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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 Hydrodynamical helicity ： ウィキペディア英語版 Hydrodynamical helicity :''This page is about helicity in fluid dynamics. For helicity of magnetic fields, see magnetic helicity. For helicity in particle physics, see helicity (particle physics).'' In fluid dynamics, helicity is, under appropriate conditions, an invariant of the Euler equations of fluid flow, having a topological interpretation as a measure of linkage and/or knottedness of vortex lines in the flow (Moffatt 1969). Let $\backslash mathbf(x,t)$ be the velocity field and $\backslash nabla\backslash times\backslash mathbf$ the corresponding vorticity field. Under the following three conditions, the vortex lines are transported with (or 'frozen in') the flow: (i) the fluid is inviscid; (ii) either the flow is incompressible ($\backslash nabla\backslash cdot\backslash mathbf\; =\; 0$), or it is compressible with a barotropic relation $p\; =\; p(\backslash rho)$ between pressure $p$ and density $\backslash rho$; and (iii) any body forces acting on the fluid are conservative. Under these conditions, any closed surface $S$ on which $n\; \backslash cdot\; (\backslash nabla\backslash times\backslash mathbf)\; =\; 0$ is, like vorticity, transported with the flow. Let $V$ be the volume inside such a surface. Then the helicity in $V$ is defined by :$$ H=\int_\mathbf\cdot\left(\nabla\times\mathbf\right)\,dV \;. For a localised vorticity distribution in an unbounded fluid, $V$ can be taken to be the whole space, and $H$ is then the total helicity of the flow. $H$ is invariant precisely because the vortex lines are frozen in the flow and their linkage and/or knottedness is therefore conserved, as recognized by Lord Kelvin (1868). Helicity is a pseudo-scalar quantity: it changes sign under change from a right-handed to a left-handed frame of reference; it can be considered as a measure of the handedness (or chirality) of the flow. Helicity is the only known integral invariant of the Euler equations, apart from energy, momentum and angular momentum. For two linked unknotted vortex tubes having circulations $\backslash kappa\_1$ and $\backslash kappa\_2$, and no internal twist, the helicity is given by $H\; =\; \backslash plusmn\; 2n\; \backslash kappa\_1\; \backslash kappa\_2$, where $n$ is the Gauss linking number of the two tubes, and the plus or minus is chosen according as the linkage is right- or left-handed. For a single knotted vortex tube with circulation $\backslash kappa$, then, as shown by Moffatt & Ricca (1992), the helicity is given by $H\; =\; \backslash kappa^2\; (Wr\; +\; Tw)$, where $Wr$ and $Tw$ are the writhe and twist of the tube; the sum $Wr\; +\; Tw$ is known to be invariant under continuous deformation of the tube. The invariance of helicity provides an essential cornerstone of the subject topological fluid dynamics and magnetohydrodynamics, which is concerned with global properties of flows and their topological characteristics. ==Meteorology== In meteorology, helicity corresponds to the transfer of vorticity from the environment to an air parcel in convective motion. Here the definition of helicity is simplified to only use the horizontal component of wind and vorticity: ::$$ H = \int \cdot \vec \zeta_h \,d = \int \cdot \nabla \times \vec V_h \,d \qquad \qquad \begin Z = Altitude \\ \vec V_h = Horizontal\ velocity \\ \vec \zeta_h = Horizontal\ vorticity \end According to this formula, if the horizontal wind does not change direction with altitude, H will be zero as $V\_h$ and $\backslash nabla\; \backslash times\; V\_h$ are perpendicular one to the other making their scalar product nil. H is then positive if the wind veers (turns clockwise) with altitude and negative if it backs (turns counterclockwise). This helicity used in meteorology has energy units per units of mass ($/$) and thus is interpreted as a measure of energy transfer by the wind shear with altitude, including directional. This notion is used to predict the possibility of tornadic development in a thundercloud. In this case, the vertical integration will be limited below cloud tops (generally 3 km or 10,000 feet) and the horizontal wind will be calculated to wind relative to the storm in subtracting its motion: ::$SRH\; =\; \backslash int\; \backslash cdot\; \backslash nabla\; \backslash times\; \backslash vec\; V\_h\; \backslash ,d$ \qquad \qquad \begin \vec C = Cloud\ motion\ to\ the\ ground \end Critical values of SRH (Storm Relative Helicity) for tornadic development, as researched in North America, are: * SRH = 150-299 ... supercells possible with weak tornadoes according to Fujita scale * SRH = 300-499 ... very favourable to supercells development and strong tornadoes * SRH > 450 ... violent tornadoes * When calculated only below 1 km (4,000 feet), the cut-off value is 100. Helicity in itself is not the only component of severe thunderstorms, and these values are to be taken with caution.〔(【引用サイトリンク】url=http://www.spc.noaa.gov/exper/mesoanalysis/help/help_srh.html )〕 That is why the Energy Helicity Index (EHI) has been created. It is the result of SRH multiplied by the CAPE (Convective Available Potential Energy) and then divided by a threshold CAPE: EHI = (CAPE x SRH) / 160,000. This incorporates not only the helicity but the energy of the air parcel and thus tries to eliminate weak potential for thunderstorms even in strong SRH regions. The critical values of EHI: * EHI = 1 ... possible tornadoes * EHI = 1-2 ... moderate to strong tornadoes * EHI > 2 ... strong tornadoes 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「Hydrodynamical helicity」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.