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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 Enstrophy ： ウィキペディア英語版 Enstrophy In fluid dynamics, the enstrophy $\backslash mathcal$ can be interpreted as another type of potential density (''ie''. see probability density); or, more concretely, the quantity directly related to the kinetic energy in the flow model that corresponds to dissipation effects in the fluid. It is particularly useful in the study of turbulent flows, and is often identified in the study of thrusters as well as the field of combustion theory. The enstrophy can be described as the integral of the square of the vorticity $\backslash omega$, :$\backslash mathcal(\backslash boldsymbol\; \backslash omega)\; \backslash equiv\; \backslash frac\; \backslash int\_\; \backslash boldsymbol\; \backslash omega^dS.$ or, in terms of the flow velocity, :$\backslash mathcal(\backslash mathbf)\; \backslash equiv\; \backslash frac\; \backslash int\_\; (\backslash nabla\; \backslash times\; \backslash mathbf\; u)^dS.$ Here, since the curl gives a scalar field in 2-dimensions (vortex) corresponding to the vector-valued velocity solving in the incompressible Navier–Stokes equations, we can integrate its square over a surface S to retrieve a continuous linear operator on the space of possible velocity fields, known as a ''current''. This equation is however somewhat misleading. Here we have chosen a simplified version of the enstrophy derived from the incompressibility condition, which is equivalent to vanishing divergence of the velocity field, :$\backslash nabla\; \backslash cdot\; \backslash mathbf\; =\; 0.$ More generally, when not restricted to the incompressible condition, or to two spatial dimensions, the enstrophy may be computed by: :$\backslash mathcal(\backslash mathbf)\; =\; \backslash int\_\; |\backslash nabla\; (\backslash mathbf)|^dS.$ where :$|\backslash nabla\; (\backslash mathbf)|$ is the Frobenius norm of the gradient of the velocity field $\backslash mathbf$. == External links == * * 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「Enstrophy」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.