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- Author or Editor: Earl E. Gossard x
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Abstract
Two theoretical models of shear layers in the atmosphere are examined. The conditions for their dynamic stability are found and their predictions of wavelength to layer-thickness ratio are compared with classical models and with available observational data. Although the models are only rigorously applicable to in-compressible fluids, it is suggested that they also represent conditions in the atmosphere, and clear-air returns published by Katz from the high-power pulse radar at Wallops Island are especially emphasized. Model 2 appears to be able to account for the narrow band characteristic of many of the observed events and also to explain better than other models the observed wavelength to layer-thickness ratios.
Abstract
Two theoretical models of shear layers in the atmosphere are examined. The conditions for their dynamic stability are found and their predictions of wavelength to layer-thickness ratio are compared with classical models and with available observational data. Although the models are only rigorously applicable to in-compressible fluids, it is suggested that they also represent conditions in the atmosphere, and clear-air returns published by Katz from the high-power pulse radar at Wallops Island are especially emphasized. Model 2 appears to be able to account for the narrow band characteristic of many of the observed events and also to explain better than other models the observed wavelength to layer-thickness ratios.
Abstract
The advent of Doppler clear-air radars for wind-height profiling opens the way for their use in a variety of other applications. This paper uses knowledge of the clear-air Doppler spectrum from a zenith-pointing radar together with the measured water droplet Doppler vertical velocity spectrum to calculate spectra of drop number density through clouds of droplets having substantial fall velocity. The method has been applied by Japanese scientist to measure drop-size distributions of precipitation particles from data acquired at the VHF MU radar facility. Here the method is applied to records obtained with a 915 MHz wind profiler located at Denver, Colorado, and the resulting spectra are presented and compared with the spectra that would have been obtained if the clear-air information were ignored. From the number density drop-size distribution, the corresponding liquid water distribution can be calculated. It is concluded that failure to take into account turbulence in the medium can result in order-of-magnitude errors in number density and liquid water. The requirements and limitations of a radar remote sensing drop spectrometer are discussed.
Abstract
The advent of Doppler clear-air radars for wind-height profiling opens the way for their use in a variety of other applications. This paper uses knowledge of the clear-air Doppler spectrum from a zenith-pointing radar together with the measured water droplet Doppler vertical velocity spectrum to calculate spectra of drop number density through clouds of droplets having substantial fall velocity. The method has been applied by Japanese scientist to measure drop-size distributions of precipitation particles from data acquired at the VHF MU radar facility. Here the method is applied to records obtained with a 915 MHz wind profiler located at Denver, Colorado, and the resulting spectra are presented and compared with the spectra that would have been obtained if the clear-air information were ignored. From the number density drop-size distribution, the corresponding liquid water distribution can be calculated. It is concluded that failure to take into account turbulence in the medium can result in order-of-magnitude errors in number density and liquid water. The requirements and limitations of a radar remote sensing drop spectrometer are discussed.
Abstract
A new technique is examined for using Doppler radars to extract information about the size spectrum of cloud droplets too small to have terminal velocities large enough to be resolvable by the radar. If the drops are very small, motions of the drops are dominated by turbulent fluctuations in the medium rather than their fall velocity. Their motion is then the convolution of the terminal velocity with the turbulent velocity probability density function, and size information about the population can be obtained only by deconvolving the spectra. Doppler radars can extract this velocity and size information, as well as cloud liquid and liquid flux, using a surprisingly simple and accurate technique assuming some functional form (e.g., gamma) for the drop number density spectrum. The method also allows Doppler radars to extract drop size information independent of up-/downdrafts in the medium in which they are embedded. Various gamma and lognormal functions are compared, and finally, a “Stokes range” of drop sizes is added and found to he important. Examples are shown and errors are discussed.
Abstract
A new technique is examined for using Doppler radars to extract information about the size spectrum of cloud droplets too small to have terminal velocities large enough to be resolvable by the radar. If the drops are very small, motions of the drops are dominated by turbulent fluctuations in the medium rather than their fall velocity. Their motion is then the convolution of the terminal velocity with the turbulent velocity probability density function, and size information about the population can be obtained only by deconvolving the spectra. Doppler radars can extract this velocity and size information, as well as cloud liquid and liquid flux, using a surprisingly simple and accurate technique assuming some functional form (e.g., gamma) for the drop number density spectrum. The method also allows Doppler radars to extract drop size information independent of up-/downdrafts in the medium in which they are embedded. Various gamma and lognormal functions are compared, and finally, a “Stokes range” of drop sizes is added and found to he important. Examples are shown and errors are discussed.
Seasonal charts of air-sea difference in refractive index are presented for the Mediterranean and Southeast Asia areas. The charts are discussed briefly in terms of the climatic regimes of the area, and applications to extended radar coverage are suggested.
Seasonal charts of air-sea difference in refractive index are presented for the Mediterranean and Southeast Asia areas. The charts are discussed briefly in terms of the climatic regimes of the area, and applications to extended radar coverage are suggested.
Abstract
This review begins with a brief look at the early perspectives on turbulence and the role of Dave Atlas in the unfolding of mysteries concerning waves and turbulence as seen by powerful radars. The remainder of the review is concerned with recent developments that have resulted in part from several decades of radar and Doppler radar profiler research that have been built upon the earlier foundation.
A substantial part of this review is concerned with evaluating the intensity of atmospheric turbulence. The refractivity turbulence structure-function parameter C 2 n , where n is radio refractive index, is a common metric for evaluating the intensity of refractivity turbulence and progress has been made in evaluating its climatology. The eddy dissipation rate is a common measure of the intensity of turbulence and a key parameter in the Kolmogorov theory for locally homogeneous isotropic turbulence. Much progress has been made in the measurement of the eddy dissipation rate under a variety of meteorological conditions including within clouds and in the presence of precipitation. Recently, a new approach using dual frequencies has been utilized with improved results.
It has long been recognized that atmospheric turbulence especially under hydrostatically stable conditions is nonhomogeneous and layered. The layering means that the eddy dissipation and eddy diffusivity is highly variable especially in the vertical. There is ample observational evidence that layered fine structure is responsible for the aspect sensitive echoes observed by vertically directed very high frequency VHF profilers. In situ observations by several groups have verified that coherent submeter-scale structure is present in the refractivity field sufficient to account for the “clear air” radar echoes. However, despite some progress there is still no consensus on how these coherent structures are produced and maintained.
Advances in numerical modeling have led to new insights by simulating the structures observed by radars. This has been done utilizing direct numerical simulation (DNS) and large eddy simulation (LES). While DNS is especially powerful for examining the breaking of internal waves and the transition to turbulence, LES had been especially valuable in modeling the atmospheric boundary layer.
Internal gravity waves occupy the band of intrinsic frequencies bounded above by the Brunt–Väisälä frequency and below by the inertial frequency. These waves have many sources and several studies in the past decade have improved our understanding of their origin. Observational studies have shown that the amplitude of the mesoscale spectrum of motions is greater over mountainous regions than over flat terrain or oceans. Thus, it would appear that flow over nonuniform terrain is an important source for waves. Several numerical studies have successfully simulated the generation of internal waves from convection. Most of these are believed to result from deep convection with substantial wave motion extending into the upper troposphere, stratosphere, and mesosphere. Gravity waves known as convection waves are often seen in the stable free atmosphere that overlay convective boundary layers.
Abstract
This review begins with a brief look at the early perspectives on turbulence and the role of Dave Atlas in the unfolding of mysteries concerning waves and turbulence as seen by powerful radars. The remainder of the review is concerned with recent developments that have resulted in part from several decades of radar and Doppler radar profiler research that have been built upon the earlier foundation.
A substantial part of this review is concerned with evaluating the intensity of atmospheric turbulence. The refractivity turbulence structure-function parameter C 2 n , where n is radio refractive index, is a common metric for evaluating the intensity of refractivity turbulence and progress has been made in evaluating its climatology. The eddy dissipation rate is a common measure of the intensity of turbulence and a key parameter in the Kolmogorov theory for locally homogeneous isotropic turbulence. Much progress has been made in the measurement of the eddy dissipation rate under a variety of meteorological conditions including within clouds and in the presence of precipitation. Recently, a new approach using dual frequencies has been utilized with improved results.
It has long been recognized that atmospheric turbulence especially under hydrostatically stable conditions is nonhomogeneous and layered. The layering means that the eddy dissipation and eddy diffusivity is highly variable especially in the vertical. There is ample observational evidence that layered fine structure is responsible for the aspect sensitive echoes observed by vertically directed very high frequency VHF profilers. In situ observations by several groups have verified that coherent submeter-scale structure is present in the refractivity field sufficient to account for the “clear air” radar echoes. However, despite some progress there is still no consensus on how these coherent structures are produced and maintained.
Advances in numerical modeling have led to new insights by simulating the structures observed by radars. This has been done utilizing direct numerical simulation (DNS) and large eddy simulation (LES). While DNS is especially powerful for examining the breaking of internal waves and the transition to turbulence, LES had been especially valuable in modeling the atmospheric boundary layer.
Internal gravity waves occupy the band of intrinsic frequencies bounded above by the Brunt–Väisälä frequency and below by the inertial frequency. These waves have many sources and several studies in the past decade have improved our understanding of their origin. Observational studies have shown that the amplitude of the mesoscale spectrum of motions is greater over mountainous regions than over flat terrain or oceans. Thus, it would appear that flow over nonuniform terrain is an important source for waves. Several numerical studies have successfully simulated the generation of internal waves from convection. Most of these are believed to result from deep convection with substantial wave motion extending into the upper troposphere, stratosphere, and mesosphere. Gravity waves known as convection waves are often seen in the stable free atmosphere that overlay convective boundary layers.
Abstract
The relationship between the variances of temperature and vertical velocity fluctuations is examined experimentally and theoretically. Comparison of the variance data and the mean gradient data recorded on the 300 m tower at the Boulder Atmospheric Observatory leads to the conclusion that the remotely sensed ratio of the temperature and velocity variances offers hope of measuring gradients of temperature and radar refractive index from ground-based acoustic or radar clear-air sounders. Relationships in which temperature gradient depends only on the ratio of the variances of temperature and vertical velocity are found both from the flux equation and from the energy budget/temperature variance equations. From the two independent relations, a theoretical expression for Prandtl number versus Richardson number is found for a limited range of Richardson numbers. Finally, the character and magnitude of the influence of the stress and conductivity terms are estimated from the linearized problem, and solutions are found in terms of eddy viscosity and conductivity.
Abstract
The relationship between the variances of temperature and vertical velocity fluctuations is examined experimentally and theoretically. Comparison of the variance data and the mean gradient data recorded on the 300 m tower at the Boulder Atmospheric Observatory leads to the conclusion that the remotely sensed ratio of the temperature and velocity variances offers hope of measuring gradients of temperature and radar refractive index from ground-based acoustic or radar clear-air sounders. Relationships in which temperature gradient depends only on the ratio of the variances of temperature and vertical velocity are found both from the flux equation and from the energy budget/temperature variance equations. From the two independent relations, a theoretical expression for Prandtl number versus Richardson number is found for a limited range of Richardson numbers. Finally, the character and magnitude of the influence of the stress and conductivity terms are estimated from the linearized problem, and solutions are found in terms of eddy viscosity and conductivity.
Abstract
When long-wavelength radars are used to observe the atmosphere, there are occasions when radar return from a volume of cloud is unexpectedly large relative to that predicted by the classical incoherent scatter from individual cloud droplets. The assumption of incoherence predicts the scattered power to be proportional to the inverse fourth power of the wavelength. The observed weaker wavelength dependence could result from Bragg-coherent scatter from the ensemble of droplets or it could result from an enhancement by the cloud of inhomogeneities in the dielectric constant of the gaseous medium within the cloud. Both mechanisms are discussed and compared with data acquired in a forward-scatter mode by two 3 cm wavelength radars of NOAA's Wave Propagation Laboratory. Observed differences between the in-cloud and out-of-cloud refractive index spectra are discussed and conclusions are suggested.
Abstract
When long-wavelength radars are used to observe the atmosphere, there are occasions when radar return from a volume of cloud is unexpectedly large relative to that predicted by the classical incoherent scatter from individual cloud droplets. The assumption of incoherence predicts the scattered power to be proportional to the inverse fourth power of the wavelength. The observed weaker wavelength dependence could result from Bragg-coherent scatter from the ensemble of droplets or it could result from an enhancement by the cloud of inhomogeneities in the dielectric constant of the gaseous medium within the cloud. Both mechanisms are discussed and compared with data acquired in a forward-scatter mode by two 3 cm wavelength radars of NOAA's Wave Propagation Laboratory. Observed differences between the in-cloud and out-of-cloud refractive index spectra are discussed and conclusions are suggested.
Abstract
The dynamic instability and the kinematics of a multi-layer, shear model of a convective boundary layer are analyzed. Important features of the model include a capping temperature inversion that may or may not be accompanied by a wind discontinuity, a surface-based superadiabatic layer, and a statically stable upper atmosphere. It is shown that the capping inversion can result in a relatively narrow band of dynamically unstable wavenumbers that depend on shear layer thickness, implying a strong selection of scale in growing disturbances. The influence of the various model parameters on selection of the “most unstable” scales is shown and their corresponding propagation velocities are calculated.
A simple form of the model is also used to examine the characteristics of the convectively unstable modes. It is found that two-dimensional disturbances aligned transverse to the wind shear are most dynamically unstable, whereas two-dimensional disturbances parallel to the wind shear are most convectively unstable.
The vorticity and general kinematics of the disturbances are affected in an important way by the presence of a critical level within the height range occupied by the disturbance.
Abstract
The dynamic instability and the kinematics of a multi-layer, shear model of a convective boundary layer are analyzed. Important features of the model include a capping temperature inversion that may or may not be accompanied by a wind discontinuity, a surface-based superadiabatic layer, and a statically stable upper atmosphere. It is shown that the capping inversion can result in a relatively narrow band of dynamically unstable wavenumbers that depend on shear layer thickness, implying a strong selection of scale in growing disturbances. The influence of the various model parameters on selection of the “most unstable” scales is shown and their corresponding propagation velocities are calculated.
A simple form of the model is also used to examine the characteristics of the convectively unstable modes. It is found that two-dimensional disturbances aligned transverse to the wind shear are most dynamically unstable, whereas two-dimensional disturbances parallel to the wind shear are most convectively unstable.
The vorticity and general kinematics of the disturbances are affected in an important way by the presence of a critical level within the height range occupied by the disturbance.
Abstract
A model having smooth wind and density profiles, for which a new solution of the Taylor-Goldstein equation can be found, is described. This model is particularly suitable for comparison with the analogous piecewise linear model so that the influence of “corners” in profiles can be judged. Such corners are found in models studied by Rayleigh, Goldstein, Taylor, Howard, Holmboe, and Gossard.
Abstract
A model having smooth wind and density profiles, for which a new solution of the Taylor-Goldstein equation can be found, is described. This model is particularly suitable for comparison with the analogous piecewise linear model so that the influence of “corners” in profiles can be judged. Such corners are found in models studied by Rayleigh, Goldstein, Taylor, Howard, Holmboe, and Gossard.
