Albert Barcilon

Stochastic Dynamics of El Nino-Southern Oscillation*

A stochastically forced nonlinear dynamic model for El Nino-Southern Oscillation is advanced to explore the nature of the highly irregular ENSO cycle. The model physics includes nonlinear dynamics of the coupled ocean-atmosphere system, high-frequency stochastic forcing, and the annual forcing of a prescribed climato- logical basic state. The model irregular ENSO-like oscillation arises from three different origins: stochastic resonance, coupled nonlinear instability, and stochastic transition. When the basic state is stable, the stochastic forcing excites irregular oscillations by stochastic resonance. When the system is unstable and the coupled dynamics sustains a nonlinear oscillation (stable limit cycle), the stochastic forcing perturbs the deterministic trajectory of the limit cycle in the phase space, generating irregularities and modifying the oscillation period. When the system possesses multiequilibrium states, the stochastic forcing may render the system oscillatory by randomly switching the system between a warm and a cold stable steady state. The stochastic response depends not only on the nonlinear dynamic regimes of the ENSO system but also on the temporal structure (spectrum) and strength of the stochastic forcing. White and red noises are shown to be much more effective than band-limited white noises in stochastic resonance and in altering the characteristics of the nonlinear oscillation. The intraseasonal noise can alter the dominant period of intrinsic nonlinear oscillation, favoring biennial oscillation, especially when the intraseasonal forcing is modulated by the monsoon (annual) cycle. Stronger forcing yields an enhanced resonant oscillation with a prolonged period. A sufficiently strong white noise forcing, however, can destroy the nonlinear or resonant oscillation, leading to a Markovian process. The basic-state annual variation tends to enhance the resonant oscillation but reduces the oscillation period considerably in the marginally stable regime. The model results suggest that ENSO may arise from multimechanisms. The different mechanisms may be at work in various phases of the ENSO evolution, depending on the basic state and the nonlinear dynamics of the system. The monsoon may affect ENSO through modulation of intraseasonal stochastic forcing, enhancing the biennial component of ENSO.

Marginal instability in Taylor–Couette flows at a very high Taylor number

We report on a set of turbulent flow experiments of the Taylor type in which the fluid is contained between a rotating inner circular cylinder and a fixed concentric outer cylinder, focusing our attention on very large Taylor number values, i.e. \[ 10^3 \leqslant T/T_c \leqslant 10^5, \] where T c is the critical value of the Taylor number T for onset of Taylor vortices. At such large values of T , the turbulent vortex flow structure is similar to the one observed when T – T c is small and this structure is apparently insensitive to further increases in T . These flows are characterized by two widely separated length scales: the scale of the gap width which characterizes the Taylor vortex flow and a much smaller scale which is made visible by streaks in the form of a ‘herring-bone’-like pattern visible at the walls. These are conjectured to be Gortler vortices which arise as a result of centrifugal instability in the wall boundary layers. Ideas of marginal instability by which we postulate that both the Taylor and Gortler vortex structures are marginally unstable on their own scale seem to provide good quantitative agreement between predicted and observed Gortler vortex spacings.

Type B Cyclogenesis in a Zonally Varying Flow

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. T...

Dust devil formation

Abstract A review of the literature on observations of dust devils suggests that these whirls form like the rolling-up of a vertical vortex sheet when the stratification is slightly unstable. The linearized equations governing the stability of such flows are formulated. These are solved when the basic flow is a vertical vortex sheet in a fluid with uniform Brunt-Vaisala frequency. Also, the effects of a shear layer of finite width are considered. It is found how unstable stratification strongly intensifies the shear instability. Increase of stable stratification may decrease stability of some special disturbances.

On the two-dimensional, hydrostatic flow of a stream of moist air over a mountain ridge

Abstract The small perturbation of a steady, two-dimensional horizontal stream of a moist inviscid, Boussinesq fluid is treated analytically by use of an asymptotic method when a certain parameter ∊ is small and numerically by use of an iterative method for general values of ∊. This parameter is a measure of the difference between dry and wet adiabats in the model atmosphere, which is absolutely stable and which contains a moist layer near the ground. Vapour condenses (evaporates) where the vertical displacement of a fluid particle exceeds the ascent condensation level and the vertical motion is upward (downward). The condensation of vapour and release of latent heat are nonlinear phenomena which are treated, but otherwise the equations of motion and boundary conditions are linearized. We limit our attention to an airflow of uniform properties over a mountain ridge. The hydrostatic approximation is made. As a result, the horizontal wavelengths must be long compared to the vertical ones and lee waves are a...

Organized structures in turbulent Taylor-Couette flow

A simple mathematical model is constructed to describe the regime of flow, extending over a wide range of values of Taylor number, in which turbulent Taylor–Couette flow in the annular region between two coaxial circular cylinders is characterized by the coexistence of steady coherent motion on two widely separated scales. These scales of motion, corresponding to the gap width of the annular region and to a boundary-layer thickness, are each identified as the consequence of a centrifugal instability, and are described as Taylor vortices and Gortler vortices respectively. The assumption that both scales of motion are near marginal stability gives a closure to a pair of coupled eigenvalue problems, and the results of a linear analysis are shown to be in good agreement with many features of experimental observations.

A Theoretical and Experimental Model for a Dust Devil

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.

Low-Frequency Variability and Wavenumber Selection in Models with Zonally symmetric Forcing

Abstract The authors consider a two-layer quasigeostrophic model with linear surface drag and forcing that relaxes to a zonal baroclinically unstable equilibrium state consisting of a meridionally confined temperature gradient. It is observed that the most energetic wave in the time-mean climate has near zero frequency and is not driven by upscale nonlinear energy transfers. This wave has a zonal scale near the long-wave cutoff of the equilibrium state, and its energy balance is mainly between baroclinic generation and dissipation. This maintenance mechanism is different from that suggested by, β-plane, two-dimensional, and quasigeostrophic turbulence arguments and may be relevant to the dynamics of zonally asymmetric low-frequency variability in the atmosphere, particularly in the Southern Hemisphere.

Genesis of Mobile Troughs in the Upper Westerlies

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 propaga...

Moist stability of a baroclinic zonal flow with conditionally unstable stratification

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 Kuos 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 t...