Computational Methods for the Atmosphere and the Oceans

This book provides a survey of the frontiers of research in the numerical modeling and mathematical analysis used in the study of the atmosphere and oceans. The details of the current practices in global atmospheric and ocean models, the assimilation of observational data into such models and the numerical techniques used in theoretical analysis of the atmosphere and ocean are among the topics covered.

. Truly interdisciplinary: scientific interactions between specialties of atmospheric and ocean sciences and applied and computational mathematics
. Uses the approach of computational mathematicians, applied and numerical analysts and the tools appropriate for unsolved problems in the atmospheric and oceanic sciences
. Contributions uniquely address central problems and provide a survey of the frontier of research

Part 1. Modeling
1.) Finite-Volume Methods in Meteorology
2.) Computational Kernel Algorithms for Fine-Scale, Multi-Process, Long-Time Oceanic Simulations

Part 2. Nonlinear Methods
3.) Bifurcation analysis of ocean, atmosphere and climate models
4.) Time-Periodic Flows in Geophysical and Classical Fluid Dynamics
5.) Discrete momentum maps for lattice EPDiff
6.) Numerical generation of stochastic differential equations in climate models

Part 3. Turbulence
7.) Large-eddy simulations for geophysical fluid dynamics
8.) Two examples from geophysical and astrophysical turbulence on modeling disparate scale interactions

Part 4. Data Assimilation
9.) Data Assimilation for Geophysical Fluids
10.) Continuum and Discrete Covariance Propagation for Advective Dynamics

Part 5. Analysis
11.) The 3D Primitive Equations in the absence of viscosity: Boundary Conditions and well-posedness in the linearized case
12.) Some Mathematical Problems in Geophysical Fluid Dynamics