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- Author or Editor: H. L. Kuo x

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## Abstract

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## Abstract

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## Abstract

On including a frictional drag proportional and opposite to the velocity of a rotating cylinder or vortex placed in a shearing current, it is found that the combined influence of the drag and the rotor force resulting from the net pressure acting on the cylinder (vortex) is to make the cylinder or vortex move in a mean direction at an angle to the mean flow, toward the right if the circulation& Γ around the cylinder is positive, and toward the left if Γ is negative. In addition, the center of the cylinder also undergoes an oscillatory motion about its mean path, and the period of this oscillation and the shape of the path depend both on Γ and on the mean current.

The analysis also shows that when the absolute vorticity of the basic flow is not uniform, another force in the direction of the vorticity gradient acts on the vortex, which tends to drive cyclonic vortices toward higher vorticity regions and anticyclonic vortices toward lower vorticity regions.

## Abstract

On including a frictional drag proportional and opposite to the velocity of a rotating cylinder or vortex placed in a shearing current, it is found that the combined influence of the drag and the rotor force resulting from the net pressure acting on the cylinder (vortex) is to make the cylinder or vortex move in a mean direction at an angle to the mean flow, toward the right if the circulation& Γ around the cylinder is positive, and toward the left if Γ is negative. In addition, the center of the cylinder also undergoes an oscillatory motion about its mean path, and the period of this oscillation and the shape of the path depend both on Γ and on the mean current.

The analysis also shows that when the absolute vorticity of the basic flow is not uniform, another force in the direction of the vorticity gradient acts on the vortex, which tends to drive cyclonic vortices toward higher vorticity regions and anticyclonic vortices toward lower vorticity regions.

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## Abstract

The three-dimensional flow in the boundary layer of a tornado-like vortex, with a core region of large vorticity and an outer region of nearly zero vorticity, is obtained by alternatingly solving the two nonlinear boundary-layer equations for the radial and the vertical distributions of the velocities. It is found that in the inner region the flow is of the Ekman-layer type, with an oscillatory distribution of the velocities in the vertical, while in the outer region the flow is of the ordinary boundary-layer type, with the velocity components approaching their respective values asymptotically without oscillation at a large distance from the boundary. This distribution of the radial velocity results in a weak descending motion in the outer region and a relatively strong ascending motion in the inner region with a sharp maximum upward motion occurring inside the radius of the maximum tangential wind where the boundary-layer thickness increases most rapidly outward.

## Abstract

The three-dimensional flow in the boundary layer of a tornado-like vortex, with a core region of large vorticity and an outer region of nearly zero vorticity, is obtained by alternatingly solving the two nonlinear boundary-layer equations for the radial and the vertical distributions of the velocities. It is found that in the inner region the flow is of the Ekman-layer type, with an oscillatory distribution of the velocities in the vertical, while in the outer region the flow is of the ordinary boundary-layer type, with the velocity components approaching their respective values asymptotically without oscillation at a large distance from the boundary. This distribution of the radial velocity results in a weak descending motion in the outer region and a relatively strong ascending motion in the inner region with a sharp maximum upward motion occurring inside the radius of the maximum tangential wind where the boundary-layer thickness increases most rapidly outward.

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## Abstract

The thermal interaction between the atmosphere and the underlying earth, as related to the diurnal heat wave, is investigated through the use of a modified virtual conduction model in which the influences of turbulence and thermal convection are simulated by diffusion while the influence of terrestrial radiation is approximated partly by diffusion and partly by a Newtonian cooling, the ratio between the two parts increasing from summer to winter. The virtual thermal diffusivity is assumed to vary both in time and in space in order to represent the various physical processes involved in accomplishing the actual heat transfer. It is shown that a mean upward transport of heat is maintained through the diurnal variation of the transfer process although the mean lapse rate is stable, thereby removing a long-standing difficulty in evalutating the turbulent heat flux from the mean potential temperature distribution.

The solar energy received at the surface is found to be partitioned into the two media and to space in proportion to the effective heat capacities and the surface radiation factor; the former are defined as 1) the product of the respective heat capacity ρ*c _{p}
* and the square roots of the frequency

*q*and the thermal dffiusivity

*K*in case

*K*is constant, and 2) the product of ρ

*c*and the vertical gradient of

_{p}*K*when

*dK*/

*dz*is very large near the surface. Further, a large

*dK*/

*dz*tends to increase the attenuation rate and to reduce the time lag of the temperature wave, therefore tending to maintain a steep temperature gradient at the boundary. The effect of the terrestrial radiation at the surface is to increase the cooling rate in the afternoon and to reduce it during the night, thereby helping to shift the time of the temperature maximum forward.

The analysis also shows that the temperature wave in the lowest few hundred meters of the atmosphere is influenced appreciably by the absorption of the solar radiation and by the interactions between *K* and *T* waves, and this is especially so for the mean temperature. Comparison of the theoretical results with observations made at O'Neill in summer shows that the observed temperature wave in the first 500 m can be approximated closely by the solution corresponding to a *K* profile which increases from a small value (from 3–10 cm^{2} sec^{−1}) at the surface to about 10^{5} cm^{2} sec^{−1} at 10 m, and by consideration of the direct absorption of solar radiation and *K*–*T* interaction terms. The winter observations are approximated very closely by the solutions of the simple one-layer power law diffusivity models without consideration of the absorption of solar radiation and the interaction terms, provided a much larger surface value of the diffusivity is used. These results indicate that the transfer of terrestrial radiation is of importance at the surface in winter.

## Abstract

The thermal interaction between the atmosphere and the underlying earth, as related to the diurnal heat wave, is investigated through the use of a modified virtual conduction model in which the influences of turbulence and thermal convection are simulated by diffusion while the influence of terrestrial radiation is approximated partly by diffusion and partly by a Newtonian cooling, the ratio between the two parts increasing from summer to winter. The virtual thermal diffusivity is assumed to vary both in time and in space in order to represent the various physical processes involved in accomplishing the actual heat transfer. It is shown that a mean upward transport of heat is maintained through the diurnal variation of the transfer process although the mean lapse rate is stable, thereby removing a long-standing difficulty in evalutating the turbulent heat flux from the mean potential temperature distribution.

The solar energy received at the surface is found to be partitioned into the two media and to space in proportion to the effective heat capacities and the surface radiation factor; the former are defined as 1) the product of the respective heat capacity ρ*c _{p}
* and the square roots of the frequency

*q*and the thermal dffiusivity

*K*in case

*K*is constant, and 2) the product of ρ

*c*and the vertical gradient of

_{p}*K*when

*dK*/

*dz*is very large near the surface. Further, a large

*dK*/

*dz*tends to increase the attenuation rate and to reduce the time lag of the temperature wave, therefore tending to maintain a steep temperature gradient at the boundary. The effect of the terrestrial radiation at the surface is to increase the cooling rate in the afternoon and to reduce it during the night, thereby helping to shift the time of the temperature maximum forward.

The analysis also shows that the temperature wave in the lowest few hundred meters of the atmosphere is influenced appreciably by the absorption of the solar radiation and by the interactions between *K* and *T* waves, and this is especially so for the mean temperature. Comparison of the theoretical results with observations made at O'Neill in summer shows that the observed temperature wave in the first 500 m can be approximated closely by the solution corresponding to a *K* profile which increases from a small value (from 3–10 cm^{2} sec^{−1}) at the surface to about 10^{5} cm^{2} sec^{−1} at 10 m, and by consideration of the direct absorption of solar radiation and *K*–*T* interaction terms. The winter observations are approximated very closely by the solutions of the simple one-layer power law diffusivity models without consideration of the absorption of solar radiation and the interaction terms, provided a much larger surface value of the diffusivity is used. These results indicate that the transfer of terrestrial radiation is of importance at the surface in winter.

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## Abstract

The nature of slow oscillations in the coupled atmosphere–ocean system in equatorial regions is investigated with a coupled atmosphere–ocean model in which surface wind stress and surface latent heat flux and other heat inputs associated with SST variations created by upwelling and horizontal advection are taken as the mechanical and thermal coupling mechanisms. The flow in the stratified ocean is confined to the mixed top layer. Because of the large difference in the equivalent depths of the two media, two different scalings were used to investigate the coupling effects on the free oscillations in the two media. It is found that the fast moving gravity waves and mixed Rossby–gravity waves of the two media are almost unaltered by these couplings but the slowly moving Rossby waves are greatly modified by them. Specifically, upwelling SST changes make the frequency of the oceanic Rossby waves diminish, make those of zonal wavenumbers 1 and 2 move eastward, and destabilize some of the oceanic and many atmospheric modes. On the other hand, the E–W SST advection makes all the oceanic Rossby waves unstable, while N–S advection destabilizes both the oceanic and atmospheric Rossby waves. Under representative values of the coupling parameter, the most common periods of the significantly unstable disturbances are 60 to 110 days and 0.5, 1, 1.5 and 2 years, but a large number of others have periods in the 3–9 year range. Evidently, many of these disturbances will be involved in the nonlinear processes in ENSO.

The question whether Kelvin waves are also destabilized in the coupled model is also examined. The frequency equation for pure Kelvin waves shows that, under the effect of upwelling, the Kelvin waves become unstable and stationary when the coupling parameter is greater than the square of the zonal wavenumber. It is also found, however, that an unbalanced meridional pressure gradient is produced by the projection of the pure Kelvin wave in the other medium, and hence meridional velocities will always be produced in the coupled model and the frequency relation altered.

## Abstract

The nature of slow oscillations in the coupled atmosphere–ocean system in equatorial regions is investigated with a coupled atmosphere–ocean model in which surface wind stress and surface latent heat flux and other heat inputs associated with SST variations created by upwelling and horizontal advection are taken as the mechanical and thermal coupling mechanisms. The flow in the stratified ocean is confined to the mixed top layer. Because of the large difference in the equivalent depths of the two media, two different scalings were used to investigate the coupling effects on the free oscillations in the two media. It is found that the fast moving gravity waves and mixed Rossby–gravity waves of the two media are almost unaltered by these couplings but the slowly moving Rossby waves are greatly modified by them. Specifically, upwelling SST changes make the frequency of the oceanic Rossby waves diminish, make those of zonal wavenumbers 1 and 2 move eastward, and destabilize some of the oceanic and many atmospheric modes. On the other hand, the E–W SST advection makes all the oceanic Rossby waves unstable, while N–S advection destabilizes both the oceanic and atmospheric Rossby waves. Under representative values of the coupling parameter, the most common periods of the significantly unstable disturbances are 60 to 110 days and 0.5, 1, 1.5 and 2 years, but a large number of others have periods in the 3–9 year range. Evidently, many of these disturbances will be involved in the nonlinear processes in ENSO.

The question whether Kelvin waves are also destabilized in the coupled model is also examined. The frequency equation for pure Kelvin waves shows that, under the effect of upwelling, the Kelvin waves become unstable and stationary when the coupling parameter is greater than the square of the zonal wavenumber. It is also found, however, that an unbalanced meridional pressure gradient is produced by the projection of the pure Kelvin wave in the other medium, and hence meridional velocities will always be produced in the coupled model and the frequency relation altered.

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## Abstract

The parameterization scheme devised by the author in a previous study has been extended to include both deep cumulus convection and shallow convection and a more rigorous derivation is given. In this scheme, the amounts and the vertical distributions of the latent heat released and the sensible heat transported by the deep cumulus are expressed solely in terms of the temperature difference between the cloud and the environment and the convergence of moisture produced by the large-scale flow. It is shown that the often stressed heating by compression in the descending region is automatically taken into consideration in this formulation. A comparison between the calculated results and the observational data of Reed and Recker for the composite easterly wave show that they are in good agreement in the regions of low-level convergence.

A separate scheme is devised from the energy equations to represent the transports of heat and moisture by the shallow convection maintained by the thermal boundary layer.

## Abstract

The parameterization scheme devised by the author in a previous study has been extended to include both deep cumulus convection and shallow convection and a more rigorous derivation is given. In this scheme, the amounts and the vertical distributions of the latent heat released and the sensible heat transported by the deep cumulus are expressed solely in terms of the temperature difference between the cloud and the environment and the convergence of moisture produced by the large-scale flow. It is shown that the often stressed heating by compression in the descending region is automatically taken into consideration in this formulation. A comparison between the calculated results and the observational data of Reed and Recker for the composite easterly wave show that they are in good agreement in the regions of low-level convergence.

A separate scheme is devised from the energy equations to represent the transports of heat and moisture by the shallow convection maintained by the thermal boundary layer.

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## Abstract

A new model is constructed for the explanation of the several types of large-scale wave motions detected in the tropical troposphere and lower stratosphere through observational investigations. The model also attributes the origin of these disturbances to the CISK mechanism, but it operates with a period-dependent self-regulating process. This process is based on the consideration that the deep cumulus convection, organized by the convergence field of the wave disturbances in the conditionally unstable tropical atmosphere, works as an overturning process and hence requires a continuous supply of moisture through evaporation from the surface for their continued existence as a wave train. This suggests that, for waves with periods, τ shorter than a limiting value τ_{0} obtainable from the average evaporation rate, the available moisture for the particular wave is equal to the normal value multiplied by τ/τ_{0}. When this influence is taken into consideration, it is found that most of the large-scale disturbances observed in the tropical atmosphere can he identified with the most unstable waves.

It is also found that, when the influence of the vertical suction of the planetary boundary layer is included, especially when the normal stable stratification is taken into consideration, the symmetric mixed Rossby waves and Kelvin waves with periods of about 4–5 days become more prominent, while the antisymmetric waves with periods around 9 days grow faster than others. The wavelengths of these most favored disturbances are all in the vicinity of 10×10^{3} km. In addition, Kelvin waves of periods about 15 days and wavelengths about 10×10^{3} km also become prominent under the influence of the vertical suction of a neutral boundary layer.

## Abstract

A new model is constructed for the explanation of the several types of large-scale wave motions detected in the tropical troposphere and lower stratosphere through observational investigations. The model also attributes the origin of these disturbances to the CISK mechanism, but it operates with a period-dependent self-regulating process. This process is based on the consideration that the deep cumulus convection, organized by the convergence field of the wave disturbances in the conditionally unstable tropical atmosphere, works as an overturning process and hence requires a continuous supply of moisture through evaporation from the surface for their continued existence as a wave train. This suggests that, for waves with periods, τ shorter than a limiting value τ_{0} obtainable from the average evaporation rate, the available moisture for the particular wave is equal to the normal value multiplied by τ/τ_{0}. When this influence is taken into consideration, it is found that most of the large-scale disturbances observed in the tropical atmosphere can he identified with the most unstable waves.

It is also found that, when the influence of the vertical suction of the planetary boundary layer is included, especially when the normal stable stratification is taken into consideration, the symmetric mixed Rossby waves and Kelvin waves with periods of about 4–5 days become more prominent, while the antisymmetric waves with periods around 9 days grow faster than others. The wavelengths of these most favored disturbances are all in the vicinity of 10×10^{3} km. In addition, Kelvin waves of periods about 15 days and wavelengths about 10×10^{3} km also become prominent under the influence of the vertical suction of a neutral boundary layer.

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## Abstract

The formation of the intertropical convergence zone is attributed to the self-excitation of a large-scale, zonally symmetric disturbance in the conditionally unstable and convectively activated tropical atmosphere, and the nature of the disturbance is represented by a nonlinear quasigeostrophic model. The solutions are obtained by representing the space variations by Fourier series in the ascending region and exponential series in the descending region, and the coefficients are represented by power series of a small parameter defined in terms of the CISK parameter *B*. These solutions show that the circulation created is mainly a zonal wind system endowed with large horizontal shear in the ascending region, the major portion of which is independent of height when *B* is greater than twice the critical value of *B* and, consequently, the total wind is concentrated in the lower levels. Both the vertical and the horizontal profiles given by the theory resemble the available observed profiles closely. The vertical diffusion and radiative cooling coefficients needed by the theory are about 2-5 m^{2}sec^{−1} and 2×10^{−6}sec^{−1} respectively. The time development of the disturbance was analyzed by a second-order approximation. It is shown that the disturbance approaches its equilibrium amplitude asymptotically through damped oscillations.

## Abstract

The formation of the intertropical convergence zone is attributed to the self-excitation of a large-scale, zonally symmetric disturbance in the conditionally unstable and convectively activated tropical atmosphere, and the nature of the disturbance is represented by a nonlinear quasigeostrophic model. The solutions are obtained by representing the space variations by Fourier series in the ascending region and exponential series in the descending region, and the coefficients are represented by power series of a small parameter defined in terms of the CISK parameter *B*. These solutions show that the circulation created is mainly a zonal wind system endowed with large horizontal shear in the ascending region, the major portion of which is independent of height when *B* is greater than twice the critical value of *B* and, consequently, the total wind is concentrated in the lower levels. Both the vertical and the horizontal profiles given by the theory resemble the available observed profiles closely. The vertical diffusion and radiative cooling coefficients needed by the theory are about 2-5 m^{2}sec^{−1} and 2×10^{−6}sec^{−1} respectively. The time development of the disturbance was analyzed by a second-order approximation. It is shown that the disturbance approaches its equilibrium amplitude asymptotically through damped oscillations.

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## Abstract

When the temperature and pressure perturbations are taken into consideration in the boundary layer equations, the stable stratification is found to inhibit the steady, Ekman-type flow when the global Richardson number is of or exceeds order unity. This inhibiting influence of the stable stratification is mitigated greatly at middle and higher latitudes when the flow is oscillatory even at low frequency, but the boundary layer flow fades away at low latitudes.

When a surface temperature anomaly is present, the stratification also generates a thermally driven boundary layer flow. This flow increases toward the equator and with the global Richardson number. At the equator the surface friction tends to produce a downward velocity when the surface wind is westerly.

Under a normal stratification and the slipping lower boundary condition valid for natural flow, the maximum vertical velocity just above the surface boundary layer has an absolute maximum around latitude 10° and a minimum at the equator. This distribution of the lifting velocity can be used to explain the frequent occurrences of the intertropical convergence zone in this region and the lack of convective activities at the equator.

## Abstract

When the temperature and pressure perturbations are taken into consideration in the boundary layer equations, the stable stratification is found to inhibit the steady, Ekman-type flow when the global Richardson number is of or exceeds order unity. This inhibiting influence of the stable stratification is mitigated greatly at middle and higher latitudes when the flow is oscillatory even at low frequency, but the boundary layer flow fades away at low latitudes.

When a surface temperature anomaly is present, the stratification also generates a thermally driven boundary layer flow. This flow increases toward the equator and with the global Richardson number. At the equator the surface friction tends to produce a downward velocity when the surface wind is westerly.

Under a normal stratification and the slipping lower boundary condition valid for natural flow, the maximum vertical velocity just above the surface boundary layer has an absolute maximum around latitude 10° and a minimum at the equator. This distribution of the lifting velocity can be used to explain the frequent occurrences of the intertropical convergence zone in this region and the lack of convective activities at the equator.

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## Abstract

No abstract available.

## Abstract

No abstract available.