Analysis of energy conserving low-order models.

It is well known in Mathematical Physics that the Volterra gyrostat and many of its special cases including the Euler gyroscope represent a prototype of energy conserving dynamical systems. It is formally proved in this dissertation that the systems of coupled Volterra gyrostats are special cases of LOMs that satisfies the new sufficient conditions. We also introduce the definition of the generalized Volterra gyrostats that contains nonlinear feedback. Exploiting the inherent relation between the energy conserving LOMs satisfying the sufficient conditions and the systems of coupled generalized Volterra gyrostats, it turns out that these two sets of systems are equivalent. Using the class of generalized Volterra gyrostats as basic building block, any energy conserving low-order model that routinely arise in fluid dynamics, turbulence and atmospheric sciences can be converted into a system of coupled generalized gyrostats. An algorithm for doing such a transformation is provided.Low-order models of order n, denoted by LOM( n), naturally arise in the application of Galerkin type projection techniques to a system of partial differential equations of interest in geophysical domain. In order for the LOM(n) to represent physically meaningful solution, it is necessary that LOM(n) conserves energy. The Galerkin projection technique does not incorporate any explicit criteria for the choice of the order and the modes to guarantee energy conservation. With this study, we derive a new set of sufficient conditions on the structural parameter of LOM(n) for conserving energy.Motivated by the importance and the central role played by the Volterra gyrostat in studying LOMs, this study also analyze the stability properties of the classical Volterra gyrostat and all of its special cases

Recurrent climate winter regimes in reconstructed and modelled 500hPa geopotential height fields over the North Atlantic/European sector 1659-1990

Recurrent climate winter regimes are examined from statistically reconstructed and modelled 500hPa geopotential height fields over the North Atlantic/European sector for the period 1659-1990. We investigate the probability density function of the state space spanned by the first two empirical orthogonal functions of combined winter data. Regimes are detected as patterns that correspond to areas of the state space with an unexpected high recurrence probability using a Monte Carlo approach. The reconstruction and the model reveal four recurrent climate regimes. They correspond to the two phases of the North Atlantic Oscillation and two opposite blocking patterns. Complemented by the investigation of the temporal evolution of the climate regimes this leads to the conclusion that the reconstructed and the modelled data for this geographic sector reproduce low-frequency atmospheric variability in the form of regime-like behaviour. The overall evidence for recurrent climate regimes is higher for the model than for the reconstruction. However, comparisons with independent data sources for the period 1659-1990 revealed a more realistic temporal evolution of the regimes for the reconstructed dat