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Peter R. Bannon

Abstract

A barotropic, primitive equation model on an equatorial beta plane is used to investigate the transient behavior of the East African jet. Both analytic and numerical solutions provide insight into the jet response to a diurnal fluctuation in the friction coefficient over land and to temporal variations in the upstream (eastward) and southern boundary forcings.

Results indicate that the diurnal variation in the strength of the surface drag over land can account for the observed increase in the speed and westward shift of the jet core during the night. The observed large variations in the meridional wind just offshore and in the zonal wind field are not explained by the theory.

In contrast to the diurnal variations in the finestructure of the jet, time-dependent variations in the upstream and southern boundary forcings can produce changes in the large-scale features of the jet. For either type of transient perturbation, the change in the jet speed can be significant and may explain the observed jet surges. In the case of southern. boundary forcing, this result demonstrates that eastward propagating, middle-latitude disturbances can have a significant effect on the flow at the equator in the presence of an impermeable western boundary.

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Peter R. Bannon
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Peter R. Bannon

Abstract

The equations describing the dynamics and thermodynamics of cloudy air are derived using the theories of multicomponent fluids and multiphase flows. The formulation is completely general and allows the hydrometeors to have temperatures and velocities that differ from those of the dry air and water vapor. The equations conserve mass, momentum, and total thermodynamic energy. They form a complete set once terms describing the radiative processes and the microphysical processes of condensation, sublimation, and freezing are provided.

An equation for the total entropy documents the entropy sources for multitemperature flows that include the exchange of mass, momentum, and energy between the hydrometeors and the moist air. It is shown, for example, that the evaporation of raindrops in unsaturated air need not produce an increase in entropy when the drops are cooler than the air.

An expression for the potential vorticity in terms of the density of the moist air and the virtual potential temperature is shown to be the correct extension of Ertel's potential vorticity to moist flows. This virtual potential vorticity, along with the density field of the hydrometeors, can be inverted to obtain the other flow variables for a balanced flow.

In their most general form the equations include prognostic equations for the hydrometeors' temperature and velocity. Diagnostic equations for these fields are shown to be valid provided the diffusive timescales of heat and momentum are small compared to the dynamic timescales of interest. As a consequence of this approximation, the forces and heating acting on the hydrometeors are added to those acting on the moist air. Then the momentum equation for the moist air contains a drag force proportional to the weight of the hydrometeors, a hydrometeor loading. Similarly, the thermal energy equation for the moist air contains the heating of the hydrometeors. This additional heating of the moist air implies a diabatic loading for which the heating of the hydrometeors is realized by the moist air.

The validity of the diagnostic equations fails for large raindrops, hail, and graupel. In these cases the thermal diffusive timescales of the hydrometeors can be several minutes, and prognostic rather than diagnostic equations for their temperatures must be solved. However, their diagnostic momentum equations remain valid.

Anelastic and Boussinesq versions of the equations are also described.

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Peter R. Bannon

Abstract

This paper presents the linear solution to the initial value problem for the Eady model of baroclinic instability including condensational heating using a wave–CISK formulation with a uniform heating profile in the vertical. As in the dry case, the continuous spectrum completes the class of free mode solutions but is asymptotically stable. In the moist case, both the dry and the moist normal modes contribute to the solution to the initial value problem.

Analysis of the moist Eady dispersion relation indicates that the heating increases the growth rate and the wavenumber of the most unstable mode and of the short-wave cutoff. For all values of the heating amplitude, the growth rate is bounded, both wavenumbers are finite, and the very short waves are always stable. Shallow clouds, however, increase both wavenumbers more than deep clouds. For sufficiently large values of the heating amplitude, the free modes display unphysical behavior with steering levels either above the rigid-lid tropopause or below the ground. The absence of any free modes when the wind shear vanishes implies that no free, inviscid, quasi-geostrophic, wave–CISK disturbances exist on the f-plane.

The temporal and spatial structure of the most unstable moist Eady wave with shallow convective heating compares favorably to observations of intermediate scale disturbances on the Baiu front.

The Appendix treats the case of condensational heating from large-scale ascent in an atmosphere with a saturated layer.

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Peter R. Bannon

Abstract

The problem of quasi-geostrophic frontogenesis due to a horizontal deformation field is re-examined. Exact analytic solutions of all flow fields for all times are found for the case of a vertically semi-infinite, uniformly stratified, Boussinesq atmosphere. The imposed horizontal deformation field is assumed independent of height but may translate horizontally relative to the initial potential temperature distribution and to the variable bottom topography. Only straight, infinitely long fronts and ridge-like topographies are considered. The solutions in the absence of orography confirm and extend earlier investigations for surface and occluded fronts.

It is shown that the presence of monotonically sloping topography below a region of deformation leads to the formation of a surface discontinuity in potential temperature in the absence of an initial horizontal thermal gradient. The associated secondary circulation is the sum of a closed thermally direct and indirect component.

The analysis for a translating deformation field interacting with an isolated orographic feature yields many interesting features. A cyclone-anticyclone couplet initially forms over the high ground. The cyclonic low pressure disturbance of reduced static stability can descend the leeside of the mountain before the arrival of the deformation field. The cold anticyclone remains fixed over the orography. A surface front translating with the imposed deformation field experiences a reduction in static stability before and after its passage over the mountain. An increase in static stability occurs while the front is over the mountain. The horizontal temperature gradient of a cold front is temporarily weakened as it approaches the mountain and strengthened after climbing the mountain peak. The ageostrophic vertical deformation field associated with the mountain acts to retard and weaken a surface cold front and to tilt its frontal zone (i.e., axis of maximum horizontal potential temperature gradient) toward the vertical on the upslope side of the mountain. The converse holds on the downslope. The subsequent interaction of a surface cold front with the leeside orographic cyclone leads to an increase in the low-level baroclinicity.

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Peter R. Bannon

Abstract

Solutions for steady inviscid quasi- and semi-geostrophic flow over a mountain ridge on the f-plane are degenerate in the sense that an arbitrary constant mountain-parallel flow can be added to the solution. It is shown that consideration of the problem as an initial value one removes this degeneracy. The quasi-geostrophic results presented here for a semi-infinite atmosphere vary for different initial conditions according to whether the flow is Boussinesq, anelastic, or deep. We enumerate conditions for which a mountain drag and an upstream influence exists.

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Peter R. Bannon

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Dynamic explanations of mountain drag usually invoke viscous effects and/or wave momentum flux by either Rossby or internal gravity waves. This paper explores an alternative mechanism in terms of the unsteadiness of the incident flow. The reaction to acceleration (local time rate of change) of the flow put a stationary obstacle can manifest itself as a contribution to the drag on the flow.

A simple model provides an estimate of this acceleration reaction in a geophysically relevant context. The shallow-water flow of a periodic current around a right-circular cylinder is determined for subinertial periods and arbitrary rotational Froude number. The results of this prototype calculation support the hypothesis that acceleration reaction may provide a substantial contribution to the mountain drag exerted by mesoscale and synoptic-scale obstacles.

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Peter R. Bannon

Abstract

Deep quasi-geostrophic theory applies to large-scale flow whose vertical depth scale is comparable to the potential temperature scale height. The appropriate expression for the potential vorticity equation is derived from the general formulation due to Ertel. It is further shown that the potential temperature field on a lower boundary acts as a surface charge of potential vorticity.

Deep equivalent barotropic Rossby waves in the presence of a mean zonal wind exhibit an enhanced beta effect but a reduced phase speed. This behavior, analogous to that displayed in shallow water theory, arises due to the inclusion of compressibility effects in the deep theory. These results help clarify the applicability of shallow water theory to barotropic atmospheric flows.

A conceptual model of the role of a surface charge of potential vorticity gradient in generating a change in the relative vorticity of a fluid parcel is described.

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Peter R. Bannon

Abstract

A new derivation of local available energy for a compressible, multicomponent fluid that allows for frictional, diabatic, and chemical (e.g., phase changes) processes is presented. The available energy is defined relative to an arbitrary isothermal atmosphere in hydrostatic balance with uniform total chemical potentials. It is shown that the available energy can be divided into available potential, available elastic, and available chemical energies. Each is shown to be positive definite.

The general formulation is applied to the specific case of an idealized, moist, atmospheric sounding with liquid water and ice. The available energy is dominated by available potential energy in the troposphere but available elastic energy dominates in the upper stratosphere. The available chemical energy is significant in the lower troposphere where it dominates the available elastic energy. The total available energy increases with increasing water content.

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Peter R. Bannon

Abstract

An alternative derivation of the available energy for a geophysical fluid system is presented. It is shown that determination of the equilibrium temperature of the system by the minimization of an energy availability function is equivalent to that found by the vanishing of the entropy difference between the fluid and its equilibrium state. Applications to the atmosphere and the ocean are presented.

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