The project is devoted to spatially extended dynamical systems with randomness and oscillations. Applications concern environment and climate. The project is based on the idea of the Statistical Near-Identity Transformation, which advances perturbation methods along the lines of the normal forms in classical mechanics. It is known that resonance interactions are essential in describing the evolution of wave turbulence. This project shows that "almost" resonance interactions are crucial as well. In particular, the Statistical Near-Identity Transformation promises to provide an understanding of resonance interactions in acoustic waves. The project also aims to explain the spectrum of long (baroclinic) Rossby waves, recently obtained from satellite observation data. The idea of the explanation is based on an extra invariant for Rossby waves (discovered in earlier research).
This project develops a new mathematical technique that has applications to modeling a variety of important physical processes, including concentration of pollutants and of plankton on the surface of the ocean, interaction of nonlinear acoustic waves, and the spectrum of Rossby waves, huge structures in the atmosphere and ocean that, to a large extent, determine weather and climate on our planet. The results of this project will furnish new tools for environmental and climatological investigations.
