翻訳と辞書 Words near each other ・ Orrs Springs, California ・ Orrstown, Pennsylvania ・ Orrtanna, Pennsylvania ・ Orrum, North Carolina ・ Orrvar Dalby ・ Orrviken ・ Orrville ・ Orrville City School District ・ Orrville High School ・ Orrville, Alabama ・ Orrville, Indiana ・ Orrville, Ohio ・ Orry ・ Orry-Kelly ・ Orry-la-Ville ・ Orr–Sommerfeld equation ・ ORS ・ Ors ・ ORS Direct ・ ORSA ・ Orsa ・ Orsa (moth) ・ Orsa Church ・ Orsa Grönklitt ・ Orsa Lake ・ Orsa Lia ・ Orsa Municipality ・ Orsa Spelmän ・ Orsa-class torpedo boat ・ Orsabaris Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Orr–Sommerfeld equation ： ウィキペディア英語版 Orr–Sommerfeld equation The Orr–Sommerfeld equation, in fluid dynamics, is an eigenvalue equation describing the linear two-dimensional modes of disturbance to a viscous parallel flow. The solution to the Navier–Stokes equations for a parallel, laminar flow can become unstable if certain conditions on the flow are satisfied, and the Orr–Sommerfeld equation determines precisely what the conditions for hydrodynamic stability are. The equation is named after William McFadden Orr and Arnold Sommerfeld, who derived it at the beginning of the 20th century. ==Formulation== The equation is derived by solving a linearized version of the Navier–Stokes equation for the perturbation velocity field :$\backslash mathbf\; =\; \backslash left(U(z)+u\text{'}(x,z,t),\; 0\; ,w\text{'}(x,z,t)\backslash right)$, 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 for the flow, the following dimensional form of the Orr–Sommerfeld equation is obtained: :$\backslash frac\; \backslash left(\; -\; \backslash alpha^2\backslash right)^2\; \backslash varphi\; =\; (U\; -\; c)\backslash left(\; -\; \backslash alpha^2\backslash right)\; \backslash varphi\; -\; U\text{'}\text{'}\; \backslash varphi$, where $\backslash mu$ is the dynamic viscosity of the fluid, $\backslash rho$ is its density, and $\backslash varphi$ is the potential or stream function. The equation can be written in non-dimensional form by measuring velocities according to a scale set by some characteristic velocity $U\_0$, and by measuring lengths according to channel depth $h$. Then the equation takes the form :$\backslash left(\; -\; \backslash alpha^2\backslash right)^2\; \backslash varphi\; =\; (U\; -\; c)\backslash left(\; -\; \backslash alpha^2\backslash right)\; \backslash varphi\; -\; U\text{'}\text{'}\; \backslash varphi$, where :$Re=\backslash frac$ is the Reynolds number of the base flow. The relevant boundary conditions are the no-slip boundary conditions at the channel top and bottom $z\; =\; z\_1$ and $z\; =\; z\_2$, :$\backslash alpha\; \backslash varphi\; =\; =\; 0$ at $z\; =\; z\_1$ and $z\; =\; z\_2,$ in the case where $\backslash varphi$ is the potential function. Or: :$\backslash alpha\; \backslash varphi\; =\; =\; 0$ at $z\; =\; z\_1$ and $z\; =\; z\_2,$ in the case where $\backslash varphi$ is the stream function. The eigenvalue parameter of the problem is $c$ and the eigenvector is $\backslash varphi$. If the imaginary part of the wave speed $c$ is positive, then the base flow is unstable, and the small perturbation introduced to the system is amplified in time. 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「Orr–Sommerfeld 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.