The Mathematics of Large-Scale Atmosphere and Ocean

by Mike Cullen (Author)
Buy for $138.00 Excerpt

The high predictability of the atmosphere and ocean depends on the existence of a 'slow manifold', which contains the solutions of equations describing only large-scale motions. This unique compendium succinctly describes major recent advances in showing that these equations can be solved independently.The book is a new edition of a similar book published 15 years ago. The explanation of the mathematical techniques has been expanded. Many new theoretical results are included. Illustrations derived from production atmosphere and ocean models are also incorporated to cover the full range between rigorous mathematics and state-of-the-art numerical modelling.The author is a dynamical meteorologist with long experience and international standing. The mathematical results in the book were proved by many of the world's leading analysts. The results come from the Met Office Unified Model, which is one of the world's leading weather and climate models.Contents:

  • Dedication
  • Preface
  • Introduction
  • The Governing Equations and Asymptotic Approximations to Them:
    • Basic Equations
    • Scale Analysis, Key Dimensionless Parameters, and Reduced Equations
    • Various Approximations to the Shallow Water Equations
    • Various Approximations to the Three-Dimensional Hydrostatic Boussinesq Equations
    • Large Scale Solutions of the Fully Compressible Equations in Spherical Geometry
    • Illustrations of Asymptotic Behaviour from Observations
    • The Appropriateness of the Semi-Geostrophic Approximation for Large-Scale Flows in the Atmosphere
  • Solution of the Semi-Geostrophic Equations in Plane Geometry:
    • The Solution as a Sequence of Minimum Energy State
    • Solution as a Mass Transport Problem
    • The Shallow Water Semi-Geostrophic Equations
    • Discrete Solutions of the Semi-Geostrophic Equations
    • Rigorous Results on Existence of Solutions
    • Approximation of Euler Solutions by Semi-Geostrophic Solutions
  • Solution of the Semi-geostrophic and Related Equations in More General Cases:
    • Solution of the Semi-Geostrophic Equations for Compressible Flow
    • Semi-Geostrophic Theory on a Sphere
    • The Shallow Water Spherical Semi-Geostrophic Equations
    • The Theory of Axisymmetric Flows
    • Zonal Flows on the Sphere
    • Stability Theorems for Semi-Geostrophic Flow
  • Properties and Validation of Asymptotic Limit Solutions:
    • Numerical Methods for Solving the Semi-Geostrophic Equations
    • Shallow Water Solutions
    • The Eady Wave
    • Simulations of Baroclinic Waves
    • Orographic Flows
    • Tropical-Extratropical Interaction
  • Inclusion of Additional Physics:
    • Inclusion of Friction
    • Inclusion of Moisture
  • Summary
  • Bibliography
  • Index

Readership: Researchers, professionals, academics and graduate students in climatology, oceanography, fluid mechanics and functional analysis.Semi-Geostrophic;Optimal Transport00

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Publication date
June 04, 2021
Page count
File size
12 MB