翻訳と辞書 Words near each other ・ Mildred Jeffrey ・ Mildred Joanne Smith ・ Mildred Jordan ・ Mildred K. Nobles ・ Milczany, Świętokrzyskie Voivodeship ・ Mild ・ Mild ale ・ Mild and Bitter ・ Mild and Hazy ・ Mild androgen insensitivity syndrome ・ Mild cognitive impairment ・ Mild hybrid ・ Mild Maniac Orchestra ・ Mild Thing ・ Mild-Mannered Supermen ・ Mild-slope equation ・ Milda ・ Milda (gastropod) ・ Milda cincta ・ Milda garretti ・ Milda Jankauskaitė ・ Milda Lauberte ・ Milda Sauliūtė ・ Milda Valčiukaitė ・ Milda, Germany ・ Mildam ・ Mildbraedia ・ Mildbraedia carpinifolia ・ Mildbraediodendron ・ Mildburh 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 Mild-slope equation ： ウィキペディア英語版 Mild-slope equation In fluid dynamics, the mild-slope equation describes the combined effects of diffraction and refraction for water waves propagating over bathymetry and due to lateral boundaries—like breakwaters and coastlines. It is an approximate model, deriving its name from being originally developed for wave propagation over mild slopes of the sea floor. The mild-slope equation is often used in coastal engineering to compute the wave-field changes near harbours and coasts. The mild-slope equation models the propagation and transformation of water waves, as they travel through waters of varying depth and interact with lateral boundaries such as cliffs, beaches, seawalls and breakwaters. As a result, it describes the variations in wave amplitude, or equivalently wave height. From the wave amplitude, the amplitude of the flow velocity oscillations underneath the water surface can also be computed. These quantities—wave amplitude and flow-velocity amplitude—may subsequently be used to determine the wave effects on coastal and offshore structures, ships and other floating objects, sediment transport and resulting geomorphology changes of the sea bed and coastline, mean flow fields and mass transfer of dissolved and floating materials. Most often, the mild-slope equation is solved by computer using methods from numerical analysis. A first form of the mild-slope equation was developed by Eckart in 1952, and an improved version—the mild-slope equation in its classical formulation—has been derived independently by Juri Berkhoff in 1972. Thereafter, many modified and extended forms have been proposed, to include the effects of, for instance: wave–current interaction, wave nonlinearity, steeper sea-bed slopes, bed friction and wave breaking. Also parabolic approximations to the mild-slope equation are often used, in order to reduce the computational cost. In case of a constant depth, the mild-slope equation reduces to the Helmholtz equation for wave diffraction. == Formulation for monochromatic wave motion == For monochromatic waves according to linear theory—with the free surface elevation given as $\backslash zeta(x,y,t)=\backslash Re\backslash left\backslash \backslash right\backslash \}$ and the waves propagating on a fluid layer of mean water depth $h(x,y)$—the mild-slope equation is:〔See Dingemans (1997), pp. 248–256 & 378–379.〕 :$\backslash nabla\backslash cdot\backslash left(\; c\_p\backslash ,\; c\_g\backslash ,\; \backslash nabla\; \backslash eta\; \backslash right)\backslash ,\; +\backslash ,\; k^2\backslash ,\; c\_p\backslash ,\; c\_g\backslash ,\; \backslash eta\backslash ,\; =\backslash ,\; 0,$ where: *$\backslash eta(x,y)$ is the complex-valued amplitude of the free-surface elevation $\backslash zeta(x,y,t);$ *$(x,y)$ is the horizontal position; *$\backslash omega$ is the angular frequency of the monochromatic wave motion; *$i$ is the imaginary unit; *$\backslash Re\backslash$ means taking the real part of the quantity between braces; *$\backslash nabla$ is the horizontal gradient operator; *$\backslash nabla\backslash cdot$ is the divergence operator; *$k$ is the wavenumber; *$c\_p$ is the phase speed of the waves and *$c\_g$ is the group speed of the waves. The phase and group speed depend on the dispersion relation, and are derived from Airy wave theory as:〔See Dingemans (1997), p. 49.〕 :$$ \begin \omega^2 &=\, g\, k\, \tanh\, (kh), \\ c_p &=\, \frac \quad \text \\ c_g &=\, \frac12\, c_p\, \left(1\, +\, kh\, \frac \right ) \end where *$g$ is Earth's gravity and *$\backslash tanh$ is the hyperbolic tangent. For a given angular frequency $\backslash omega$, the wavenumber $k$ has to be solved from the dispersion equation, which relates these two quantities to the water depth $h$. 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「Mild-slope 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.