Numerical modeling of ocean circulation / Robert N. Miller.

Includes bibliographical references and index.

Cover -- Title -- Copyright -- Contents -- Preface -- 1 Introduction -- 2 Some basic results from numerical analysis -- 2.1 Simple discretizations of a linear advection equation -- 2.2 Analysis of numerical results -- 2.2.1 Consistency, stability, convergence: the fundamentals -- 2.3 Implicit methods -- 2.4 Dissipation and dispersion -- 2.5 A (very) brief introduction to finite-element methods -- 2.6 Higher-order methods -- 2.7 A first look at boundary-value problems -- 2.8 Well- and ill-posed problems -- 2.9 Exercises -- 3 Shallow-water models: the simplest ocean models -- 3.1 Introduction -- 3.2 Discrete methods for the shallow-water equations -- 3.3 Special considerations for nonlinear problems -- 3.3.1 Stability considerations for advection-diffusion equations -- 3.3.2 Nonlinear instability -- 3.4 Conservation laws and conservative difference schemes -- 3.5 Artificial dissipation revisited -- 3.6 Finite-element methods in two space dimensions -- 3.7 Open-boundary conditions -- 3.8 Examples -- 3.8.1 An early model of basin-scale circulation -- 3.8.2 Stable and unstable equilibria in shallow-water models -- 3.9 Choice of computational parameters: an example -- 3.10 Exercises -- 4 Primitive equation models -- 4.1 Specification of the primitive equation model -- 4.2 Dissipation -- 4.3 Dynamics of the rigid lid -- 4.3.1 Derivation of a practical rigid lid PE model -- 4.3.2 Examples with simple dynamics -- 4.3.3 Stability restrictions -- 4.4 Spinup of 3D models -- 4.5 Consequences of discretization -- 4.6 The importance of vertical resolution -- 4.7 Example: Transport in the Drake Passage and the large-scale circulation -- 4.8 Example: Separation of the Brazil current from the coast -- 4.9 Generalized vertical coordinates -- 4.10 Layer models -- 4.11 Open-boundary conditions -- 4.12 Finely resolved calculations -- 4.13 Exercises -- 5 Quasigeostrophic models -- 5.1 Background and notation -- 5.2 Computation -- 5.2.1 Vertical discretization -- 5.3 Dissipation -- 5.4 Open-boundary models -- 6 Models of the coastal ocean -- 6.1 Introduction -- 6.2 Example: A high-resolution two-dimensional model of upwelling circulation on the Oregon shelf -- 6.3 Example: A three-dimensional calculation off the coast of California -- 6.4 Example: A finite-element model -- 6.5 Summary -- 6.6 Exercises -- 7 Models of the tropical ocean -- 7.1 Introduction -- 7.2 Waves in the equatorial ocean -- 7.3 Simple models of the tropical oceans -- 7.3.1 A simple gridded model of the tropical ocean -- 7.3.2 Example: Application of a simple model of the tropical Pacific Ocean -- 7.3.3 Simple models of the tropical Atlantic Ocean -- 7.4 Application of general circulation models -- 7.4.1 Comparisons to simple models -- 7.4.2 Example: Dynamic balances in model equatorial undercurrents -- 7.5 Conclusions -- 7.6 Exercises -- References -- Index.

Print version record.

The modelling of ocean circulation is important not only for its own sake, but also in terms of the prediction of weather patterns and the effects of climate change. This 2007 book introduces the basic computational techniques necessary for all models of the ocean and atmosphere, and the conditions they must satisfy. It describes the workings of ocean models, the problems that must be solved in their construction, and how to evaluate computational results. Major emphasis is placed on examining ocean models critically, and determining what they do well and what they do poorly. Numerical analysis is introduced as needed, and exercises are included to illustrate major points. Developed from notes for a course taught in physical oceanography at the College of Oceanic and Atmospheric Sciences at Oregon State University, this book is ideal for graduate students of oceanography, geophysics, climatology and atmospheric science, and researchers in oceanography and atmospheric science.

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