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Application of the Nambu mechanics formalism in atmospheric dynamics
Procházková, Zuzana ; Šácha, Petr (advisor) ; Badin, Gualtiero (referee)
Nambu mechanics is a generalization of Hamiltonian mechanics that uses multiple conserved quantities as Hamiltonians. In this thesis, we review Nambu mechanics and its application on the equations of incompressible flow and shallow water equations. The Nambu form of the equations of incompressible flow is guessed based on its Hamiltonian form and derived conserved quantities. With the example of the shallow water equations a more general method of Nambu form derivation is illustrated. Based only on the knowledge of the Hamiltonian and the potential enstrophy moments conservation, the shallow water equations are written as a sum of the Nambu brackets and a Poisson bracket. For the classical potential enstrophy, the derived equations are up to constant factors equivalent to the known form of the shallow water equations. The notation by antisymmetric Nambu brackets is convenient for finding conservative schemes and the theory can be also used for example for the study of deviations of flow from stationary flow.
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Application of the Nambu mechanics formalism in atmospheric dynamics
Procházková, Zuzana ; Šácha, Petr (advisor) ; Badin, Gualtiero (referee)
Nambu mechanics is a generalization of Hamiltonian mechanics that uses multiple conserved quantities as Hamiltonians. In this thesis, we review Nambu mechanics and its application on the equations of incompressible flow and shallow water equations. The Nambu form of the equations of incompressible flow is guessed based on its Hamiltonian form and derived conserved quantities. With the example of the shallow water equations a more general method of Nambu form derivation is illustrated. Based only on the knowledge of the Hamiltonian and the potential enstrophy moments conservation, the shallow water equations are written as a sum of the Nambu brackets and a Poisson bracket. For the classical potential enstrophy, the derived equations are up to constant factors equivalent to the known form of the shallow water equations. The notation by antisymmetric Nambu brackets is convenient for finding conservative schemes and the theory can be also used for example for the study of deviations of flow from stationary flow.
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Spatial and temporal scales of atmospheric dynamics
Jajcay, Nikola ; Paluš, Milan (advisor) ; Masoller, Christina (referee) ; Dijkstra, H.A. (referee)
DOCTORAL THESIS Nikola Jajcay Spatial and temporal scales of atmospheric dynamics Abstract Earth climate, in general, varies on many temporal and spatial scales. In particular, climate observables exhibit recurring patterns and quasi- oscillatory phenomena with different periods. Although these oscillations might be weak in amplitude, they might have a non-negligible influence on variability on shorter time-scales due to cross-scale interactions, recently observed by Paluš[1]. This thesis supplies an introductory material for inferring the cross-scale information transfer from observational data, where the time series of interest are obtained using wavelet transform, and possible information transfer is studied using the tools from information theory. Finally, cross- scale interactions are studied in two climate phenomena: air temperature variability in Europe, in which we study phase-amplitude coupling from a slower oscillatory mode with an 8-year period on faster variability and its effects, and El Niño/ Southern Oscillation where we observe a causal chain of phase-phase and phase-amplitude couplings among distinct oscillatory modes. [1] M. Paluš. Multiscale atmospheric dynamics: cross-frequency phase-amplitude coupling in the air temperature. Physical Review Letters, 112(7):078702, 2014.
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