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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Taylor–Goldstein equation ： ウィキペディア英語版 Taylor–Goldstein equation The Taylor–Goldstein equation is an ordinary differential equation used in the fields of geophysical fluid dynamics, and more generally in fluid dynamics, in presence of quasi-2D flows. It describes the dynamics of the Kelvin–Helmholtz instability, subject to buoyancy forces (e.g. gravity), for stably stratified fluids in the dissipation-less limit. Or, more generally, the dynamics of internal waves in the presence of a (continuous) density stratification and shear flow. The Taylor–Goldstein equation is derived from the 2D Euler equations, using the Boussinesq approximation.〔 The equation is named after G.I. Taylor and S. Goldstein, who derived the equation independently from each other in 1931. The third independent derivation, also in 1931, was made by B. Haurwitz. ==Formulation== The equation is derived by solving a linearized version of the Navier–Stokes equation, in presence of gravity $g$ and a mean density gradient (with gradient-length $L\_\backslash rho$), for the perturbation velocity field :$\backslash mathbf\; =\; \backslash left(0\; ,w\text{'}(x,z,t)\backslash right),\; \backslash ,$ where $(U(z),\; 0,\; 0)$ is the unperturbed or basic flow. The perturbation velocity has the wave-like solution $\backslash mathbf\text{'}\; \backslash propto\; \backslash exp(i\; \backslash alpha\; (x\; -\; c\; t))$ (real part understood). Using this knowledge, and the streamfunction representation $u\_x\text{'}=d\backslash tilde\backslash phi\; /\; dz,\; u\_z\text{'}=-i\backslash alpha\backslash tilde\backslash phi$ for the flow, the following dimensional form of the Taylor–Goldstein equation is obtained: : Note that a purely imaginary Brunt–Väisälä frequency $N$ results in a flow which is always unstable. This instability is known as the Rayleigh–Taylor instability. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Taylor–Goldstein equation」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.