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An extension of a simplified, quasi-geostrophic, baroclinic theory of long waves set forth by Hess is presented. The ramifications of the stability aspects of the model and the results of adding a form of y-dependence to the system are examined. Finally, a steady state, adiabatic energy equation is added to the model as a diagnostic tool for specifying vertical profiles of the basic westerly current U (p) as a function of the parameters of the problems and as a function of particular vertical temperature profiles. Profiles U (p) for the model proposed by Hess are obtained and investigated as to their physical realism. The analogous profiles for the y-dependent case are not explicitly set forth due to mathematical difficulties. However, their general form is discussed in the light of the prior results of the investigation. (Author).
The study of hydrodynamic stability is fundamental to many subjects, ranging from geophysics and meteorology through to engineering design. This treatise covers both classical and modern aspects of the subject, systematically developing it from the simplest physical problems, then progressing chapter by chapter to the most complex, considering linear and nonlinear situations, and analysing temporal and spatial stability. The authors examine each problem both analytically and numerically: many chapters end with an appendix outlining relevant numerical techniques. All relevant fluid flows are treated, including those where the fluid may be compressible, or those from geophysics, or those that require salient geometries for description. Details of initial-value problems are explored equally with those of stability. As a result, the early transient period as well as the asymptotic fate for perturbations for a flow can be assessed. The text is enriched with many exercises, copious illustrations and an extensive bibliography and the result is a book that can be used with courses on hydrodynamic stability or as an authoritative reference for researchers.
Includes entries for maps and atlases.