Search Results

You are looking at 11 - 20 of 54 items for

  • Author or Editor: Peter R. Bannon x
  • Refine by Access: All Content x
Clear All Modify Search
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.

Full access
Peter R. Bannon

Abstract

The effect of a vertical incident wind shear on rotating airflow over a mountain ridge is discussed physically from a variety of perspectives. The apparent paradox that the shear reduces both the vertical displacement of fluid parcels aloft and the mountain anticyclone is resolved. The importance of meridional displacements in representing the static stability field is also demonstrated.

Full access
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.

Full access
Peter R. Bannon

Abstract

No abstract available.

Full access
Peter R. Bannon

Abstract

The linear Eady model of baroclinic instability with the geostrophic momentum (GM) approximation is solved analytically in physical space and shown to be identical to linear three-dimensional semigeostrophic theory. Both the growth rates and the wavenumber of the short-wave cutoff are larger than those predicted by quasi-geostrophic (QG) theory. This behavior arises because the effective static stability is reduced in the GM case. These results are opposite to those using standard nongeostrophic (NG) theory, and the discrepancy increases with decreasing Richardson number. Energetically, the unstable GM normal modes enhance the conversion of available potential energy compared to the QG modes and also convert available kinetic energy to eddy kinetic energy. With regards to the structure of the unstable modes, the northward tilt with height in the GM case is more consistent with NG theory than is the QG solution which displays no meridional tilt.

Additional analysis addresses the effect of assuming that either the meridional or zonal component of the perturbation wind field is geostrophic.

Full access
Peter R. Bannon

Abstract

An examination of the anelastic equations of Lipps and Hemler shows that the approximation requires the temperature and potential temperature scale heights of the base state are large compared to the pressure and density scale heights. As a consequence the fractional changes of the temperature and potential temperature fields relative to their base state values are equivalent. Alternatively this equivalency requires that the ratio of the ideal gas constant to the specific heat capacity at constant pressure is small.

The anelastic equations are examined for their ability to conserve potential vorticity (PV). The equations are shown to be “PV correct” in the sense that they conserve potential vorticity in a manner consistent with Ertel's theorem and with the assumptions of the anelastic approximation.

The ability to conserve potential vorticity helps the anelastic system capture the integrated effect of the acoustic modes in Lamb's hydrostatic adjustment problem. This prototype problem considers the response of a stably stratified atmosphere to an instantaneous heating that is vertically confined but horizontally uniform. In the anelastic case, the state variables adjust instantaneously to be in hydrostatic balance with the potential temperature perturbation generated by the heating. The anelastic solutions for the pressure, density, and temperature fields are identical to those for the compressible case. In contrast there is a mutual adjustment of the pressure, density, and thermal fields in the compressible case, which is not instantaneous. The total energy in the final state for the two cases is the same.

The other versions of the anelastic approximation are examined for their PV correctness and for their ability to parameterize Lamb's acoustic hydrostatic adjustment process.

Full access
Peter R. Bannon

Abstract

The virtual temperature of a moist air parcel is defined as the temperature of a dry air parcel having the same mass, volume, and pressure. It is shown here that a virtual air parcel can be formed diabatically by warming the parcel to its virtual temperature while replacing its water vapor with the equivalent mass of dry air under isobaric, isochoric conditions. Conversely a saturated virtual air parcel can be formed diabatically by cooling the parcel to its saturated virtual temperature while replacing some of its dry air with the equivalent mass of water vapor under isobaric, isochoric conditions. These processes of virtualization can be represented on a vapor pressure–temperature diagram. This diagram facilitates the comparison of the relative density of two moist air parcels at the same pressure. The effects of liquid and/or solid water can also be included.

Full access
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.

Full access
Peter R. Bannon

Abstract

A new derivation of local available energy for a compressible, multicomponent fluid whose base state need not be one of rest that allows for frictional and diabatic processes is presented. The available energy is the sum of the kinetic energy and the available potential and available elastic energies. These energy contributions are defined relative to an arbitrary reference state that can be in motion. Invoking a Lagrangian perspective, it is natural to choose the reference state as the initial state of the parcel. Then the resulting energies are consistent with published formulas for single and binary compressible fluids under inviscid, adiabatic conditions.

When the parcel-theory assumption (that the pressure of the parcel is always that of the environment) is invoked, the available elastic energy is identically zero and a fluid parcel will conserve the sum of its kinetic and available potential energies for inviscid, adiabatic flow. In this case, the parcel's available potential energy is the departure of the parcel's static energy (i.e., the sum of its potential energy and enthalpy) from its initial value. Applications of the theory are made to inertial and symmetric instabilities. Typically the instability is characterized by an increase in kinetic energy at the expense of the available potential energy that becomes negative. In the inertial case, the available potential energy is the negative of the work done by the horizontal pressure gradient force. In the symmetric case, it is the negative of the work done by the horizontal pressure gradient force and the buoyancy force, and it is a modified form of the slantwise convective energy (SCAPE) that includes the work done by the transverse (i.e., perpendicular to the mean flow) Coriolis forces. A convenient method to determine the longitudinal (i.e., parallel to the mean flow) and transverse contributions to the kinetic energy is presented. For upright convection, the decrease in the parcel's available potential energy equals its convective available potential energy. Comparison to traditional energetics is made.

Full access
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.

Full access