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Peter R. Bannon and Pe-Cheng Chu

Abstract

Scale analysis indicates that five nondimensional parameters (R 0 2 ε, μ λ and kλ) characterize the disturbance generated by the steady flow of a uniform wind (U 0, V 0) incident on a mountain ridge of width a in an isothermal, uniformly rotating, uniformly stratified, vertically semi-infinite atmosphere. Here μ = h 0/H R is the ratio of the mountain height h 0 to the deformation depth H R = fa/N where f is the Coriolis parameter and N is the static buoyancy frequency. The parameters λ = H R/H and kλ are the ratios of HR to the density scale height H and the potential temperature scale height H/k respectively. There are two Rossby numbers: One based on the incident flow that is parallel to the mountain. ε = V 0/fa, and one normal to the mountain, R 0 = U 0/fa. If R 0 2 ≪1, then the mountain-parallel flow is in approximate geostrophic balance and the flow is semigeostrophic.

The semigeostrophic case reduces to the quasi-geostrophic one in the limit as μ and ε tend to zero. If the flow is Boussinesq (λ = 0), then the semigeostrophic solutions expressed in a streamfunction coordinate can be derived from the quasi-geostrophic solutions in a geometric height coordinate.

If the flow is anelastic (λ ≈ 1), no direct correspondence between the two approximations was found. However the anelastic effects are qualitatively similar for the two and lead to: (i) an increase in the strength of the mountain anticyclone, (ii) a reduction in the extent (and possible elimination) of the zone of blocked, cyclonic flow, (iii) a permanent turning of the flow proportional to the mass of air displaced by the mountain, and (iv) an increase in the ageostrophic cross-mountain flow. The last result implies an earlier breakdown of semigeostrophic theory for anelastic flow over topography.

Apart from a strengthening of the cold potential temperature anomaly over the mountain, the presence of a finite potential temperature scale height (i.e., k nonzero) does not significantly alter the flow solution.

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Glenn M. Auslander and Peter R. Bannon

Abstract

This study examines the diurnal response of a mixed-layer model of the dryline system to localized anomalies of surface heat flux, topography, mixed-layer depth, and inversion strength. The two-dimensional, mixed-layer model is used to simulate the dynamics of a cool, moist layer east of the dryline capped by an inversion under synoptically quiescent conditions. The modeled domain simulates the sloping topography of the U.S. Great Plains. The importance of this study can be related to dryline bulges that are areas with enhanced convergence that may trigger convection in suitable environmental conditions.

All anomalies are represented by a Gaussian function in the horizontal whose amplitude, size, and orientation can be altered. A positive, surface-heat-flux anomaly produces increased mixing that creates a bulge toward the east, while a negative anomaly produces a westward bulge. Anomalies in topography show a similar trend in bulge direction with a peak giving an eastward bulge, and a valley giving a westward bulge. Anomalies in the initial mixed-layer depth yield an eastward bulge in the presence of a minimum and a westward bulge for a maximum. An anomaly in the initial inversion strength results in a westward bulge when the inversion is stronger, and an eastward bulge when the inversion is weak. The bulges observed in this study at 1800 LT ranged from 400 to 600 km along the dryline and from 25 to 80 km across the dryline.

When the heating ceases at night, the entrainment and eastward movement of the line stops, and the line surges westward. This westward surge at night has little dependence on the type of anomaly applied. Whether a westward or eastward bulge was present at 1800 LT, the surge travels an equal distance toward the west. However, the inclusion of weak nocturnal friction reduces the westward surge by 100 to 200 km due to mechanical mixing of the very shallow leading edge of the surge.

All model runs exhibit peaks in the mixed-layer depth along the dryline at 1800 LT caused by enhanced boundary layer convergence and entrainment of elevated mixed-layer air into the mixed layer. These peaks appear along the section of the dryline that is least parallel to the southerly flow. They vary in amplitude from 4 to 9 km depending on the amplitude of the anomaly. However, the surface-heat-flux anomalies generally result in peaks at the higher end of this interval. It is hypothesized that the formation of these peaks may be the trigger for deep convection along the dryline in the late afternoon.

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Paul F. Fanelli and Peter R. Bannon

Abstract

A nonlinear, numerical model of a compressible atmosphere is used to simulate the hydrostatic and geostrophic adjustment to a localized prescribed heating applied over five minutes with a size characteristic of an isolated, deep, cumulus cloud. This thermal forcing generates both buoyancy waves and a horizontally propagating Lamb wave packet as well as a steady state rich in potential vorticity. The adjustments in three model atmospheres (an isothermal, a constant lapse rate, and one with a stratosphere) are studied.

The Lamb wave packet and the two lowest-order buoyancy waves are relatively unaffected by nonlinearities but the higher-order modes and the steady state are. The heating generates a vertically stacked dipole of potential vorticity with a cyclonic perturbation below an anticyclonic perturbation. In contrast to the linear results, the nonlinear dipole is severely distorted by vertical and horizontal advections. In addition, the Lamb wave packet contains some weak positive perturbation potential vorticity.

The energetics is examined using traditional and Eulerian available energetics. Traditional energetics consists of kinetic, internal, and potential energies. It is shown that the Lamb wave packet contains more total traditional energy than that input to the atmosphere by the heating. The traditional energy in the packet resides primarily in the form of internal energy and only secondarily in the form of potential energy. The passage of the Lamb wave packet produces an atmosphere that, overall, is cooler, less dense, and with less total traditional energy than the initial atmosphere. Eulerian available energetics consists of kinetic, available potential, and available elastic energies. The heating generates both available elastic and potential energy that is then converted into kinetic energy. Most of the available elastic energy projects onto the Lamb packet, while almost all of the available potential energy is associated with the buoyancy waves and the steady state.

The effects of varying the spatial and temporal scale of the heating, while keeping the net heating the same, are examined. As the duration of the heating decreases, the amount of energy projected onto the waves increases. Increasing the size of the heating decreases the amount of energy projected onto the waves.

The adjustment is kinetically more vigorous in the nonisothermal atmospheres because of the reduction in the base-state static stability. The presence of a stratosphere produces large anomalies at and above the tropopause that are linked to the vertical motions of the buoyancy wave field.

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Richard D. Twigg and Peter R. Bannon

Abstract

The effect of friction on frontogenesis driven by a stretching deformation field is studied analytically in both a quasigeostrophic and a semigeostrophic framework for a semi-infinite, adiabatic, Boussinesq fluid on an f plane. Friction is incorporated into the model in terms of a boundary layer pumping term.

The solutions demonstrate that the effect of friction is frontolytic. The quasigeostrophic fronts always equilibrate at a finite horizontal scale. The semigeostrophic fronts equilibrate at a finite horizontal scale if the strength of the frontogenesis is below a threshold value. Above this threshold, the front is predicted to collapse to a discontinuity in its thermal and momentum fields.

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Peter R. Bannon and Joseph A. Zehnder

Abstract

Flow incident on a mountain ridge with a linear vertical windshear is studied for a Boussinesq, adiabatic, inviscid fluid on the f-plane. A scale analysis indicates that the semigeostrophic approximation of a geostrophic mountain-parallel wind holds for sufficiently shallow mountain slopes if the Rossby number squared is small. In such a limit, the equation for the vertical displacement of a fluid parcel is elliptic if there is forward shear (wind increasing with height) or weak backward shear (wind decreasing with height) but hyperbolic if there is strong backward shear such that the incident wind vanishes at some level in the flow.

Steady-state results indicate that forward shear weakens the cold-core geostrophic mountain anticyclone predicted by barotropic theory while weak backshear strengthens it. This behavior arises from the warm- (cold-) air advection in the forward (backward) shear case. While the total ageostrophic flux of mass across the mountain peak is greater for the forward shear case, the maximum ageostrophic cross-mountain wind is less.

Results for the semigeostrophic initial-value problem with a critical level depict the development of a stronger and narrower baroclinic lee trough than for quasi-geostrophic theory.

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Magda Luzimar de Abreu and Peter R. Bannon

Abstract

The world's driest coastal desert is in South America along the coasts of Peru and Chile. The desert's maintenance is investigated by studying the local dynamics of the low-level southerly flow along the coast. A linear boundary-layer model is used in which a Boussinesq atmosphere is driven by a surface thermal contrast on a β plane. The resting basic state is stably stratified. Constant mechanical and thermal diffusivities are assumed in the momentum and heat equations, respectively. The dynamics of the buoyancy field is governed by a three-dimensional eighth-order differential equation in which the meridional dependence enters parametrically. Results are shown for different values of the constants involved as well as for solutions on an f plane and a semigeostrophic β plane.

The results indicate that the effect of nonuniform rotation is responsible for the presence of subsidence along the coast and inland. This coastal subsidence helps maintain the desert by increasing the static stability and suppressing deep convection. The predicted vertical wind profiles agree well with the observations for Lima, Peru. Sensitivity tests indicate that the flow depends on the interplay between stratification, friction, and the Coriolis parameter and its variation (β). The mechanical frictional effects are mainly constrained to a shallow Ekman layer, whereas the thermal effects are manifested in deeper layers controlled by the β effect.

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Patrick A. Jones and Peter R. Bannon

Abstract

This study examines the diurnal behavior of the dryline system using a mixed-layer model to represent the cool moist air capped by an inversion to the east of the line. This inversion is referred to as the dry front, and the intersection of this dry front with the terrain is the dryline. The results indicate that boundary layer heating is sufficient to drive the dryline and explain its diurnal variation.

The daytime eastward propagation of the model dryline of 200 km agrees well with other numerical studies and is in approximate agreement with dryline observations. The present model results also indicate a nearly vertical inversion slope up to a height of 2 km in the early afternoon. Model simulations with sloping terrain consistently yield a nocturnal low-level jet between 0000 local time (LT) and 0100 LT, with a speed of 20–25 m s−1, located below the inversion.

The effect of each mixed-layer process, such as entrainment, surface heat flux, and nighttime cooling, is examined. Entrainment tends to steepen the slope of the dry front near the dryline but has little impact on its eastward advance. The dryline advance is most sensitive to the amplitude of the surface heat flux relative to the depth of the mixed layer and the strength of the inversion. Large heat fluxes, in combination with a shallow mixed layer and a weak inversion, produce the greatest dryline advance. The westward surge of the dryline at dusk is most sensitive to the amplitude of the nighttime cooling: larger cooling produces a larger surge.

The model simulations consistently predict a local maximum in the inversion height (called a spike) near the dryline at dusk associated with entrainment and boundary layer convergence. This process may be one of the possible triggers for the deep convection often seen just to the east of the dryline.

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Jeffrey M. Chagnon and Peter R. Bannon

Abstract

The adjustment of a compressible, stably stratified atmosphere to sources of hydrostatic and geostrophic imbalance is investigated using a linear model. Imbalance is produced by prescribed, time-dependent injections of mass, heat, or momentum that model those processes considered “external” to the scales of motion on which the linearization and other model assumptions are justifiable. Solutions are demonstrated in response to a localized warming characteristic of small isolated clouds, larger thunderstorms, and convective systems.

For a semi-infinite atmosphere, solutions consist of a set of vertical modes of continuously varying wavenumber, each of which contains time dependencies classified as steady, acoustic wave, and buoyancy wave contributions. Additionally, a rigid lower-boundary condition implies the existence of a discrete mode—the Lamb mode— containing only a steady and acoustic wave contribution. The forced solutions are generalized in terms of a temporal Green's function, which represents the response to an instantaneous injection.

The response to an instantaneous warming with geometry representative of a small, isolated cloud takes place in two stages. Within the first few minutes, acoustic and Lamb waves accomplish an expansion of the heated region. Within the first quarter-hour, nonhydrostatic buoyancy waves accomplish an upward displacement inside of the heated region with inflow below, outflow above, and weak subsidence on the periphery—all mainly accomplished by the lowest vertical wavenumber modes, which have the largest horizontal group speed. More complicated transient patterns of inflow aloft and outflow along the lower boundary are accomplished by higher vertical wavenumber modes. Among these is an outwardly propagating rotor along the lower boundary that effectively displaces the low-level inflow upward and outward.

A warming of 20 min duration with geometry representative of a large thunderstorm generates only a weak acoustic response in the horizontal by the Lamb waves. The amplitude of this signal increases during the onset of the heating and decreases as the heating is turned off. The lowest vertical wavenumber buoyancy waves still dominate the horizontal adjustment, and the horizontal scale of displacements is increased by an order of magnitude. Within a few hours the transient motions remove the perturbations and an approximately trivial balanced state is established.

A warming of 2 h duration with geometry representative of a large convective system generates a weak but discernible Lamb wave signal. The response to the conglomerate system is mainly hydrostatic. After several hours, the only signal in the vicinity of the heated region is that of inertia–gravity waves oscillating about a nontrivial hydrostatic and geostrophic state.

This paper is the first of two parts treating the transient dynamics of hydrostatic and geostrophic adjustment. Part II examines the potential vorticity conservation and the partitioning of total energy.

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Jeffrey M. Chagnon and Peter R. Bannon

Abstract

This second part of a two-part study of the hydrostatic and geostrophic adjustment examines the potential vorticity and energetics of the acoustic waves, buoyancy waves, Lamb waves, and steady state that are generated following the prescribed injection of heat into an isothermal atmosphere at rest. The potential vorticity is only nonzero for the steady class and depends only on the spatial and time-integrated properties of the injection. The waves contain zero net potential vorticity, but undergo a time-dependent vorticity exchange involving latent and relative vorticities.

The energy associated with a given injection may be partitioned distinctly among the various wave classes. The characteristics of this partitioning depend on the spatiotemporal detail of the injection, as well as whether the imbalance is generated by injection of heat, mass, or momentum. Spatially, waves of a scale similar to that of the injection are preferentially excited. Temporally, an extended duration injection preferentially filters high-frequency waves. An instantaneous injection, that is, the temporal Green’s function, contains the largest proportions of the high-frequency waves.

The proportions of kinetic, available elastic, and available potential energies that are carried by the various waves are functions of the homogeneous system. For example, deep buoyancy waves of small horizontal scale primarily contain equal portions of available potential and vertical kinetic energy. The steady state contains more available potential energy than kinetic energy at small horizontal scale, and vice versa. These qualities of the wave energetics illustrate the mechanisms that characterize the physics of each wave class.

The evolution and spectral partitioning of the energetics following localized warmings identical to those in Part I are presented in order to illustrate some of these basic properties of the energetics. For example, a heating lasting longer than a few minutes does not excite acoustic waves. However, Lamb waves of wide horizontal scale can be excited by a heating of several hours. The first buoyancy waves to be filtered by an extended duration heating are those of the deepest and narrowest structure that have a frequency approaching the buoyancy frequency. The energetics of the steady state depends only on the spatial and time-integrated properties of the warming. However, the energetics and transient evolution toward a given steady state depend on the temporal properties of the warming and may differ widely.

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Jonathan W. Smith and Peter R. Bannon

Abstract

The response to an instantaneous diabatic warming and the resulting hydrostatic and geostrophic adjustment in compressible and anelastic models is examined. The comparison of the models includes examining the initial conditions, time evolution, potential vorticity, and both the traditional and available energetics. Between the two models, the buoyancy flow fields and potential vorticity perturbations are qualitatively and quantitatively similar. Traditional and available energetics can both be accurately conserved within the models. There are some short-lived (e.g., several minutes) differences in the model solutions as the compressible model undergoes an acoustic adjustment that contains vertically propagating acoustic waves and horizontally propagating Lamb waves. The acoustic waves are effectively eliminated in an upper-level numerical sponge layer using Rayleigh damping. Moreover, the relative computational efficiency and accuracy of the two models are assessed.

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