Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Fluid dynamics --- Compressibility --- Conservation laws (Mathematics) --- Variables (Mathematics) --- Compressibility. --- Fluid dynamics. --- Conservation laws (Mathematics). --- Variables (Mathematics). --- Analyse numérique. --- Numerical analysis --- Analyse numérique.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

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.

Ergodic theory. Information theory --- Discrete mathematics --- Mathematics --- Classical mechanics. Field theory --- Fluid mechanics --- Geophysics --- Gases handling. Fluids handling --- vloeistofstroming --- aerodynamica --- grafentheorie --- systeemtheorie --- wiskunde --- geofysica --- dynamica --- informatietheorie --- vloeistoffen

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

In this text, modern applied mathematics and physical insight are used to construct the simplest and first nonlinear dynamical model for the Madden-Julian oscillation (MJO), i.e. the stochastic skeleton model. This model captures the fundamental features of the MJO and offers a theoretical prediction of its structure, leading to new detailed methods to identify it in observational data. The text contributes to understanding and predicting intraseasonal variability, which remains a challenging task in contemporary climate, atmospheric, and oceanic science. In the tropics, the Madden-Julian oscillation (MJO) is the dominant component of intraseasonal variability. One of the strengths of this text is demonstrating how a blend of modern applied mathematical tools, including linear and nonlinear partial differential equations (PDEs), simple stochastic modeling, and numerical algorithms, have been used in conjunction with physical insight to create the model. These tools are also applied in developing several extensions of the model in order to capture additional features of the MJO, including its refined vertical structure and its interactions with the extratropics. This book is of interest to graduate students, postdocs, and senior researchers in pure and applied mathematics, physics, engineering, and climate, atmospheric, and oceanic science interested in turbulent dynamical systems as well as other complex systems.

Mathematics. --- Probabilities. --- Climate. --- Mathematics of Planet Earth. --- Probability Theory and Stochastic Processes. --- Climate, general. --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Math --- Science --- Stochastic analysis. --- Analysis, Stochastic --- Mathematical analysis --- Stochastic processes --- Climatology.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Differential equations, Partial --- Congresses --- -Partial differential equations --- -Congresses --- Équations aux dérivées partielles --- Differential equations, Partial - Congresses