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1

Impact of the surface temperature and vertical shear of zonal wind on the dynamics of a simple two-layer model of the atmosphere

Brojewski R., Jakubiak B., Jasiński J.

Acta Geophysica

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2007

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Vol. 55, no. 2

231-252

EN

The paper presents and analyzes, from the point of view of smooth dynamic systems theory, a two-layer baroclinic model of the troposphere in geostrophic approximation. The model describes airflow in β-channel within the tropospheric part of the main Hadley circulation cell. It enables to obtain, after application of the Galerkin method, a fairly simple low-parametric dynamic system describing the phenomena of nonlinear interactions, bifurcations and blocking in the atmosphere. This enables to take into consideration such basic factors influencing the atmospheric dynamics like the heat exchange within the surface, orography, vertical variability of zonal wind and hydrostatic stability. Impact of zonal thermal variability of the surface and vertical shear of zonal wind in the troposphere on the orographic bifurcation was investigated and the oscillation character in the dynamic system after Hopf bifurcation of the second kind was analyzed. Additionally, the model dynamics was investigated in conditions in-cluding momentum forcing in the upper and lower parts of the troposphere and excluding orographic interaction, as well as in the conditions of thermal interaction between the troposphere and the surface for the vertical shear of zonal wind in both tropospheric layers. Impact of the mean zonal wind in the troposphere on the prop-erties of model dynamics was assessed. It was proved that zonally varied surface temperature and layered mean zonal wind in the atmosphere are the parameters that have basic influence on the model dynamics. They cause numerous bifurcations and strongly influence the periods of oscillations of the model variables. They are often Hopf bifurcations of the second kind during which tropospheric states fairly distant from the ones before the bifurcations are generated. This significantly influences the model predictability.

2

Dynamics of a 2L-baroclinic model of the troposphere. Part 2: impact of the zonal drift on bifurcations in the model

Brojewski R., Jakubiak B., Jasiński J.

Journal of Technical Physics

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2005

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Vol. 46, no 4

203-218

EN

The paper presents results of numerical analyses related with assessment of the impact of mean zonal drift in the troposphere on the properties of the dynamics of a simple two-layer model of the baroclinic troposphere. It was proved that the model dynamics is mainly influenced by zonally differentiated surface temperature. It causes numerous bifurcations. They are often Hopf bifurcations of the second kind during which tropospheric states quite distant from the states before the bifurcations are generated. It significantly influences the model predictability. The paper contributes to the assessment of applicability of hydrodynamic models to weather forecasting for periods longer than two weeks.

3

Dynamics of a 2L-baroclinic model of the troposphere. Part 1: Thermal bifurcation and blocking

Brojewski R., Jakubiak B., Jasiński J.

Journal of Technical Physics

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2005

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Vol. 46, no 3

131-147

EN

The paper analyzes, from the point of view of the theory of smooth dynamic systems, a simple two-layer model of baroclinic atmosphere applied within the main Hadley cell of circulation. The dynamics of the model was investigated in conditions excluding orographic influence but including momentum forcing in the upper and lower layers of the troposphere and thermal interaction between the troposphere and the surface for various vertical differentiations of the zonal drift in two tropospheric layers. The obtained results contribute to a profound view onto the applicability of classical weather forecasting models based on the hydrodynamic attitude.

4

Impact of the surface temperature and the zonal drift on the orographic bifurcation and blocking in 2l-baroclinic model of the troposphere

Brojewski R., Jakubiak B., Jasiński J.

Journal of Technical Physics

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2004

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Vol. 45, no 3

217-235

EN

The paper presents a 2-layer baroclinic model of the troposphere in geostrophic approximation that enables to obtain, after application of the Galerkin method, a fairly simple low-parametric dynamic system describing the phenomena of nonlinear interactions, bifurcations, blocking and auto-regulation in the atmosphere. It enables to take into consideration such basic factors molding the atmospheric dynamics like heat exchange with the surface, orography, vertical diversity of the zonal drift and hydrostatic stability. Conditions oforographic bifurcation of the model were investigated and confronted with the results obtained from a barotropic model. Impact of the zonal thermal diversity of the surface and the vertical diversity of the zonal drift of the troposphere on the orographic bifurcation was assessed. Oscillation character analysis was made in the dynamic system after Hopf bifurcation of the second kind.

5

Influence of the method of dry convection in the atmosphere modeling on the dynamic properties of the model

Brojewski R., Jasiński J.

Journal of Technical Physics

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2003

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Vol. 44, no 2

215-233

EN

This paper presents the problem of modeling dry convection in the atmosphere based on scaling of the movement equations resulting from the assumption that convection streams are mainly generated by the Archimedes draught force. This approach leads to description of the atmosphere movement different than in the Boussinesq approximation. The simplest case of Galerkin type equations in 3D phase space was considered. The obtained equations have different dynamics than the equations of the classical Lorenz model of dry convection. Lorenz model dynamics is controlled by the configuration of 2 non-dimensional numbers, while the dynamics of the proposed model is controlled by 3 numbers. It is presented in the language of symbolic dynamics, illustrated with numerous examples - indicating its different character than in the classical Lorenz model, among others: different values of Rayleigh number for which the systems loose structural stability.

6

About the properties of attraction sets of two models of physics of the atmosphere

Brojewski R., Jasiński J.

Journal of Technical Physics

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2003

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Vol. 44, no 3

311-328

EN

Dynamical properties of two simple models derived from the equations of physics of the atmosphere are investigated in this paper. Attention was paid to the structure of attraction sets (especially to their borders) of the attractors existing in the models. The influence of precision of the integrating procedures' on some of the attractors identification was investigated. The mechanism of destroying a strange attractor (by the nonlinear resonance) in a Lorenz system with thermal forcing was found.

7

Structural equivalence and stability of some atmospheric air flow models

Brojewski R.

Journal of Technical Physics

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2001

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Vol. 42, no 3

305-325

EN

Two ways of modeling of flows in lower atmosphere forced by stationary flows in upper layers of the atmosphere are presented in the paper. Attention is paid to inequivalence, due to the Coriolis force, of differential models based on 3-D equations of flow of liquid and based on the flow description by means of the stream function. Numerical difficulties of the two ways of solving the flow problem and a way of overcoming them are presented. Structural instability of the models is proved and some of the responsible factors are indicated. Among others are also formal parameters of the model, e.g. the time step of integration.

8

Predictability of some spectral and differential models of physics of atmosphere and their structural stability

Brojewski R.

Journal of Technical Physics

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1999

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Vol. 40, no 4

485-504

EN

The paper considers the influence of structural stability of the difference and spectral models and nonlinear equations of gravity waves on their predictability during integration in longer ranges of time. The influence of singular disturbances in the initial condition on the predictability of a grid model not filtered from gravity waves is demonstrated on the basis of the example of the shallow water equations. The influence of the structural instability of the spectral model on the topology of attractors in the Lorenz model is presented as well as the ability to forecast of the divergent-barotropic model in the situation of occurrence of a bifurcation related to orography. It is stated that the models constructed in Hilbert space have the dynamics more similar to the real one in comparison with the difference models constructed on calculation grids. It is demonstrated on examples that the difference models are more vulnerable to chaotic solutions.

9

Modelling effectivity of atmospheric advection-diffusion processes

Brojewski R.

Journal of Technical Physics

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1999

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Vol. 40, no 1

57-83

EN

Some methods of solving the advection-diffusion problems useful in the field of atmospheric physics are presented and analyzed in the paper. The most effective one ( from the point of view of computer applications) was chosen. This is the method of problem decomposition with respect to the directions, followed by secondary decomposition of the problem with respect to the physical phenomena. Introducing some corrections to the classical numerical methods of solving the problems, a hybrid composed of the finite element method for the advection problems and the implicit method with averaging for the diffusion processes was achieved. This hybrid method and application of the corrections produces a very effective means for solving the problems of substance transportation in atmosphere.