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Albert Barcilon

Abstract

The flow field found in a steady, axially-symmetric, strong atmospheric vortex of the dust-devil type is considered. The meridional plane containing the axis of the vortex is divided into an inviscid region where an unstratified free-vortex flow prevails, a plate boundary layer region, a corner region, and an axial boundary layer region. All these regions are strongly linked by a meridional circulation cell. Each of these regions is considered in turn and a solution to the overall flow field is found by matching the flow conditions at the interface between two adjacent regions. Using this model one can predict some of the features found in a model where the inviscid flow is stratified. Finally, an experimental demonstration is discussed in which the fluid is given an unstable temperature stratification with height and a source of angular momentum. A vortex of the dust-devil type forms under certain conditions.

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Bin Wang and Albert Barcilon

Abstract

Cold season atmospheric observations of vacillation point to a wave-mean flow interaction of baroclinic, planetary waves with their mean flow, and the observational data show that wave 2 is the largest contributor to the energetics and the heat flux. To verify this hypothesis we present a weakly nonlinear analysis of the evolution of a single, most unstable Green mode interacting with mean zonal flow in the presence of internal and Ekman layer dissipations, the former being larger than the latter.

The derived amplitude equations for the wave and the mean fields transform into a Lorenz set of equations that admits stable, finite amplitude wave gates. No stable limit cycle or aperiodic solutions were found in the realistic parameter ranges that typify atmospheric winter conditions. When the system is disturbed away from these gable states, there is a monotonic or vacillators approach to equilibrium. Damped vacillation occurs when the internal dissipative time scale is longer than the efolding time scale of the inviscid, Green mode, a condition realized in the winter atmosphere. During the vacillation, due to the presence of the internal dissipation the tilt of the constant phase line may remain westward, and the horizontal he-at flux may be poleward throughout most of the cycle.

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Bin Wang and Albert Barcilon

Abstract

The moist stability of a midlatitude zonal flow with a conditionally unstable layer in the presence of an Ekman layer is investigated. The vertical velocity employed in a simplified Kuo's parameterization is sustained by baroclinic wave forcing, diabatic heating and Ekman pumping. A general dispersion relation and eigenfunction are derived analytically for a class of flows with various vertical heating profiles.

The moist unstable mode may be regarded as a baroclinic wave modified by the bulk effect of the convective heating, for which the fundamental dependences of the baroclinic growth rate on the Burger number and vertical shear remain qualitatively valid. Waves longer than the Rossby radius of deformation are not appreciably affected, while the shorter waves are significantly destablized by the convective heating. The growth rates and wavelengths of the most unstable modes are nonlinear functions of the averaged specific humidity of the moist layer, and there is an optimum specific humidity that minimizes the preferred wavelength, this value being proportional to the static stability for a representative heating profile. The quasi-geostrophic constraints and baroclinity appear to be decisive factors that suppress short waves and lead to a finite preferred wavelength.

The destabilizing effect of the convective heating is considerably enhanced by the reduction of the static stability. Among the other influential parameters that affect the growth rate, relatively lower cloud top and a deep moist layer have a profound effect an the stability. Because of the cooperative interactions between favorable factors, the simultaneous occurrence of several of the mechanisms listed above may produce explosive-like growth. The relatively shallow convention and the Ekman layer will slow down the wave propagation speed.

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Bin Wang and Albert Barcilon

Abstract

The weakly nonlinear evolutions of the Green and Charney waves are compared for two regimes: (1) when internal dissipation is the dominant dissipation; (2) when Ekman friction is the dominant dissipation.

When the Ekman dissipation is dominant, we obtain a large amplitude equilibrated wave state which depends upon the initial conditions but not upon the magnitudes of the dissipation; the steady wave features a barotropic structure, and does not transport heat in the meridional direction. In sharp contrast, when internal dissipation is dominant, a small amplitude, equilibrated wave state is found, which is independent of the initial conditions but depends on the magnitude of the internal dissipation. The steady wave exhibits a westward phase tilt and transports heat poleward by an amount proportional to the internal dissipation.

The presence of a large planetary vorticity gradient stabilizes the finite amplitude evolution of the planetary waves and leads to a stable equilibrium planetary wave state.

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Joseph Lau and Albert Barcilon

Abstract

We investigate the reflection and nonlinear interaction between the first and second harmonics of a two-dimensional Boussinesq wavetrain. Effects of topography are included, the depth departing from a constant in a finite region. It is found that topography can speed up or retard energy transfer between first and second harmonics. The reflection coefficient in the present context is significantly different from the one obtained by using linear theory. This is partly due to partitioning of energy between harmonics.

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Albert I. Barcilon

Abstract

The solution of buoyant jets in a calm stratified atmosphere is considered. The Morton model yields a set of differential equations that can be solved in a closed form in a phase space having for coordinates the integral with height of the mass flux, the mass flux, and the derivative with height of the mass flux. By using an approximate expression that relates the mass flux integral with height to a given height, we are able to transfer knowledge of the phase space solution to physical space.

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Richard L. Pfeffer and Albert Barcilon

Abstract

Drazin's (1972) weakly nonlinear theory of the self interaction of a single, slightly unstable, normal mode in a viscous, baroclinic fluid with a continuous density distribution is used to determine eddy fluxes of heat and eddy temperature variances as a function of rotation and internal thermal gradients. The calculations are applied to annulus experiments in that portion of the regular wave regime in which the observed flow is dominated by a single mode. V. Barcilon's (1964) linear theory for a viscous fluid is used for the purpose of mode selection at each point in dimensionless-parameter space. The geostrophic eddy heat flux and temperature variance are then determined from Drazin's lowest order nonlinear theory (which is a direct extension of Barcilon's theory).

It is found that the eddy beat flux and temperature variance depend upon internal thermal gradients at marginal stability and upon the distance of the point in dimensionless-parameter space from marginal stability for each mode. This result is different from those obtained from linear theory (e.g., by Green, 1970; Saltzman and Vernekar, 1971; Stone, 1972) but agrees in essence with that obtained by Hart (1974) from a nonlinear analysis of a two-layer model.

Numerical calculations from the theoretically derived formulas show that the eddy beat flux and temperature variance corresponding to each mode increase with increasing rotation rate when the imposed temperature contrast is held constant, but that there is an abrupt drop in the magnitude of both quantities when the wavenumber changes to the next higher integral value. Experimental evidence obtained by Pfeffer et al. (1978) verifies that real fluids behave in this way. Another feature observed in laboratory experiments and predicted by the theory is that at fixed rotation rate (or Taylor number) the eddy heat flux and the eddy temperature variance may be either larger or smaller at larger values of the imposed temperature contrast, depending on the location of the experiments in dimensionless-parameter space. If we think of seasons being brought about by changes in imposed temperature contrast at constant rotation rate, this result implies that only in certain regions of dimensionless-parameter space is winter (defined as the season with the highest imposed temperature contrast) the season with the largest eddy heat flux or eddy temperature variance.

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Terrence R. Nathan and Albert Barcilon

Abstract

Jin and Ghil demonstrate that for topographically resonant flow, low-frequency finite-amplitude oscillations may arise from wave–wave interactions and topographic form drag. Their model is extended to include a zonally asymmetric vorticity source, which is shown to interact with the perturbation field to produce zonally rectified wave fluxes that dramatically alter the Hopf bifurcation from stationary solutions to low-frequency oscillations. The frequency, intensity, and general character of these oscillations are shown to depend crucially upon the phasing and relative strength of the forcings.

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Jeffrey S. Whitaker and Albert Barcilon

Abstract

It is hypothesized that surface cyclogenesis in the Northern Hemisphere storm-track regions can be described by the structural modification of baroclinic wave packets traversing a zonally varying flow field. We test this hypothesis using a linear, quasigeostrophic model with a zonally varying basic state and zonally varying Ekman layer eddy viscosity. At midchannel, the basic state consists of a region of strong low-level baroclinicity and weak Ekman dissipation, surrounded by regions of weak low-level baroclinicity, strong Ekman dissipation, and enhanced low-level static stability. Eigenanalyses and initial-value integrations support this model of Type B cyclogenesis. The results can be summarized as follows:1) A disturbance initiated upstream of the midchannel baroclinic zone rapidly evolves into a wave packet with maximum amplitude near the tropopause. The wave packet undergoes a structural modification upon entering the low-level baroclinic zone, developing maximum amplitude at the surface. The storm track in this model results from the transient amplification and structural modification of wave packets passing through the midchannel baroclinic zone.2) The effective growth rate of the surface disturbance exceeds those of the most unstable mode of the zonally varying basic state, and of the most unstable mode of zonally homogeneous basic-state characteristic of the midchannel baroclinic zone.3) The transient evolution of the wave packet is a result of the superposition and interference between the many global eigenmodes with different structures and frequencies excited by the initial condition. The surface cyclogenesis can be interpreted as a local constructive interference between these eigenmodes.4) From a potential vorticity perspective, the evolution of the baroclinic wave packet is a two-stage process. Initially, the growth of upper-level disturbances results from the mutual interaction of potential vorticity anomalies near the tropopause and in the lower troposphere. After the wave packet enters the storm-track region, the growth of surface cyclones is associated with the interaction between tropospheric potential vorticity anomalies and surface-temperature anomalies.5) The addition of a simple parameterization of moist physics in the midchannel baroclinic zone does not significantly alter the initial stages of surface cyclogenesis, but results in a longer period of rapid development and a reduction in the characteristic scale of the disturbance.

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Jeffrey S. Whitaker and Albert Barcilon

Abstract

Stability calculations on basic-state velocity profiles representative of the preferred regions for the development of the upper-level disturbances active in Type B cyclogenesis show that conditions in these regions (weak low-level baroclinicity, large low-level static stability, and large surface roughness) are favorable for the growth of baroclinic waves with maximum amplitude near the tropopause. The structure of these waves compares favorably with observations of developing short-wavelength upper-level troughs in the atmosphere. Basic states characteristic of the storm track regions (strong low-level baroclinicity and small surface roughness) favor the development of baroclinic waves with maximum amplitude at the surface. The dynamics of both the surface-trapped and the upper-tropospheric waves can be interpreted concisely using concepts of potential vorticity. Based on these results, a possible mechanism for Type B cyclogenesis in the storm track regions is proposed that involves the propagation and structural modification of baroclinic wave packets in a zonally varying basic flow.

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