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- Author or Editor: J. E. Geisler x

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## Abstract

A simple two-dimensional model is used to demonstrate the importance of the vertical distribution of latent heat release for the functioning of CISK, When the horizontal scale of the prescribed heat source in the model is small (100 km), substantial heating at low levels is required in order to bring the zone of boundary-layer convergence into coincidence with the heat source. This effect is much less important for a large-scale (1000 km) source. In addition, lowering the base of the heated region favors CISK by increasing the upward mass transport per unit of prescribed heat release.

## Abstract

A simple two-dimensional model is used to demonstrate the importance of the vertical distribution of latent heat release for the functioning of CISK, When the horizontal scale of the prescribed heat source in the model is small (100 km), substantial heating at low levels is required in order to bring the zone of boundary-layer convergence into coincidence with the heat source. This effect is much less important for a large-scale (1000 km) source. In addition, lowering the base of the heated region favors CISK by increasing the upward mass transport per unit of prescribed heat release.

## Abstract

In this paper we present results of a model study of the Walker Circulation defined as the steady response of a stratified atmosphere to an isolated equatorial heat source. The model equations are linearized with respect to a basic state of no motion and constant static stability. Cumulus friction provides the momentum damping. In the absence of cumulus friction, the center of the overturning in the equatorial plane is near 500 mb. With the addition of cumulus friction in an amount consistent with a zonally averaged precipitation of 2 m year^{−1}, the center is lowered to 600 mb. Cumulus friction in this amount also seems to provide reasonable amplitudes in the response. It is found that the branch of the overturning in the equatorial plane east of the heating is weaker than and has a larger longitudinal scale than the branch west of the heating. This asymmetry becomes more pronounced with a narrowing of the longitudinal width of the heat source. The mass flux in meridional overturnings is found to be comparable to that in the zonal overturnings. The pair of meridional cells to the west of the center of the heat source rotate in the same sense as the Hadley circulation, while the pair to the east of the center of the heat source rotate in the sense opposite to the Hadley circulation. It is suggested that the superposition of the eastern pair of cells and the Hadley cell should produce zones of low-level convergence parallel to the equator over the Pacific.

## Abstract

In this paper we present results of a model study of the Walker Circulation defined as the steady response of a stratified atmosphere to an isolated equatorial heat source. The model equations are linearized with respect to a basic state of no motion and constant static stability. Cumulus friction provides the momentum damping. In the absence of cumulus friction, the center of the overturning in the equatorial plane is near 500 mb. With the addition of cumulus friction in an amount consistent with a zonally averaged precipitation of 2 m year^{−1}, the center is lowered to 600 mb. Cumulus friction in this amount also seems to provide reasonable amplitudes in the response. It is found that the branch of the overturning in the equatorial plane east of the heating is weaker than and has a larger longitudinal scale than the branch west of the heating. This asymmetry becomes more pronounced with a narrowing of the longitudinal width of the heat source. The mass flux in meridional overturnings is found to be comparable to that in the zonal overturnings. The pair of meridional cells to the west of the center of the heat source rotate in the same sense as the Hadley circulation, while the pair to the east of the center of the heat source rotate in the sense opposite to the Hadley circulation. It is suggested that the superposition of the eastern pair of cells and the Hadley cell should produce zones of low-level convergence parallel to the equator over the Pacific.

## Abstract

The low-level circulation in summer over the western Indian Ocean is characterized by southeast trades that are channeled near the African coast into a concentrated southerly flow across the equator and thence north-eastward into the southwest monsoon over the Arabian Sea. It is widely accepted that deflection by the East African highlands is responsible for this flow configuration. Existing theoretical models to a greater or lesser extent, build in this deflection by imposing a western boundary extending all the way to the top of the fluid or by prescribing longitudinally dependent sources and sinks for driving the flow.

The purpose of this study is to determine what flow configuration occurs when these constraints are removed. For this we use zonally symmetric forcing to drive a planetary boundary layer model formulated in a terrain-following coordinate system that permits fluid to flow over as well as along, a topographic barrier. The results support the conclusion that East African topography alone can channel incident flow into a pattern with most of the observed features. An analysis of the diurnal oscillation in the model suggests a mechanism for the diurnal variation of low-level wind observed in northeastern Somalia.

## Abstract

The low-level circulation in summer over the western Indian Ocean is characterized by southeast trades that are channeled near the African coast into a concentrated southerly flow across the equator and thence north-eastward into the southwest monsoon over the Arabian Sea. It is widely accepted that deflection by the East African highlands is responsible for this flow configuration. Existing theoretical models to a greater or lesser extent, build in this deflection by imposing a western boundary extending all the way to the top of the fluid or by prescribing longitudinally dependent sources and sinks for driving the flow.

The purpose of this study is to determine what flow configuration occurs when these constraints are removed. For this we use zonally symmetric forcing to drive a planetary boundary layer model formulated in a terrain-following coordinate system that permits fluid to flow over as well as along, a topographic barrier. The results support the conclusion that East African topography alone can channel incident flow into a pattern with most of the observed features. An analysis of the diurnal oscillation in the model suggests a mechanism for the diurnal variation of low-level wind observed in northeastern Somalia.

## Abstract

A 5-day zonal wavenumber 1 oscillation has been well-documented from analysis of surface pressure data, and it has been suggested that it corresponds to the gravest symmetric low-frequency external normal mode of the atmosphere. Previous discussions of such global normal modes have assumed a basic state atmosphere at rest. In this investigation we solve linearized equations governing this mode in an atmosphere with a realistic distribution of zonal winds and including the surface temperature gradient in the lower boundary condition. Time-dependent solutions are obtained for zonal wavenumber 1 on a sphere using finite differences in the latitude-altitude plane. The frequency of symmetric forcing at the lower boundary is varied to find the resonant frequency of the gravest mode. In the presence of solstice zonal winds there is a large latitudinal asymmetry in the response in the upper stratosphere and in the mesosphere. An important feature of this asymmetry is relatively large amplitudes in the summer mesosphere. The amplitude of the temperature wave in the summer mesosphere is 10 K if the amplitude of the solution is scaled to give agreement with surface pressure observations and dissipation by Newtonian cooling is included in the calculation. The period of the mode is very little changed from its value for a basic state atmosphere at rest due to the fact that zonal winds and the temperature gradient at the lower boundary produce almost equal but opposite changes in period. Cancellation of the effects of zonal winds and lower boundary temperature gradient also appears to be responsible for the absence of a significant hemispheric asymmetry in mode structure in the troposphere and lower stratosphere. The time required for the mode to respond completely to lower boundary forcing is on the order of a month.

## Abstract

A 5-day zonal wavenumber 1 oscillation has been well-documented from analysis of surface pressure data, and it has been suggested that it corresponds to the gravest symmetric low-frequency external normal mode of the atmosphere. Previous discussions of such global normal modes have assumed a basic state atmosphere at rest. In this investigation we solve linearized equations governing this mode in an atmosphere with a realistic distribution of zonal winds and including the surface temperature gradient in the lower boundary condition. Time-dependent solutions are obtained for zonal wavenumber 1 on a sphere using finite differences in the latitude-altitude plane. The frequency of symmetric forcing at the lower boundary is varied to find the resonant frequency of the gravest mode. In the presence of solstice zonal winds there is a large latitudinal asymmetry in the response in the upper stratosphere and in the mesosphere. An important feature of this asymmetry is relatively large amplitudes in the summer mesosphere. The amplitude of the temperature wave in the summer mesosphere is 10 K if the amplitude of the solution is scaled to give agreement with surface pressure observations and dissipation by Newtonian cooling is included in the calculation. The period of the mode is very little changed from its value for a basic state atmosphere at rest due to the fact that zonal winds and the temperature gradient at the lower boundary produce almost equal but opposite changes in period. Cancellation of the effects of zonal winds and lower boundary temperature gradient also appears to be responsible for the absence of a significant hemispheric asymmetry in mode structure in the troposphere and lower stratosphere. The time required for the mode to respond completely to lower boundary forcing is on the order of a month.

## Abstract

No abstract available.

## Abstract

No abstract available.

## Abstract

This analysis treats the transient inertia-gravity wave response of a shallow fluid to an impulsive addition of momentum. The Coriolis parameter varies with latitude, but Rossby waves are not considered. The square of the Coriolis term is approximated by a constant term plus a term linear in the northward coordinate. In this approximation, monochromatic waves, which reach a turning point at the latitude where the wave frequency equals the local Coriolis frequency, are given by Airy functions. A contour integral solution to the initial value problem is expressed as a Fourier integral over wave frequency with an Airy function argument and is evaluated approximately using the stationary phase technique. The solution at a given latitude is first dominated by waves from the source and then waves reflected from turning points poleward of the source. The results are applied to give a qualitative description of the wake of a hurricane moving over a stratified ocean.

## Abstract

This analysis treats the transient inertia-gravity wave response of a shallow fluid to an impulsive addition of momentum. The Coriolis parameter varies with latitude, but Rossby waves are not considered. The square of the Coriolis term is approximated by a constant term plus a term linear in the northward coordinate. In this approximation, monochromatic waves, which reach a turning point at the latitude where the wave frequency equals the local Coriolis frequency, are given by Airy functions. A contour integral solution to the initial value problem is expressed as a Fourier integral over wave frequency with an Airy function argument and is evaluated approximately using the stationary phase technique. The solution at a given latitude is first dominated by waves from the source and then waves reflected from turning points poleward of the source. The results are applied to give a qualitative description of the wake of a hurricane moving over a stratified ocean.

## Abstract

This paper treats the initial value problem of a forced Rossby wave encountering a critical level in a barotropic zonal shear flow which can change in response to the wave momentum flux divergence. The main result of the calculation is that the shape of the zonal flow profile changes with time in such a way as to reduce the potential vorticity gradient (β−*U*
_{yy}) to zero at the critical level. For this configuration the wave is totally reflected at the critical level and in the absence of dissipation no longer interacts with the zonal flow. Details of the evolution toward the steady state depend on the ratio of two time scales, one a measure of the wave amplitude and the other representing the time it takes for the wave momentum flux to be concentrated in a well-defined critical layer.

The steady-state balance between wave and mean flow probably never occurs in the atmosphere because the time required to set it up is long compared to the expected time scale of natural variability of the zonal flow. More relevant to atmospheric flows is the fact that excursions of (β−*U*
_{yy}) to negative values during the approach to a steady state are attended by over reflection of the incident wave and a temporary reversal of the wave momentum flux. After the first of these excursions, occurring on a time scale comparable to that required to set up a critical layer, the zonal flow is never far from the final equilibrium profile.

## Abstract

This paper treats the initial value problem of a forced Rossby wave encountering a critical level in a barotropic zonal shear flow which can change in response to the wave momentum flux divergence. The main result of the calculation is that the shape of the zonal flow profile changes with time in such a way as to reduce the potential vorticity gradient (β−*U*
_{yy}) to zero at the critical level. For this configuration the wave is totally reflected at the critical level and in the absence of dissipation no longer interacts with the zonal flow. Details of the evolution toward the steady state depend on the ratio of two time scales, one a measure of the wave amplitude and the other representing the time it takes for the wave momentum flux to be concentrated in a well-defined critical layer.

The steady-state balance between wave and mean flow probably never occurs in the atmosphere because the time required to set it up is long compared to the expected time scale of natural variability of the zonal flow. More relevant to atmospheric flows is the fact that excursions of (β−*U*
_{yy}) to negative values during the approach to a steady state are attended by over reflection of the incident wave and a temporary reversal of the wave momentum flux. After the first of these excursions, occurring on a time scale comparable to that required to set up a critical layer, the zonal flow is never far from the final equilibrium profile.

## Abstract

The vertical motion field in the thermosphere is calculated from the continuity equation. This calculation is based on a field of horizontal winds and an intermediate model of the thermospheric temperature field consistent with the density structure inferred from satellite drag data. The vertical motion consists of a component due to rise and fall of constant pressure surfaces and a component due to horizontal maas divergences, both components being of the order of 1 m. sec.^{−1} Only the latter component is of importance for thermodynamic considerations. The adiabatic warming associated with the diurnally variable part of the vertical motion due to mass divergence gives a *second heat source* which is of magnitude comparable to the heating by solar radiation. The time-averaged meridional circulation also implies large adiabatic warming and cooling. This computed mean meridional circulation cannot be reconciled with the heat balance of the thermosphere. The thermospheric temperature field at low levels in high latitudes can be changed so as to reverse the direction of the mean meridional pressure gradient and thus to give a mean meridional circulation consistent with heat balance considerations. Existing global thermospheric models could be improved by adjustment of the temperature field at low levels in such a way that vertical motions computed from horizontal winds give a plausible adiabatic heating field.

## Abstract

The vertical motion field in the thermosphere is calculated from the continuity equation. This calculation is based on a field of horizontal winds and an intermediate model of the thermospheric temperature field consistent with the density structure inferred from satellite drag data. The vertical motion consists of a component due to rise and fall of constant pressure surfaces and a component due to horizontal maas divergences, both components being of the order of 1 m. sec.^{−1} Only the latter component is of importance for thermodynamic considerations. The adiabatic warming associated with the diurnally variable part of the vertical motion due to mass divergence gives a *second heat source* which is of magnitude comparable to the heating by solar radiation. The time-averaged meridional circulation also implies large adiabatic warming and cooling. This computed mean meridional circulation cannot be reconciled with the heat balance of the thermosphere. The thermospheric temperature field at low levels in high latitudes can be changed so as to reverse the direction of the mean meridional pressure gradient and thus to give a mean meridional circulation consistent with heat balance considerations. Existing global thermospheric models could be improved by adjustment of the temperature field at low levels in such a way that vertical motions computed from horizontal winds give a plausible adiabatic heating field.

## Abstract

Thermally driven flows in rotating laboratory containers with cylindrical geometry can he axially symmetric or they can be wavelike, depending on experimental parameters. In the traditional *regime diagram* of thermal Rossby number versus Taylor number the region of axially symmetric motion is separated from the regime of wavelike motion by a knee-shaped boundary. The simplest theoretical model that predicts the shape of this curve is due to Barcilon (1964) and consists of the Eady model of baroclinic instability applied to a rotating channel with Ekman layers at the top and bottom. Anticipating that rotating fluid experiments might soon be done in spherical shell geometry, we have extended Barcilon's model to a beta-plane channel. The purpose of our study is to predict with a simple model the changes which the beta-effect should produce in the shape and position of the boundary separating the regions of axially symmetric and wavelike motion.

## Abstract

Thermally driven flows in rotating laboratory containers with cylindrical geometry can he axially symmetric or they can be wavelike, depending on experimental parameters. In the traditional *regime diagram* of thermal Rossby number versus Taylor number the region of axially symmetric motion is separated from the regime of wavelike motion by a knee-shaped boundary. The simplest theoretical model that predicts the shape of this curve is due to Barcilon (1964) and consists of the Eady model of baroclinic instability applied to a rotating channel with Ekman layers at the top and bottom. Anticipating that rotating fluid experiments might soon be done in spherical shell geometry, we have extended Barcilon's model to a beta-plane channel. The purpose of our study is to predict with a simple model the changes which the beta-effect should produce in the shape and position of the boundary separating the regions of axially symmetric and wavelike motion.