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3 Journal of Technical Physics

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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

2003

Vol. 44, no 2

215-233

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.

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

Brojewski R., Jasiński J.

Journal of Technical Physics

2003

Vol. 44, no 3

311-328

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.

Structural equivalence and stability of some atmospheric air flow models

Brojewski R.

Journal of Technical Physics

2001

Vol. 42, no 3

305-325

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.