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## Abstract

An analysis of the kinetics and dynamics of the relative dispersion of particles in a stratified rotating fluid is made. The expressions for the relative displacement tensor, and the power- and cross-spectra of the relative velocity are derived. Their characteristics for large and small diffusion times are examined. The governing equations for the motion of marked fluid particles are separated into two sets of equations, one governing the motion of the center of mass and the other governing the motion of individual particles relative to the center of mass. Discussions of the concentration distribution in clusters of marked fluid particles are made. A turbulent diffusion model is constructed for the estimate of the effects of thermal stratification and rotation on the dispersion of particles in the atmosphere.

## Abstract

An analysis of the kinetics and dynamics of the relative dispersion of particles in a stratified rotating fluid is made. The expressions for the relative displacement tensor, and the power- and cross-spectra of the relative velocity are derived. Their characteristics for large and small diffusion times are examined. The governing equations for the motion of marked fluid particles are separated into two sets of equations, one governing the motion of the center of mass and the other governing the motion of individual particles relative to the center of mass. Discussions of the concentration distribution in clusters of marked fluid particles are made. A turbulent diffusion model is constructed for the estimate of the effects of thermal stratification and rotation on the dispersion of particles in the atmosphere.

## Abstract

The governing equations, power and cross spectra for the atmospheric motion, and transports in the frequency, wave-number space are derived. Discussions are made of the contributions of the nonlinear interactions of atmospheric waves in velocity and temperature fields to the conversion of kinetic and potential energies, and to the meridional transports of angular momentum and sensible heat in the atmosphere.

## Abstract

The governing equations, power and cross spectra for the atmospheric motion, and transports in the frequency, wave-number space are derived. Discussions are made of the contributions of the nonlinear interactions of atmospheric waves in velocity and temperature fields to the conversion of kinetic and potential energies, and to the meridional transports of angular momentum and sensible heat in the atmosphere.

## Abstract

The properties of the volume integral of momentum vorticity are examined. These results are applied to the study of the maintenance of zonal circulation of a polar cap. It is shown that the rate of change of the vertical component of relative momentum vorticity is mainly due to (1) the effect of the convergence of meridional flux of angular momentum and its lateral boundary surface, (2) the frictional force at the earth's surface, and (3) the action of the mountains on the atmosphere. A model for the mean state of the atmosphere in the northern hemisphere, based on the distribution of the mean surface zonal wind, is studied; and the maintenance of the zonal circulation is discussed on the basis of the meridional transports of both angular momentum and momentum vorticity. It is shown that in the middle latitudes the meridional transfer of momentum vorticity is directed toward the north pole, whereas in the lower latitudes, as well as in the polar region, the transport is directed toward the equator. These results agree with the mean meridional transport of momentum vorticity in the month of January 1949, computed from the geostrophic winds.

## Abstract

The properties of the volume integral of momentum vorticity are examined. These results are applied to the study of the maintenance of zonal circulation of a polar cap. It is shown that the rate of change of the vertical component of relative momentum vorticity is mainly due to (1) the effect of the convergence of meridional flux of angular momentum and its lateral boundary surface, (2) the frictional force at the earth's surface, and (3) the action of the mountains on the atmosphere. A model for the mean state of the atmosphere in the northern hemisphere, based on the distribution of the mean surface zonal wind, is studied; and the maintenance of the zonal circulation is discussed on the basis of the meridional transports of both angular momentum and momentum vorticity. It is shown that in the middle latitudes the meridional transfer of momentum vorticity is directed toward the north pole, whereas in the lower latitudes, as well as in the polar region, the transport is directed toward the equator. These results agree with the mean meridional transport of momentum vorticity in the month of January 1949, computed from the geostrophic winds.

## Abstract

A theoretical model is constructed and tested for the analysis and prediction of radioactive concentration in the troposphere. It is found that turbulent motion near the jet core plays the major role in the transport of radioactive debris from the stratosphere into the troposphere, whereas the mean motion of the jet core contributes to the spring maximum and autumn minimum of the concentration. A semiannual period in the variation of concentration exists, resulting from the interaction between the meridional gradient of the mean concentration and the mean motion of the jet core. It is also found that the average value of the vertical component of the eddy diffusivity in the troposphere is about 10^{7} cm^{2} sec^{−1}, and that the time required for diffusing radioactive particles from the tropopause level to the surface of the earth is about 11 hours.

## Abstract

A theoretical model is constructed and tested for the analysis and prediction of radioactive concentration in the troposphere. It is found that turbulent motion near the jet core plays the major role in the transport of radioactive debris from the stratosphere into the troposphere, whereas the mean motion of the jet core contributes to the spring maximum and autumn minimum of the concentration. A semiannual period in the variation of concentration exists, resulting from the interaction between the meridional gradient of the mean concentration and the mean motion of the jet core. It is also found that the average value of the vertical component of the eddy diffusivity in the troposphere is about 10^{7} cm^{2} sec^{−1}, and that the time required for diffusing radioactive particles from the tropopause level to the surface of the earth is about 11 hours.

## Abstract

An analytical solution to the Navier-Stokes equations for three-dimensional stationary flows of small Reynolds number in the atmospheric boundary layer over terrain is presented.

Analyses of the effects of topography, horizontal pressure gradient and Coriolis forces on the velocity distribution in the atmospheric boundary layer indicate that 1) the horizontal component of the velocity in the boundary layer turns right (left) with increasing height in the Northern (Southern) Hemisphere, 2) upward (downward) motion occurs on the windward (lee) side of the mountain, and 3) upward (downward) motion also occurs on the slope to the right (left) of the geostrophic wind in the Northern Hemisphere, whereas in the Southern Hemisphere downward (upward) motion occurs on the slope to the right (left) of the geostrophic wind.

## Abstract

An analytical solution to the Navier-Stokes equations for three-dimensional stationary flows of small Reynolds number in the atmospheric boundary layer over terrain is presented.

Analyses of the effects of topography, horizontal pressure gradient and Coriolis forces on the velocity distribution in the atmospheric boundary layer indicate that 1) the horizontal component of the velocity in the boundary layer turns right (left) with increasing height in the Northern (Southern) Hemisphere, 2) upward (downward) motion occurs on the windward (lee) side of the mountain, and 3) upward (downward) motion also occurs on the slope to the right (left) of the geostrophic wind in the Northern Hemisphere, whereas in the Southern Hemisphere downward (upward) motion occurs on the slope to the right (left) of the geostrophic wind.

## Abstract

An analysis of the wavenumber-frequency spectra of temperature in the free atmosphere is made. It is found that a striking similarity exists between the spectrum of temperature and that of the large-scale wind velocity in the free atmosphere. The wavenumber-frequency spectrum of temperature shows a preferred spectral domain of wave activities, oriented primarily from a region of low wavenumbers and low frequencies to a region of high wavenumbers and negative frequencies assigned to waves moving from west to east. In the high-wavenumber range, the wavenumber spectrum of temperature is approximately proportional to the –3 power of the wavenumber. In the high-frequency range, the frequency spectrum of temperature is approximately proportional to the –1 power of the frequency. These indicate that the structure of the temperature field in the free atmosphere is essentially affected by the large-scale two-dimensional turbulent motion. It is also found that most of the sensible heat is associated with the stationary zonal mean motion, and that there is more sensible heat associated with nonstationary waves than with stationary waves in the atmosphere.

## Abstract

An analysis of the wavenumber-frequency spectra of temperature in the free atmosphere is made. It is found that a striking similarity exists between the spectrum of temperature and that of the large-scale wind velocity in the free atmosphere. The wavenumber-frequency spectrum of temperature shows a preferred spectral domain of wave activities, oriented primarily from a region of low wavenumbers and low frequencies to a region of high wavenumbers and negative frequencies assigned to waves moving from west to east. In the high-wavenumber range, the wavenumber spectrum of temperature is approximately proportional to the –3 power of the wavenumber. In the high-frequency range, the frequency spectrum of temperature is approximately proportional to the –1 power of the frequency. These indicate that the structure of the temperature field in the free atmosphere is essentially affected by the large-scale two-dimensional turbulent motion. It is also found that most of the sensible heat is associated with the stationary zonal mean motion, and that there is more sensible heat associated with nonstationary waves than with stationary waves in the atmosphere.

## Abstract

Analyses of the isotropic and anisotropic diffusion of clusters of fluid particles in the atmosphere are made. Lin's theory of diffusion is subjected to an observational test. The autocorrelation coefficients of the vector acceleration are computed and the value of *B*
_{0} in Lin's one particle theory is found to be 3 and 5 cm^{2} sec^{−3} for two series of experiments. The mean autocorrelation coefficients of the vector relative acceleration are computed and the value of *B* in Lin's isotropic diffusion theory is found to be 68 and 28 cm^{2} sec^{−3} for two series of experiments. The horizontal eddy diffusivities for the isotropic diffusion process are found to range from 0.4×10^{3} to 6.4×10^{3} cm^{2} sec^{−1}. The mean cross-covariance coefficient of the relative acceleration is computed and the value of *B _{ij}* in Lin's anisotropic diffusion theory is found to be 30 cm

^{2}sec

^{−3}. The values of the diffusion tensor for the anisotropic diffusion process are found to range from 0.3×10

^{3}to 1.8×10

^{3}cm

^{2}sec

^{−1}.

## Abstract

Analyses of the isotropic and anisotropic diffusion of clusters of fluid particles in the atmosphere are made. Lin's theory of diffusion is subjected to an observational test. The autocorrelation coefficients of the vector acceleration are computed and the value of *B*
_{0} in Lin's one particle theory is found to be 3 and 5 cm^{2} sec^{−3} for two series of experiments. The mean autocorrelation coefficients of the vector relative acceleration are computed and the value of *B* in Lin's isotropic diffusion theory is found to be 68 and 28 cm^{2} sec^{−3} for two series of experiments. The horizontal eddy diffusivities for the isotropic diffusion process are found to range from 0.4×10^{3} to 6.4×10^{3} cm^{2} sec^{−1}. The mean cross-covariance coefficient of the relative acceleration is computed and the value of *B _{ij}* in Lin's anisotropic diffusion theory is found to be 30 cm

^{2}sec

^{−3}. The values of the diffusion tensor for the anisotropic diffusion process are found to range from 0.3×10

^{3}to 1.8×10

^{3}cm

^{2}sec

^{−1}.

## Abstract

An analysis of the linear and nonlinear interactions of atmospheric motion in the wavenumber-frequency domain indicates that the kinetic energy of the large-scale moving waves is essentially maintained by the nonlinear interactions and the pressure force. In middle latitudes where an eastward mean zonal flow prevails, the supply of kinetic energy to eastward moving waves through the nonlinear interactions is greater than the extraction of kinetic energy through the pressure force, whereas the supply of kinetic energy to westward moving waves through the pressure force is greater than the extraction of kinetic energy through the nonlinear interactions. Near the equator where a weak westward mean zonal Row occurs, the non-linear interactions generally extract kinetic energy from the eastward moving waves, but supply kinetic energy to the westward moving waves; the pressure force, however, supplies kinetic energy to both eastward and westward moving waves.

The primary contribution of the nonlinear interactions to the energy transfer in wavenumber-frequency domain is essentially through the interactions of the slowly moving waves, the stationary long waves and the zonal mean flow. The interactions between the stationary long waves and waves moving in the same (opposite) direction of the mean zonal flow generally extract (supply) kinetic energy from (to) the moving waves, whereas the interactions between the mean zonal flow and waves moving in the same (opposite) direction of the zonal flow generally supply (extract) kinetic energy to (from) the moving waves.

## Abstract

An analysis of the linear and nonlinear interactions of atmospheric motion in the wavenumber-frequency domain indicates that the kinetic energy of the large-scale moving waves is essentially maintained by the nonlinear interactions and the pressure force. In middle latitudes where an eastward mean zonal flow prevails, the supply of kinetic energy to eastward moving waves through the nonlinear interactions is greater than the extraction of kinetic energy through the pressure force, whereas the supply of kinetic energy to westward moving waves through the pressure force is greater than the extraction of kinetic energy through the nonlinear interactions. Near the equator where a weak westward mean zonal Row occurs, the non-linear interactions generally extract kinetic energy from the eastward moving waves, but supply kinetic energy to the westward moving waves; the pressure force, however, supplies kinetic energy to both eastward and westward moving waves.

The primary contribution of the nonlinear interactions to the energy transfer in wavenumber-frequency domain is essentially through the interactions of the slowly moving waves, the stationary long waves and the zonal mean flow. The interactions between the stationary long waves and waves moving in the same (opposite) direction of the mean zonal flow generally extract (supply) kinetic energy from (to) the moving waves, whereas the interactions between the mean zonal flow and waves moving in the same (opposite) direction of the zonal flow generally supply (extract) kinetic energy to (from) the moving waves.

## Abstract

The wind velocities measured by an aircraft flying parallel and perpendicular to jet streams (Project Jet Stream, 1956–1957) have been analyzed; a smoothing technique has been used to separate the meso-scale turbulence from the mean flow. Eulerian auto-correlation coefficients and energy spectra are computed for the longitudinal and transversal components of the horizontal wind velocities. The distributions of the auto-correlation coefficients and the energy spectra appear to be similar for both the longitudinal and transversal components of the velocities, whereas the corrected meso-scale energy spectrum increases with decreasing wave number and is approximately proportional to *k*
^{−2} in the range between 10^{−1} cycles km^{−1}.

An analysis is also made of the distribution of the Richardson number in a cross section perpendicular to the jet stream. A good relationship is found between the areas of turbulence and the regions of small Richardson number.

## Abstract

The wind velocities measured by an aircraft flying parallel and perpendicular to jet streams (Project Jet Stream, 1956–1957) have been analyzed; a smoothing technique has been used to separate the meso-scale turbulence from the mean flow. Eulerian auto-correlation coefficients and energy spectra are computed for the longitudinal and transversal components of the horizontal wind velocities. The distributions of the auto-correlation coefficients and the energy spectra appear to be similar for both the longitudinal and transversal components of the velocities, whereas the corrected meso-scale energy spectrum increases with decreasing wave number and is approximately proportional to *k*
^{−2} in the range between 10^{−1} cycles km^{−1}.

An analysis is also made of the distribution of the Richardson number in a cross section perpendicular to the jet stream. A good relationship is found between the areas of turbulence and the regions of small Richardson number.

## Abstract

The characteristics of the large-scale relative particle displacement tensor, the correlation functions, and spectra of the relative particle velocities at 10-, 30-, 50- and 100-mb levels are investigated; pertinent results concerning relative turbulence and diffusion at various levels in both troposphere and stratosphere are discussed and summarized. It is found that a quasi-stationary process exists in the large-scale turbulence diffusion in both the troposphere and stratosphere, the rate of relative particle dispersion being greatest in the tropopause level and generally proportional to the variance of the relative velocity. In general, the auto-correlation functions for the relative zonal velocities in both the troposphere and stratosphere behave like an exponentially decreasing function, whereas those for the relative meridional velocities shows a combination of an exponential function and a cosine function with a damping amplitude. The power spectra of the relative zonal velocities at all levels show the similar characteristics of increasing kinetic energy with decreasing frequency, whereas those of the relative meridional velocities show an energy peak near the frequency of 10^{−2} cycles hr^{−1}. The high frequency portion of the power spectra of both the zonal and meridional components of the relative velocities at all levels is found to be proportional to the minus third power of the frequency. The principal axis of the large-scale turbulent diffusion in the stratosphere is generally oriented ENE-WSW, whereas in the troposphere it is ESE-WNW.

## Abstract

The characteristics of the large-scale relative particle displacement tensor, the correlation functions, and spectra of the relative particle velocities at 10-, 30-, 50- and 100-mb levels are investigated; pertinent results concerning relative turbulence and diffusion at various levels in both troposphere and stratosphere are discussed and summarized. It is found that a quasi-stationary process exists in the large-scale turbulence diffusion in both the troposphere and stratosphere, the rate of relative particle dispersion being greatest in the tropopause level and generally proportional to the variance of the relative velocity. In general, the auto-correlation functions for the relative zonal velocities in both the troposphere and stratosphere behave like an exponentially decreasing function, whereas those for the relative meridional velocities shows a combination of an exponential function and a cosine function with a damping amplitude. The power spectra of the relative zonal velocities at all levels show the similar characteristics of increasing kinetic energy with decreasing frequency, whereas those of the relative meridional velocities show an energy peak near the frequency of 10^{−2} cycles hr^{−1}. The high frequency portion of the power spectra of both the zonal and meridional components of the relative velocities at all levels is found to be proportional to the minus third power of the frequency. The principal axis of the large-scale turbulent diffusion in the stratosphere is generally oriented ENE-WSW, whereas in the troposphere it is ESE-WNW.