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10 - Theory and Observation

Published online by Cambridge University Press:  07 October 2011

R. M. Samelson
Affiliation:
Oregon State University
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Summary

A Perturbation-Theoretical Perspective

The basic point of view around which the development in this text has been organized is that of perturbation theory. In general, perturbation theory allows the replacement of a difficult or intractable problem with a simpler approximation that includes the leading-order terms in an expansion of the original variables in powers of a suitable small parameter. In the present case, a formal expansion was not necessary because the effective leading-order terms for large-scale ocean circulation dynamics could be identified by direct scaling of terms in the fundamental equations. These leading-order terms—the perturbation theory for the large-scale ocean circulation–are the planetary geostrophic equations (2.102)–(2.107).

The planetary geostrophic theories of large-scale circulation described in this text provide deep, quantitative insight into the large-scale physical structure of the ocean. For example, the reduced-gravity and ventilated thermocline models (Chapter 5) give persuasive explanations for the basic structure of the upper main subtropical thermocline, including the characteristic downward and westward slope of thermocline isosurfaces (Figure 1.7). Similarly, the Sverdrup interior solution (3.36) for the depth-integrated wind-driven transport may be favorably compared with interior geostrophic transports determined from hydrographic measurements.

Given a solution of an approximate problem constructed using perturbation theory, one would like to know how accurately it represents the solution of the original problem. If the original problem cannot be solved theoretically by other means, as is the case with large-scale ocean circulation, then the comparison must be made to observations of the system under consideration.

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Publisher: Cambridge University Press
Print publication year: 2011

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  • Theory and Observation
  • R. M. Samelson, Oregon State University
  • Book: The Theory of Large-Scale Ocean Circulation
  • Online publication: 07 October 2011
  • Chapter DOI: https://doi.org/10.1017/CBO9780511736605.011
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  • Theory and Observation
  • R. M. Samelson, Oregon State University
  • Book: The Theory of Large-Scale Ocean Circulation
  • Online publication: 07 October 2011
  • Chapter DOI: https://doi.org/10.1017/CBO9780511736605.011
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Theory and Observation
  • R. M. Samelson, Oregon State University
  • Book: The Theory of Large-Scale Ocean Circulation
  • Online publication: 07 October 2011
  • Chapter DOI: https://doi.org/10.1017/CBO9780511736605.011
Available formats
×