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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

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

Abstract

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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Peter R. Bannon
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Peter R. Bannon

Abstract

The final equilibrium state of Lamb's hydrostatic adjustment problem is found for finite amplitude heating. Lamb's problem consists of the response of a compressible atmosphere to an instantaneous, horizontally homogeneous heating. Results are presented for both isothermal and nonisothermal atmospheres.

As in the linear problem, the fluid displacements are confined to the heated layer and to the region aloft with no displacement of the fluid below the heating. The region above the heating is displaced uniformly upward for heating and downward for cooling. The amplitudes of the displacements are larger for cooling than for warming.

Examination of the energetics reveals that the fraction of the heat deposited into the acoustic modes increases linearly with the amplitude of the heating. This fraction is typically small (e.g., 0.06% for a uniform warming of 1 K) and is essentially independent of the lapse rate of the base-state atmosphere. In contrast a fixed fraction of the available energy generated by the heating goes into the acoustic modes. This fraction (e.g., 12% for a standard tropospheric lapse rate) agrees with the linear result and increases with increasing stability of the base-state atmosphere.

The compressible results are compared to solutions using various forms of the soundproof equations. None of the soundproof equations predict the finite amplitude solutions accurately. However, in the small amplitude limit, only the equations for deep convection advanced by Dutton and Fichtl predict the thermodynamic state variables accurately for a nonisothermal base-state atmosphere.

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Peter R. Bannon

Abstract

Barotropic simulations of the East African jet are extended to include the Arabian Sea branch of the flow and to allow for flow over the mountains of Africa. Large-scale mass source-sink forcing, present to the east of the model orography, drives the low-level circulation.

Many features of the southeast trades, cross-equatorial flow and southwest monsoon are simulated. Among them are the separation of the jet from the African highlands, a wind speed maximum over the Arabian Sea and a reinforcement of the southwest monsoon by the Arabian northerlies. Splitting of the jet over the Arabian Sea is not simulated.

Starting from a state of rest, a well-developed southwest monsoon is achieved in a week of simulated time. Inclusion of a prescribed Southern Hemisphere midlatitude disturbance excites a significant response in the cross-equatorial flow, even though flow is permitted over the African mountains. Downstream, the surges excite a response over both the Arabian Sea and the Bay of Bengal. The bay response lags that over the sea by one to two days and is a factor of 2 weaker. Despite the satisfaction of the necessary condition for barotropic instability, no signs of instability appear during the onset, surge or steady-state phases of the simulations.

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Peter R. Bannon

Abstract

The role of the ambient stratification in semigeostrophic surface frontogenesis is examined. Model fronts forming in regions of large static stability 1) are weaker, 2) are tilted more toward the horizontal, and 3) propagate more slowly toward the warm air than fronts forming in regions of small static stability.

These results are discussed in light of the differences between warm and cold fronts.

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