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• W2053647653 abstract "A formulation of fluid dynamics in terms of Lagrangian variables allows one to make direct use of the standard methods of statistical mechanics. However, most observations and empirical studies of large geophysical fluid systems are in terms of Eulerian variables, and this raises the issue of how to relate quantities given in terms of one set of variables to the corresponding quantities given in terms of the other set. In a completely general treatment of fluids, one must consider both oscillatory and translational modes of motion. The oscillatory modes are wavelike and lead to correlations which are analogous to those for phonons in the solid. The translational modes are particlelike and lead to correlations which correspond to diffusion in a weakly interacting gas. In this paper we consider the class of fluids for which the translational modes can be neglected. Based upon the assumption that the statistical distribution of the canonically conjugate Lagrangian variables is of a Gaussian form, we obtain a tractable expression for the Eulerian spectra in terms of the Lagrangian spectra and show that, in general, the two types of spectra are significantly different. In particular, it is shown that the Eulerian wave-number spectrum exhibits a large wave-number power-law decay which is similar to that often observed in geophysical systems and further is independent of the detailed nature of the Lagrangian wave-number spectrum. The large wave-number decay of the Eulerian spectrum is due to advection and is strictly a kinematic effect. This also implies that experiments which focus on the large wave-number advective tail cannot yield information about the true dynamics of the system. The application of this result to the problem of explaining the observed distribution of oceanic internal waves is discussed." @default.
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• W2053647653 date "1989-05-01" @default.
• W2053647653 modified "2023-09-25" @default.
• W2053647653 title "Relation between Lagrangian and Eulerian spectra based upon a canonical statistical theory of geophysical fluid waves" @default.
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• W2053647653 doi "https://doi.org/10.1103/physreva.39.5243" @default.
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