(Frontiers in Applied Dynamical Systems: Reviews and Tutorials) 1st ed. 2016 Edition
by Andrew J. Majda (Author)
This volume is a research expository article on the applied
mathematics of turbulent dynamical systems through the paradigm of
modern applied mathematics. It involves the blending of rigorous
mathematical theory, qualitative and quantitative modeling, and novel
numerical procedures driven by the goal of understanding physical
phenomena which are of central importance to the field. The contents
cover general framework, concrete examples, and instructive qualitative
models. Accessible open problems are mentioned throughout.
Topics covered include:
· Geophysical flows with rotation, topography, deterministic and random forcing
· New statistical energy principles for general turbulent dynamical systems, with applications
· Linear statistical response theory combined with information theory to cope with model errors
· Reduced low order models
·
Recent mathematical strategies for online data assimilation of
turbulent dynamical systems as well as rigorous results for finite
ensemble Kalman filters
The volume will appeal to graduate
students and researchers working mathematics, physics and engineering
and particularly those in the climate, atmospheric and ocean sciences
interested in turbulent dynamical as well as other complex systems.
