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: - Rotating stratified fluid dynamics including simplified models for the effect of moisture



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 be of interest to graduate students, postdocs, and senior researchers in pure and applied mathematics, physics, engineering, and climate, atmosphere, ocean science interested in turbulent dynamical systems as well as other complex systems.

<