This collection contains a selection of manuscripts, many representing prepublished work by NCAR staff, written between the late 1960’s and the early 1970’s.
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A footnote on the role of diffusiophoresis in lung deposition of aerosols

The importance of diffusiophoresis in influencing the deposition of aerosol particles in human and animal lungs has been speculated upon for some time. In this note, we present calculations for the magnitude of this effect based on typical flow behavior in human lungs. Two extreme cases of breathing rate are included, corresponding to sedentary situations and to vigorous exercise. In the upper portions of the respiratory system, the diffusiophoresis velocity caused by diffusion of water vapor into inhaled air should dominate the motion of particles smaller than ~ 1 ��, as compared with Brownian motion. Where diffusion of oxygen and carbon dioxide to and from the surfaces of the lower lung occurs, diffusiophoresis is much weaker but can become significant compared with Brownian diffusion for particles in the 0.1  1.0 �� size range, particularly for conditions of heavy exercise.


A theoretical study of the compensating downward motions associated with cumulus clouds

An attempt is made to investigate theoretically the controlling influence of compensating downward motions on the development of cumulus clouds and the size of the cloudless areas associated with them. The model consists of two circular concentric air columns: the inside column corresponds to the updraft (cloud) region and the outside concentric annular column corresponds to the downward motion region. The combined cell is surrounded by the atmosphere at rest. The governing equations of both the updraft and the compensating downward motion are derived from the conservation equations of momentum, heat, moisture and mass. The differential equations are solved numerically to compute the vertical velocity, temperature, specific humidity and liquid water content in and out of the cloud as functions of height and time. Two experiments were performed with and without the effect of compensating downward motion. The main conclusions are the following: Without the effect of the compensating motion, the structure of the solitary updraft tends to a steady state. However, with the compensating motion, no tall cloud is maintained (unless there is a steady source of moisture at the cloud base) since the compensating downward motion acts as a "break". Also it was found that the most active cloud system develops when the ratio of the cloud area over the entire area (including the cloudless area associated with the updraft) is of the order of several percent.


An example of the nonuniqueness of weak solutions containing shocks in fluid dynamics

The system of nonlinear hyperbolic equations of shallow water flow over an obstacle yields different solutions containing discontinuities for the same initial conditions depending upon the form in which the equations are written. Two different solutions are obtained by numerical computations. The results are compared with two different sets of analytical solutions based upon two different formulations of shock conditions. The good agreement between the numerical and analytical results indicates that the nonuniqueness of shock solutions can be demonstrated in the numerical solutions of finite difference equations as well as in the analytical solutions of differential equations.


Comparison between wind waves at sea and in the laboratory

Correlations between laboratory and geophysical data are presented for certain statistical properties of wind waves. The parameters chosen include (a) Relations between mean wave height, and the height of the highest onethird or onetenth waves, as given by a Rayleigh probability distribution, and (b) Amplitude spectra for waves, as given by Phillips' equilibrium theory. The correlation between laboratory results and geophysical data is very satisfactory over a wide range of wave size.


Computer experiments in the global circulation of the Earth's atmosphere

The purpose of this article is to review the physical, mathematical, and computational aspects of the numerical simulation of the largescale motions of the earth's atmosphere. The discussion will not be too detailed about particular aspects, but will give a perspective view of how large, highspeed computers are being used to aid our understanding of the earth's atmosphere, not only for the sake of research, but also for social and economic benefits. The presentation will include the showing of a 16 mm color movie which demonstrates the timedependent solutions of meteorological equations in order to explain the mechanism of the global circulation and weather systems. The movie was made by a cathode ray tube plotter together with a highspeed computer.


Effects of an ensemble of convective elements on the largescale motions of the atmosphere

It has been recognized recently that the role played by organized cumulusscale convection is very important in understanding the dynamics of the general circulation of the atmosphere, particularly in the tropics. Because of large differences between the size of cumulusscale convection and of largescale motion, it is difficult to deal with both phenomena in one system of atmospheric equations. In this paper we discuss (1) the effects of an ensemble of convective elements on the largescale motion, and (2) the influence of the largescale motion on the development of organized cumulus clouds. A scheme is proposed to solve simultaneously two systems of equations for the largescale flow and for the cumulusscale convection. The effects of cumulus convection are included in the equations for the largescale motions. The largescale (synoptic) conditions are included in the equations for the cumulus convection which determine not only the structure of cumulus clouds, but also the population of the clouds.


Experimental and theoretical confirmation of the discrete heat flux transitions of Malkus

Discrete transitions in the heat flux through fluids confined between horizontal plates were first observed by Malkus. The transitions, and the remarkable linear segments in a linear plot of Nusselt number times Rayleigh number versus Rayleigh number, are confirmed experimentally up to a Rayleigh number of Ra = 2.8 x 10��� in a convection chamber of different geometry and in fluids of different Prandtl numbers than those used by Malkus. Two transitions at Ra ��� 8200 and 24,000 were always observed instead of the single transition suggested to occur at Ra ��� 18,000. The first four transitions are explained by quasilinear stability theory for the appearance of unstable vertical modes upon a distorted mean temperature gradient, ��(z) , with rigid boundaries. The approximations of substituting a constant �� in place of a realistic , ��(z), and free surfaces for rigid boundaries, are shown to produce large errors in calculated critical Rayleigh numbers for the higher modes. Prepublication review copy.


Experiments on the generation of small water waves by wind

The generation and growth of small water waves by a turbulent wind has been investigated in a laboratory channel. The evolution of these oscillations with fetch was traced from their inception with amplitudes in the micron range under conditions of steady air flow. The experiments revealed that the waves are generated at all air velocities in small bursts consisting of groups of waves of nearly constant frequency. After traveling for some distance downstream, these wavelets attain sufficient amplitude to become visible. For this condition a wind speed critical to raise waves is well defined. After the first wavelets appear, two new stages of growth are identified at longer fetches if the airspeed remains unchanged. In the second stage, the component associated with the dominant frequency of the wave spectrum initially grows most rapidly with fetch until it attains an upper limit of amplitude consistent with the well known equilibrium range, which appears to be universal for wind waves on any body of water. The frequency of this dominant wave in the second stage remains constant with fetch up to equilibrium, but tends to decrease with increasing wind shear on the water. In the third stage of growth, only wave components whose energy is lower than the equilibrium limit tend to increase in amplitude so that the wave spectrum is maintained at equilibrium in the high frequency range of the spectrum. We found no features of the mean air flow or its turbulence structure as characterized by the distribution of longitudinal intensity and energy spectra that could be attributed to disturbances by the first ripples. Under the shearing action of the wind, the first waves were found to grow exponentially. The growth rate agreed with the estimated from the viscous shearing mechanism of Miles (1962a) to a fractional error of 61% or less. Slightly better agreement was obtained with the viscous theory of Drake (1967) in which Miles' model is extended to include the effect of the drift current in the water induced by the wind. But for the magnitude of the currents observed in the tunnel, this improvement is believed to be insignificant.


Laboratory investigation of nonsteady penetrative convection

Laboratory experiments of nonsteady penetrative convection in water are performed that closely simulate the lifting of an atmospheric inversion above heated ground. Vertical profiles of horizontally averaged temperature and heat flux are measured and interpreted. The rate at which kinetic energy is destroyed by the downward heat flux in the vicinity of the inversion base is found to be a very small fraction of the rate at which it is generated in the lower convective region. The interface separating the convective region from the stable region is examined and its rate of rise explained.
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