Resonant Topographic Waves in Barotropic and Baroclinic Flows
01 Dec 1981-Journal of the Atmospheric Sciences (American Meteorological Society)-Vol. 38, Iss: 12, pp 2626-2641
TL;DR: In this paper, the problem of resonant, topographic quasi-geostrophic waves is examined analytically by exploiting simplifications that arise when the flow is nearly resonant.
Abstract: The problem of resonant, topographic quasi-geostrophic waves is examined analytically by exploiting simplifications that arise when the flow is nearly resonant. The barotropic and (two-layer) baroclinic problems are studied. In each case the topographic linear stability problem is solved explicitly and analytic expressions are given for the growth rate. The bifurcation problem in finite amplitude also is described. Some differences with earlier treatment are noted. In particular, in the barotropic problem subresonant instability may occur if the zonal wavelength is long enough. In both the barotropic and baroclinic problems the critical point at which multiple equilibria occur does not correspond to the stability thresholds of the linear problem. In the baroclinic problem Reynolds stresses are found to be of equal importance with eddy heat fluxes in altering the zonal flow although only the latter can transfer energy to the wave field for the zonal velocity profile considered. Analysis of the mar...
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TL;DR: A series of simulation experiments are presented in which assimilation of data is demonstrated into simple nonlinear models in which least-squares methods such as the (Extended)Kalman filter or the weak-constraint variational methods will not perform well.
Abstract: With very few exceptions, data assimilation methods which have been used or proposed foruse with ocean models have been based on some assumption of linearity or near-linearity. Thegreat majority of these schemes have at their root some least-squares assumption. While onecan always perform least-squares analysis on any problem, direct application of least squaresmay not yield satisfactory results in cases in which the underlying distributions are significantlynon-Gaussian. In many cases in which the behavior of the system is governed by intrinsicallynonlinear dynamics, distributions of solutions which are initially Gaussian will not remain soas the system evolves. The presence of noise is an additional and inevitable complicating factor.Besides the imperfections in our models which result from physical or computational simplifyingassumptions, there is uncertainty in forcing fields such as wind stress and heat flux which willremain with us for the foreseeable future. The real world is a noisy place, and the effects ofnoise upon highly nonlinear systems can be complex. We therefore consider the problem ofdata assimilation into systems modeled as nonlinear stochastic differential equations. When themodels are described in this way, the general assimilation problem becomes that of estimatingthe probability density function of the system conditioned on the observations. The quantitywe choose as the solution to the problem can be a mean, a median, a mode, or some otherstatistic. In the fully general formulation, no assumptions about moments or near-linearity arerequired. We present a series of simulation experiments in which we demonstrate assimilationof data into simple nonlinear models in which least-squares methods such as the (Extended)Kalman filter or the weak-constraint variational methods will not perform well. We illustratethe basic method with three examples: a simple one-dimensional nonlinear stochastic differentialequation, the well known three-dimensional Lorenz model and a nonlinear quasigeostrophicchannel model. Comparisons to the extended Kalman filter and an extension to the extendedKalman filter are presented. DOI: 10.1034/j.1600-0870.1999.t01-2-00002.x
217 citations
TL;DR: In this article, a modified cluster analysis method was developed to identify spatial patterns of planetary flow regimes, and to study transitions between them, applied first to a simple deterministic model and second to Northern Hemisphere (NH) 500 mb data.
Abstract: A modified cluster analysis method was developed to identify spatial patterns of planetary flow regimes, and to study transitions between them. This method was applied first to a simple deterministic model and second to Northern Hemisphere (NH) 500 mb data. The dynamical model is governed by the fully-nonlinear, equivalent-barotropic vorticity equation on the sphere. Clusters of point in the model's phase space are associated with either a few persistent or with many transient events. Two stationary clusters have patterns similar to unstable stationary model solutions, zonal, or blocked. Transient clusters of wave trains serve as way stations between the stationary ones. For the NH data, cluster analysis was performed in the subspace of the first seven empirical orthogonal functions (EOFs). Stationary clusters are found in the low-frequency band of more than 10 days, and transient clusters in the bandpass frequency window between 2.5 and 6 days. In the low-frequency band three pairs of clusters determine, respectively, EOFs 1, 2, and 3. They exhibit well-known regional features, such as blocking, the Pacific/North American (PNA) pattern and wave trains. Both model and low-pass data show strong bimodality. Clusters in the bandpass window show wave-train patterns in the two jet exit regions. They are related, as in the model, to transitions between stationary clusters.
205 citations
Cites methods from "Resonant Topographic Waves in Barot..."
...Bistable solutions to simple models of planetary flow over topography were obtained by Charney and DeVote [1979], Hart [1979], and Pedlosky [1981]. The relevance of bistability to low-frequency atmospheric variability was often interpreted to stand or fall by the discovery of such bimodality in NH winter data....
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TL;DR: In this article, a forced envelope Rossby soliton model was proposed to describe the interaction between an incipient block (planetary scale) and short synoptic-scale eddies.
Abstract: A new forced envelope Rossby soliton model in an equivalent barotropic beta-plane channel is proposed to describe the interaction between an incipient block (planetary scale) and short synoptic-scale eddies This model is based on two assumptions, motivated by observations that (i) there exists a zonal scale separation between the planetary-scale and synoptic-scale waves and (ii) that the range of synoptic-scale zonal wavenumber is comparable to the planetary-scale zonal wavenumber These assumptions allow an analytical treatment The evolution of the planetary-scale block under the influence of synoptic-scale eddies is described by a forced nonlinear Schrodinger equation that is solved numerically, while the feedback of block development on the preexisting synoptic-scale eddies is derived analytically It is shown that the planetary-scale projection of the nonlinear interaction between synoptic-scale eddies is the most important contributor to the amplification and decay of the planetary-scale b
122 citations
Cites background from "Resonant Topographic Waves in Barot..."
...The lateral boundary conditions at the two rigid walls are (Pedlosky 1981)...
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...…] ]c9 21 u (¹ c9 2 Fc9) 1 (b 1 Fu )0 01 2]t ]x ]x 2 2 25 2J(c9, ¹ c 1 h) 2 J(c, ¹ c9) 1 ¹ c*. (2b)S The lateral boundary conditions at the two rigid walls are (Pedlosky 1981) 2]c ] c 5 0, 5 0 at y 5 0, L , (3)y]x ]t]y where 5 limX→` (1/2X) c dx is the zonally avXc #2X eraged part of the…...
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...Finally, the bottom topography is considered to be wavy and h 5 «h9(x, y) is assumed in the quasigeostrophic regime (Pedlosky 1981)....
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...The bottom topography may be chosen to be of the following form (Pedlosky 1981) h9 5 h9 exp(ikx) sin(my/2) 1 c.c.,0 (10) where is the constant amplitude of the wavy topog-h90 raphy, k 5 2k0 is the zonal wavenumber of the wavenumber two topography, and m 5 22p/Ly....
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...The bottom topography may be chosen to be of the following form (Pedlosky 1981)...
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TL;DR: In this paper, experiments in a rotating annulus used radial pumping to generate a zonal jet under the action of the Coriolis force, and the resulting flows were nearly zonal at high forcing or blocked at low forcing.
Abstract: The mid-latitude atmosphere is dominated by westerly, nearly zonal flow. Occasionally, this flow is deflected poleward by blocking anticyclones that persist for 10 days or longer. Experiments in a rotating annulus used radial pumping to generate a zonal jet under the action of the Coriolis force. In the presence of two symmetric ridges at the bottom of the annulus, the resulting flows were nearly zonal at high forcing or blocked at low forcing. Intermittent switching between blocked and zonal patterns occurs because of the jet's interaction with the topography. These results shed further light on previous atmospheric observations and numerical simulations.
104 citations
TL;DR: In this paper, a model of atmospheric circulation able to describe the bulk of the statistical properties of the general circulation in middle latitudes is presented, based on the Charney-DeVore theory of multiple equilibria.
Abstract: In this paper we address the problem of constructing a minimal model of atmospheric circulation able to describe the bulk of the statistical properties of the general circulation in middle latitudes. After a brief reexamination of the Charney-DeVore theory of multiple equilibria, we compare the statistical properties that can be deduced from it with those resulting from analysis of observations of the northern hemisphere middle-latitude circulation at 500 mb. While the prediction concerning the amplitude of the waves seems to be confirmed by the presence of a clear bimodality of the statistical distribution, we find no trace of bimodality in the zonal wind. We show how the theory can be brought into agreement with observations by introducing nonlinearity into the wave equation in such a way that the Charney-DeVore resonance curve is bent, producing different states corresponding to the same value of the zonal wind. We finally address ourselves to the question of what physical processes determine the observed unimodal statistics of zonal wind, a subject of future work.
91 citations