Quasi-local method of wave decomposition in a slowly varying medium

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish
Article numberA56
JournalJournal of Fluid Mechanics
Volume883
DOIs
Publication statusPublished - Jan 1 2019

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Decomposition
decomposition
linear operators
transport theory
data simulation
Wave equations
Eigenvalues and eigenfunctions
Wave propagation
wave equations
Mathematical operators
wave propagation
Flow fields
flow distribution
eigenvectors
Kinematics
kinematics
Polarization
gradients
propagation
Computer simulation

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

Cite this

Quasi-local method of wave decomposition in a slowly varying medium. / Onuki, Yohei.

In: Journal of Fluid Mechanics, Vol. 883, A56, 01.01.2019.

Research output: Contribution to journalArticle

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