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- Author or Editor: G. Chimonas x
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Abstract
We show that a bivane anemometer or other elevation angle sensing device records a nonzero mean angle when responding to cross-correlated fluctuations in a mean wind. Our analysis shows how this mean offset can be used to derive the wind-aligned Reynolds stress directly.
This theory is applied to a historical data set. It is first shown that the prior derivation of a mean vertical wind component is erroneous, and then that reinterpretation of results in terms of the Reynolds stress response is consistent with other aspects of the record.
Abstract
We show that a bivane anemometer or other elevation angle sensing device records a nonzero mean angle when responding to cross-correlated fluctuations in a mean wind. Our analysis shows how this mean offset can be used to derive the wind-aligned Reynolds stress directly.
This theory is applied to a historical data set. It is first shown that the prior derivation of a mean vertical wind component is erroneous, and then that reinterpretation of results in terms of the Reynolds stress response is consistent with other aspects of the record.
Abstract
Second-order theory is formulated for a wave packet propagating in a stratified fluid, and the packet-scale flows in the system are examined. These large-scale flows originate from interactions between first-order field components with wavenumbers k and k + Δ, which force second-order motions with wavenumber Δ (large scale) as well as the more familiar harmonics. The perturbation method used produces second-order field equations in which by-products of the linearized wave packet fields appear as source terms. The large-scale part of this forced flow is extracted through a k space projection operation. This flow field is then obtained, first formally for a rather general system and then explicitly for a packet propagating in a simple model of the surface layer inversion. Flow within the body of the packet takes the form of a quasi-horizontal velocity field with a marked vertical shear structure. This flow is examined for consistency with steady-state assumptions and for stability with respect to local Kelvin-Helmholtz, wave formation. It appears that such flows can be unstable at physically realizable amplitudes, and this is suggested as a possible source of the turbulent laminae observed in atmospheric inversions.
Abstract
Second-order theory is formulated for a wave packet propagating in a stratified fluid, and the packet-scale flows in the system are examined. These large-scale flows originate from interactions between first-order field components with wavenumbers k and k + Δ, which force second-order motions with wavenumber Δ (large scale) as well as the more familiar harmonics. The perturbation method used produces second-order field equations in which by-products of the linearized wave packet fields appear as source terms. The large-scale part of this forced flow is extracted through a k space projection operation. This flow field is then obtained, first formally for a rather general system and then explicitly for a packet propagating in a simple model of the surface layer inversion. Flow within the body of the packet takes the form of a quasi-horizontal velocity field with a marked vertical shear structure. This flow is examined for consistency with steady-state assumptions and for stability with respect to local Kelvin-Helmholtz, wave formation. It appears that such flows can be unstable at physically realizable amplitudes, and this is suggested as a possible source of the turbulent laminae observed in atmospheric inversions.
Abstract
Observations of a severe form of rainband, which is comprised of a line of strong but shallow convection, suggest that the environment into which it moves is nearly neutrally stratified with respect to moist convection. A simple two-dimensional model of a severe rainband has been developed to explore how the cold air at the base of the rainband modifies local stability as it underruns the saturated surface layer. This dynamic lifting is found to have two distinct effects. First, the lifted fluid contains regions of absolute and conditional instability. Then it also reorganizes the midtroposphere into a sequence of elevated inversions set between unstable layers. This latter effect results from the intense “lee wave” response in the air flow. The elevated inversions would appear to cap the severe moist convection, establishing the rainband character rather than allowing the deep cellular convection of squall lines. The flow disturbances end abruptly at the steering level (a critical level for the waves), which appears to define the upper limit of the rainband activity.
Abstract
Observations of a severe form of rainband, which is comprised of a line of strong but shallow convection, suggest that the environment into which it moves is nearly neutrally stratified with respect to moist convection. A simple two-dimensional model of a severe rainband has been developed to explore how the cold air at the base of the rainband modifies local stability as it underruns the saturated surface layer. This dynamic lifting is found to have two distinct effects. First, the lifted fluid contains regions of absolute and conditional instability. Then it also reorganizes the midtroposphere into a sequence of elevated inversions set between unstable layers. This latter effect results from the intense “lee wave” response in the air flow. The elevated inversions would appear to cap the severe moist convection, establishing the rainband character rather than allowing the deep cellular convection of squall lines. The flow disturbances end abruptly at the steering level (a critical level for the waves), which appears to define the upper limit of the rainband activity.
Abstract
Small-scale (Kelvin-Helmholtz) shear instabilities usually display very little dispersion. However, investigations by Hazel reveal an anomalous modal structure when the length scales associated with the density and velocity gradients are sufficiently different. We examine this modal splitting, and discover two distinct families of small-scale waves. The mean phase velocities of the two families can be quite different. The result is of considerable interest in studies of nonlinear interactions among small-scale shear instabilities, since it greatly extends the phase speeds allowed to the resulting disturbances.
Abstract
Small-scale (Kelvin-Helmholtz) shear instabilities usually display very little dispersion. However, investigations by Hazel reveal an anomalous modal structure when the length scales associated with the density and velocity gradients are sufficiently different. We examine this modal splitting, and discover two distinct families of small-scale waves. The mean phase velocities of the two families can be quite different. The result is of considerable interest in studies of nonlinear interactions among small-scale shear instabilities, since it greatly extends the phase speeds allowed to the resulting disturbances.
Abstract
It has been suggested that the potential temperature of the tropical tropopause may be linked to the energy of air flowing into storms, and Previous studies have sought to correlate the subannual fluctuations of the two quantities. The formulations used in these studies also provide estimates of the mean tropopause potential temperatures, but such temperatures are much lower than the observed values. In this work we reexamine the problem. The earlier thermodynamic formulation is replaced by a more accurate form, and the appropriate humidity content of storm air is introduced and justified. The data now show that, averaged over the tropical ocean regions, the mean potential temperature of the tropopause is determined accurately and directly by the mean sea surface temperature. Continental conditions are significantly different and require further study. It appears desirable to undertake detailed investigations of the local relationship between surface storm conditions and tropopause characteristics.
Abstract
It has been suggested that the potential temperature of the tropical tropopause may be linked to the energy of air flowing into storms, and Previous studies have sought to correlate the subannual fluctuations of the two quantities. The formulations used in these studies also provide estimates of the mean tropopause potential temperatures, but such temperatures are much lower than the observed values. In this work we reexamine the problem. The earlier thermodynamic formulation is replaced by a more accurate form, and the appropriate humidity content of storm air is introduced and justified. The data now show that, averaged over the tropical ocean regions, the mean potential temperature of the tropopause is determined accurately and directly by the mean sea surface temperature. Continental conditions are significantly different and require further study. It appears desirable to undertake detailed investigations of the local relationship between surface storm conditions and tropopause characteristics.
Abstract
The stabilities of two model tropospheric jets are compared. The first jet is a simple, smooth, idealized profile governed by a single scale length of tropospheric dimensions. The second jet takes the first model flow and superimposes on it a localized deformation of much smaller scale. In this second model, the shears deriving from the small-scale structure provide the subcritical Richardson numbers that support instability. The two-scale model produces a much wider range of wave instabilities. Its Kelvin-Helmholtz waves span a wavenumber domain that is nearly two orders of magnitude wider than the domain of the one-scale model, while the gravity shear waves fill out into the small wavenumber areas of the stability diagrams. However, the growth rates of the instabilities displace significantly toward smaller scales in the two-scale model.
It is suggested that the two-scale model is probably geophysically more realistic, and removes the necessity for deep layers of subcritical Richardson numbers, making it more in agreement with radiosonde observations than are smooth one-scale models.
Abstract
The stabilities of two model tropospheric jets are compared. The first jet is a simple, smooth, idealized profile governed by a single scale length of tropospheric dimensions. The second jet takes the first model flow and superimposes on it a localized deformation of much smaller scale. In this second model, the shears deriving from the small-scale structure provide the subcritical Richardson numbers that support instability. The two-scale model produces a much wider range of wave instabilities. Its Kelvin-Helmholtz waves span a wavenumber domain that is nearly two orders of magnitude wider than the domain of the one-scale model, while the gravity shear waves fill out into the small wavenumber areas of the stability diagrams. However, the growth rates of the instabilities displace significantly toward smaller scales in the two-scale model.
It is suggested that the two-scale model is probably geophysically more realistic, and removes the necessity for deep layers of subcritical Richardson numbers, making it more in agreement with radiosonde observations than are smooth one-scale models.
Abstract
Upscale scattering of Kelvin-Helmholtz waves to gravity shear waves involves the nonlinear interaction of two Kelvin-Helmholtz waves with wavenumbers k and k′ to produce a wave with wavenumber k−k′. Calculations show that the process produces long-wavelength radiating gravity waves in atmospheric conditions that favor the Kelvin-Helmholtz instabilities. Both line and continuum evaluations are presented in the context of the unstable tropospheric jet. It is shown that even when the unstable shear in the jet is confined to a shallow sublayer, producing markedly small-scale Kelvin-Helmholtz instabilities, upscale scattering to the large-scale waves is an efficient process.
Abstract
Upscale scattering of Kelvin-Helmholtz waves to gravity shear waves involves the nonlinear interaction of two Kelvin-Helmholtz waves with wavenumbers k and k′ to produce a wave with wavenumber k−k′. Calculations show that the process produces long-wavelength radiating gravity waves in atmospheric conditions that favor the Kelvin-Helmholtz instabilities. Both line and continuum evaluations are presented in the context of the unstable tropospheric jet. It is shown that even when the unstable shear in the jet is confined to a shallow sublayer, producing markedly small-scale Kelvin-Helmholtz instabilities, upscale scattering to the large-scale waves is an efficient process.
Abstract
The thunderstorm solitary gust or bow wave, observed by Doviak and Ge, is examined from the viewpoint of boundary layer wave theory. It is concluded that all its well defined characteristics are consistently modeled as a bow wave of ducted atmospheric modes accompanying the traveling storm. Secondary features, such as the later onset of turbulence, the solitary echo in the radar return, and the apparent rarity of such events can also be understood through a bow wave model. It is also suggested that the radar echo return cannot be attributed to a homogeneous distribution of scattering centers, and more investigation into the actual scattering process is needed.
Abstract
The thunderstorm solitary gust or bow wave, observed by Doviak and Ge, is examined from the viewpoint of boundary layer wave theory. It is concluded that all its well defined characteristics are consistently modeled as a bow wave of ducted atmospheric modes accompanying the traveling storm. Secondary features, such as the later onset of turbulence, the solitary echo in the radar return, and the apparent rarity of such events can also be understood through a bow wave model. It is also suggested that the radar echo return cannot be attributed to a homogeneous distribution of scattering centers, and more investigation into the actual scattering process is needed.
Abstract
Pre-storm conditions are often characterized by an atmosphere in the presence of rather strong wind shears and a temperature inversion. The latter acts as a lid for moisture in the boundary layer. In this paper we discuss the possibility that a gravity wave generated by wind shear can reach sufficiently large amplitude to induce condensation. We show that under certain circumstances the ensuing heat release takes place in such a phase with respect to the initial gravity wave so as to reinforce it, substantially increasing its rate of growth. Thus, the lifting due to the wave will grow and so will the condensation. By showing that in the early stages after the first condensation occurs, we have a positive feedback between the gravity wave and the induced condensation, we strengthen the case for gravity waves as possible lifting agents leading to condensation and eventually to convection. The present calculations are not meant to describe the system after the onset of convection and as such they differ from existing CISK theories. The results also appear to indicate that the presence of a critical level in the region of large relative humidity may be a prerequisite for a strong feedback between the gravity wave and the induced condensation.
Abstract
Pre-storm conditions are often characterized by an atmosphere in the presence of rather strong wind shears and a temperature inversion. The latter acts as a lid for moisture in the boundary layer. In this paper we discuss the possibility that a gravity wave generated by wind shear can reach sufficiently large amplitude to induce condensation. We show that under certain circumstances the ensuing heat release takes place in such a phase with respect to the initial gravity wave so as to reinforce it, substantially increasing its rate of growth. Thus, the lifting due to the wave will grow and so will the condensation. By showing that in the early stages after the first condensation occurs, we have a positive feedback between the gravity wave and the induced condensation, we strengthen the case for gravity waves as possible lifting agents leading to condensation and eventually to convection. The present calculations are not meant to describe the system after the onset of convection and as such they differ from existing CISK theories. The results also appear to indicate that the presence of a critical level in the region of large relative humidity may be a prerequisite for a strong feedback between the gravity wave and the induced condensation.
Abstract
We present the results of an analytical and numerical calculation of the interaction between an internal gravity wave and a wave-induced turbulence. The initial atmospheric state, assumed horizontally homogeneous, is statically and dynamically stable with the background Richardson number Ri0 approaching ¼ over some height regions. An initial non-singular neutral gravity wave propagates through such a system and modifies the Richardson number. The new Richardson number Ri may become smaller than ¼ and turbulence may develop. Using a “1½th order” scheme for the turbulence, we calculate the mean and the fluctuating part of the eddy diffusion coefficient. We show that the fluctuating part of the diffusion coefficient, because of its amplitude and phase, may overcome the damping effect of its mean part and force the original wave to grow in time. As the wave grows, it may further lower the Richardson number, increase the intensity of the turbulence, and further strengthen its interaction with it. At least in its initial stages, wave-induced turbulence appears to be an effective mechanism for transfer of energy from the background state into the wave. By showing that the early stages of the wave-induced turbulence interaction can lead to energy being transferred into the wave, we strengthen the case for gravity waves as important elements in the generation of turbulence in the atmosphere. The values we obtain for the eddy diffusion coefficients suggest that the process is quite capable of producing the empirically observed mixing rates at substantial heights above the ground. While the present calculations cannot describe the long-time limit of the wave-turbulence system, one may suggest that the often observed atmospheric conditions in which turbulence and waves appear to co-exist for several hours may result from a sort of equilibrium between the roles of the mean and the fluctuating parts of the eddy diffusion coefficient in taking away from and feeding energy into the wave.
Abstract
We present the results of an analytical and numerical calculation of the interaction between an internal gravity wave and a wave-induced turbulence. The initial atmospheric state, assumed horizontally homogeneous, is statically and dynamically stable with the background Richardson number Ri0 approaching ¼ over some height regions. An initial non-singular neutral gravity wave propagates through such a system and modifies the Richardson number. The new Richardson number Ri may become smaller than ¼ and turbulence may develop. Using a “1½th order” scheme for the turbulence, we calculate the mean and the fluctuating part of the eddy diffusion coefficient. We show that the fluctuating part of the diffusion coefficient, because of its amplitude and phase, may overcome the damping effect of its mean part and force the original wave to grow in time. As the wave grows, it may further lower the Richardson number, increase the intensity of the turbulence, and further strengthen its interaction with it. At least in its initial stages, wave-induced turbulence appears to be an effective mechanism for transfer of energy from the background state into the wave. By showing that the early stages of the wave-induced turbulence interaction can lead to energy being transferred into the wave, we strengthen the case for gravity waves as important elements in the generation of turbulence in the atmosphere. The values we obtain for the eddy diffusion coefficients suggest that the process is quite capable of producing the empirically observed mixing rates at substantial heights above the ground. While the present calculations cannot describe the long-time limit of the wave-turbulence system, one may suggest that the often observed atmospheric conditions in which turbulence and waves appear to co-exist for several hours may result from a sort of equilibrium between the roles of the mean and the fluctuating parts of the eddy diffusion coefficient in taking away from and feeding energy into the wave.
