Quasi-local method of wave decomposition in a slowly varying medium
| Autor: | Yohei Onuki |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Physics
010504 meteorology & atmospheric sciences Computer simulation Wave propagation Mechanical Engineering Mathematical analysis Function (mathematics) Condensed Matter Physics Wave equation 01 natural sciences Conserved quantity 010305 fluids & plasmas Linear map Mechanics of Materials Dispersion relation 0103 physical sciences Eigenvalues and eigenvectors 0105 earth and related environmental sciences |
| Zdroj: | Journal of Fluid Mechanics. 883 |
| ISSN: | 1469-7645 0022-1120 |
| DOI: | 10.1017/jfm.2019.825 |
| Popis: | The general asymptotic theory for wave propagation in a slowly varying medium, classically known as the Wentzel–Kramers–Brillouin–Jeffreys (WKBJ) approximation, is revisited here with the aim of constructing a new data diagnostic technique useful in atmospheric and oceanic sciences. Using the Wigner transform, a kind of mapping that associates a linear operator with a function, we analytically decompose a flow field into mutually independent wave signals. This method takes account of the variations in the polarisation relations, an eigenvector that represents the kinematic characteristics of each wave component, so as to project the variables onto their eigenspace quasi-locally. The temporal evolution of a specific mode signal obeys a single wave equation characterised by the dispersion relation that also incorporates the effect from the local gradient in the medium. Combining this method with transport theory and applying them to numerical simulation data, we can detect the transfer of energy or other conserved quantities associated with the propagation of each wave signal in a wide variety of situations. |
| Databáze: | OpenAIRE |
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