation, a law for the erosion, or rate of decrease in size of these buoyant air bubbles has been proposed. The basic assumptions are that the elements erode sufficiently slowly so that the flow around them is nearly the same as if they were in equilibrium, and that they retain their shape. From combination of the erosion law and the equation of motion, an erosion parameter, E, is derived, which to the extent that the laws are valid should be constant for all isolated cloudy bubbles, regardless of air mass or location. The erosion constant has been expressed in terms of the bubble's upward velocity, acceleration, and its buoyancy. The theory is thus subject to test in the case of cumulus towers, by simple measurements from time-lapse motion pictures and an environmental temperature sounding.

Observations of twelve relatively isolated cumulus bubbles, selected from both the trade-wind region and middle latitudes, show that E is indeed constant within the limits of measurement. A case of the aggregation of several small bubbles into a larger one is also studied, and the applicability to it of the same erosion and drag laws is established. The interaction of bubbles with one another, and with the environment to form large cumulus clouds, is discussed qualitatively.

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Joanne Starr Malkus
,
Andrew F. Bunker
, and
Kenneth McCasland

A case of low-altitude veil clouds from which cumulus later grew is studied by means of airplane, photographic, and synoptic data. Convergence due to the land-sea temperature contrast is indicated as the critical factor in this unusual cloud formation. This conclusion is further supported by an airplane study of the cumulus structure.

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