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Peter R. Bannon

Abstract

A quasi-geostrophic model of cyclogenesis in the lee of the Rocky Mountains treats the cyclogenesis as a forecasting problem and uses an initial value approach. The model consists of the interaction of a growing baroclinic wave with an infinitely long mountain ridge. This transient interaction simulates many of the observed features of the phenomena, including the formation of a lee trough concurrent with the poleward displacement of the incident low on the upstream side of the mountain and the development of a lee cyclone equatorward of the unperturbed storm track. Despite this development, the low is weakened by its interaction with the orography.These results are explained physically and compared with those using a normal-mode approach to lee cyclogenesis.

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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

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

Several theories of the planetary boundary layer that retain the flow accelerations in approximate form are compared. Two special test cases focus on the role of either local or convective accelerations. The semigeotriptic theory of Cullen predicts the boundary layer pumping most accurately for the cases and parameter range considered here.

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Peter R. Bannon

Abstract

A Hamiltonian formulation for the dynamics and thermodynamics of a compressible, rotating, binary fluid subject to gravity is developed. Here, binary refers to the presence of two components of the fluid, such as solids dissolved in a liquid or gaseous and liquid water existing along with dry air. These fluids are idealized in that the influences of diffusion processes are ignored and the binary flow is restricted to a single velocity.

The equations are presented in generic form applicable to an arbitrary binary geophysical flow. The relevant Poisson bracket satisfies Jacobi's identity. Three distinct Casimir invariants are described. The first reflects the conservation of entropy and concentration of the minor component. The second is a consequence of the conservation of the absolute circulation on curves formed by the intersection of surfaces of constant entropy with surfaces of constant concentration. The third is a generic potential vorticity of the form (ω  ·  ∇λ)/ρ. Here, ω is the absolute vorticity, ρ is the total density of the fluid, and λ is any thermodynamic variable. For example, λ can be the pressure, density, temperature, or mixing ratio as well as the more common choice of potential temperature.

Available energy of the system is defined locally in the finite-amplitude as well as in the small-amplitude limit. Both definitions are partitioned into available potential and available elastic energies.

A linear stability analysis indicates that the fluid is statically stable provided the square of the sound speed is positive, the total density decreases with height, and the square of a suitably defined buoyancy frequency is positive.

The formulation is applicable to a salty ocean and to a moist atmosphere. For the atmosphere, the full theory holds in the presence of either liquid water or ice in equilibrium with its vapor.

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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

No abstract available.

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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

The prototype problem of hydrostatic adjustment for large-scale atmospheric motions is Presented. When a horizontally infinite layer of compressible fluid, initially at rest, is instantaneously heated, the fluid is no longer in hydrostatic balance since its temperature and pressure in the layer have increased while its density remains unchanged. The subsequent adjustment of the fluid is described in detail for an isothermal base-state atmosphere.

The initial imbalance generates acoustic wave fronts with trailing wakes of dispersive acoustic gravity waves. There are two characteristic timescales of the adjustment. The first is the transit time it takes an acoustic front to travel from the source region to a particular location. The second timescale, the acoustic cutoff frequency, is associated with the trailing wake. The characteristic depth scale of the adjustment is the density scale height. If the depth of the heating is small compared with the scale height, the final pressure perturbation tends to zero and the pressure field adjusts to the initial density hold. For larger depths, there is a mutual adjustment of the pressure and density fields.

Use of the one-dimensional analogue of the conservation of Ertel's potential vorticity removes hydrostatic degeneracy and determines the final equilibrium state directly. As a result of the adjustment process, the heated layer has expanded vertically. Since the region below the layer is unaltered, the region aloft is displaced upward uniformly. As a consequence of the expansion, the pressure and temperature anomalies in the layer are reduced from their initial values immediately after the heating. Aloft both the pressure and density fields are increased but there is no change in temperature. Since the base-state atmosphere is isothermal, warm advection is absent; since the vertical displacements of air parcels is uniform aloft, compressional warming is also absent.

The energetics of the adjustment are documented. Initially all the perturbation energy resides in the heated layer with a fraction γ−1 = 71.4% stored as available potential energy, while the remainder is available elastic energy, A fraction κ = R/Cp = (γ − 1)/&gamma = 28.6% of the initial energy is lost to propagating acoustic modes. Here γ = Cp/Cv is the ratio of the specific heats and R is the ideal gas constant. The remainder of the energy is partitioned between the heated layer and the region aloft. The energy aloft appears mostly as elastic energy, and the energy in the layer appears mostly as available potential energy.

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