三波, 俊郎

古池, 鋼

宇多, 高明

熊田, 貴之

石川, 仁憲

芹沢, 真澄

Kyoto University Research Information Repository

Title数値シミュレーションによる海浜変形の予測(複雑流体の数理とその応用)Author(s)芹沢, 真澄; 宇多, 高明; 熊田, 貴之; 三波, 俊郎; 古池, 鋼; 石川, 仁憲Citation数理解析研究所講究録 (2006), 1472: 1-10Issue Date2006-02URL http://hdl.handle.net/2433/48120RightType Departmental Bulletin PaperTextversionpublisherKyoto University1( ) (Masumi Serizawa)Coastal Engineering Laboratory Co. Ltd.( ) (Takaaki Uda)Public Works Research Center.( ) (Takayuki Kumada)Laboratory of Aquat ic Science Consultant Co. Ltd.( ) (Toshiro San-nami)Coastal Engineering Laboratory Co. Ltd.( ) (Kou Furuike)Coastal Engineering Laboratory Co. Ltd,( ) (Toshinori Ishikawa)Public Works Research Center.1., ( , 1997, 2004).. , ,. (2004) ,, 1) () ( -1 ), 2)( -2), 3) , 4) , 5), 6) .5) 6) ,, .,,. .1472 2006 1-1022., ( ) ,, ( ,1996). 4 (, 2002).( -3 ). ,.. , , ,.. ,. , ,$\dot{\ovalbox{\tt\small REJECT}}/$ ,. (2002), Serizawa et al. (2003) .3.(1)-4 , $\mathrm{x}$ , $\mathrm{y}$ . xy $\mathrm{z}=\mathrm{z}_{1}\ldots..\mathrm{z}_{\mathrm{k}}$. $\mathrm{z}$ ,$\mathrm{x}$$\mathrm{Y}(\mathrm{x}, \mathrm{z}, \mathrm{t})$ . $\mathrm{t}$ .$\mathrm{q}_{\mathrm{z}}$ ., ,.Dean (1991) , ,. . -3 (2). Bakker (1968) , $\tan$ \beta ,, , 0 .$\tan\beta$ $\mathrm{t}\mathrm{a}\mathfrak{n}$ \beta , $\mathrm{q}_{\mathrm{z}}$ , $\tan$ \beta $\mathrm{q}_{\mathrm{z}}$. (1) ( -3 ). $\cot\beta$ .$q_{\mathrm{Z}}=A \cdot(\frac{\cot\sqrt}{\cot\beta_{\mathrm{C}}}$ –1$)$ ....... (1) $\cot\beta=-\frac{\partial \mathrm{Y}}{\partial z}$ $\ldots..(2)$(1) A , A. -5 .3, h $\mathrm{h}_{\mathrm{R}}$. , $(\mathrm{E}\mathrm{C}\mathrm{g})_{\mathrm{b}}$ , ,. , $-\mathrm{h}_{c}$$\mathrm{h}_{\mathrm{R}}$ , , A-h $\mathrm{h}_{\mathrm{R}}$ $\mathrm{S}$ . -5, .$\frac{(EC_{g})_{b}}{S}=\frac{(EC_{g})_{b}}{h_{c}+h_{R}}\sin\overline{\beta}=(\frac{1}{h_{c}+h_{R}})\cdot(EC_{g})_{b}\sin\sqrt \mathrm{C}^{\cdot}$ $\ldots\ldots\ldots.(3)$, , .. $\epsilon \mathrm{z}(\mathrm{z})$ , K2 , A(4) , (5) . $\epsilon \mathrm{z}(\mathrm{z})$ (6) $-\mathrm{h}_{\mathrm{c}}$ $\mathrm{h}_{\mathrm{R}}$ 1.$A=\epsilon_{z}(z)\cdot K_{7,\sim}\cdot(EC_{g})_{b}\sin\sqrt \mathrm{c}$ .................... $.(4)$$q_{z}=\epsilon_{z}(z)\cdot K_{z}\cdot(EC_{g})_{b}\sin\sqrt \mathrm{c}$ . $( \frac{\cot\sqrt}{\cot\sqrt c}-1)\ldots\ldots.-\cdots..(5)$$\int_{-h_{c}}^{h_{R}}\epsilon_{\mathrm{Z}}(Z)dz=1$ ..................... $(6)$, , , $(\mathrm{E}\mathrm{C}_{\mathrm{g}})_{\mathrm{b}}$. $\alpha_{\mathrm{b}}$ , $(\mathrm{E}\mathrm{C}\mathrm{g})_{\mathrm{b}}\cos$$\alpha_{\mathrm{b}}$ , $\cos\alpha_{\mathrm{b}}$ .$q_{\mathrm{Z}}=\epsilon_{Z}(z)\cdot K_{Z}\cdot(EC_{g})_{b}\cos^{2}\alpha_{b}\sin\beta_{\mathrm{C}}$ . $( \frac{\cot\beta}{\cot\sqrt c}$.$-1)$ . ... $\ldots\ldots\ldots..(7)$$\alpha_{\mathrm{b}}$$\cos\alpha_{\mathrm{b}}.=.1$ . , (5) .$\tan$ \beta . / 4‘. $\epsilon \mathrm{z}(\mathrm{z})$ , $\epsilon$$\mathrm{x}(\mathrm{z})$ , (1996) 3 . $\mathrm{K}_{\mathrm{z}}$$\mathrm{K}_{\mathrm{x}}$ 0. 2 . , $\mathrm{q}_{\mathrm{x}}$ (1996) , (8). (8) $\alpha_{\mathrm{b}}$ -3 . ,2 .$q_{X}=\epsilon_{X}(z)\cdot K_{X}\cdot(EC_{g})_{b}$ COS $\alpha_{b}\sin\alpha_{b}$ $\ldots\ldots\ldots\ldots\ldots\ldots\ldots(8)$4, , ,,.(2). -6, . ,$-\mathrm{h}_{\mathrm{c}}$ $\mathrm{h}_{\mathrm{R}}$ , 1 , $\in \mathrm{z}(\mathrm{z})$$\epsilon \mathrm{x}(\mathrm{z})$ . -7 .$\mathrm{v}$$\mathrm{Y}_{(i)}^{\prime(k)}=\mathrm{Y}_{(i)}^{(k)}-\frac{\Delta t}{\ }(q_{x(i+1)}^{(k)}-q_{x(i)}^{(k)})- \frac{\Delta t}{\Delta z}(q_{z\langle \mathrm{i})}^{(k\rangle}-q_{z(\mathrm{i})}^{(k+1)})$ .... $\ldots\ldots\ldots\ldots\ldots..(9)$, , (5), (8) , ,(9) . .$=0$ .4.-8 , ,( :2002). $-3\mathrm{m}\sim-10\mathrm{m}$$200\mathrm{m}$h , $\langle$ . 8760, . ,., , h. ,.-9 1/10 3 $\mathrm{H}_{\mathrm{o}}’=3\mathrm{c}\mathrm{m}$ 10$\circ$( , 1987) , 100 (, 2002). , ,. -1. , ,, .$-10$ . -2 ,.56., ,. 1 \sim 100, , ,( , 1992) , , ,( , 2003, 2005).$\mathrm{O}$ (2004): , , P. 304.O (1997): , , P. 442.$\mathrm{O}$ (1996): , , No. 539,$1\mathrm{I}-35$ , PP. 121-139.$\circ$ (1992): 9000, , 39 , PP. 426-430.$\mathrm{O}$ (1987) : , , 2507 , p. 39.$\mathrm{O}$ (2002) :, , 49 , PP. 496-500.$\mathrm{O}$ (2003) :, , 50 , pp. 481-485.$\mathrm{O}$ (2005) : 3, , Vol. 21, PP. 1029-1034.OBakker, W. T. (1968) : The dynamics of a coast with groyne system, Proc. . 1 lth I $\mathrm{n}\mathrm{t}$ . Conf. on CoastalEng. , pp. 492-517,ODean, R. G. (1990 : Equilibrium beach profi les, characteristics and applicat $\mathrm{i}$ on, J. Coasta}${\rm Res}$ . $,$ $7(1)$ , pp. 53-84.OSerizawa, M. , T. Uda, T. San-nami, K. Furuike and T. Kumada (2003) : Improvement of contourline change model $\mathrm{i}\mathrm{n}$ terms of stabilization mechani sm of 1ongitudinal prof$\mathrm{i}$ le, CoastalSediments .03, $\mathrm{p}\mathrm{p}$ . 1-15.8-1 :7-2 : if-8(1)$\dot{j}_{\dot{1}}\mathrm{R}^{\mathrm{x}_{\#\iota’}}*\mathrm{Y}\ovalbox{\tt\small REJECT}_{\mathrm{j}}\backslash ff|_{\sim}J2_{\backslash }:$$\acute{\iota_{J}}^{\mathrm{t}}$$\approx.\#\cdot \mathrm{a}\Re_{\sim}$$\mathit{0}_{\backslash \phi-}{}^{\mathrm{t}}\mathrm{A}_{\}$.$-\Leftrightarrow**f*\sim n+$$–[searrow] fi\tau$.$..–\sim\lambda\vee\cdot$$-r..\cdot..\cdot.\cdot$ $*\sim$ $.*$$.\cdot-.\neg J..\cdot.l-\mathrm{A}-\mathrm{f}\mathrm{i}$$!_{arrow}*/^{\ovalbox{\tt\small REJECT}\backslash \rho}.\not\in.\ovalbox{\tt\small REJECT}_{\mathrm{r}}^{\iota_{\acute{\mathrm{i}}}}\backslash \cdot B_{\tau}$$\grave{\ovalbox{\tt\small REJECT}}^{\mathit{1}_{h}7}".\mathrm{f}_{\overline{\backslash }}\acute,-$$\mathrm{A}J.’$$:\cdot.$ . : $.\vee$$\cdot$, : $\sim$ . $.$ : -. , $\cdot$$\mathrm{g}_{\mathrm{f}\prime}^{r_{\acute{d}}}$ . $=$ $\overline{\sim*}\underline{r^{-}}_{=^{\mathrm{k}}}\cdot‘.R.\yen_{\wedge}\mathrm{p}_{\theta},\cdot$. $9,’$(2)$\blacksquare$$C\mathrm{r}\mathrm{o}\mathrm{s}\mathrm{s}\sim s11\Omega \mathrm{r}\mathrm{c}^{\eta}\backslash \mathrm{D}\mathrm{f}\mathrm{l}51\mathrm{T}\hslash 11\mathrm{l}\mathrm{S}\mathrm{p}\mathfrak{o}\mathrm{r}\mathrm{t}:q_{\mathrm{c}}$$\vee \mathrm{I}-\mathrm{B}\mathrm{S}\mathrm{s}\sim s11\Omega \mathrm{r}\mathrm{c}\backslash \mathrm{D}\mathrm{f}\mathrm{l}51\eta \mathrm{T}\hslash 11\mathrm{l}\mathrm{S}\mathrm{p}\mathfrak{o}\mathrm{r}\mathrm{t}$ : $q_{\mathrm{c}}$ $\prime_{f_{\{}^{\bigcap_{\mathrm{i}}}}_{\infty}\mathrm{V}l_{k}\overline{t}\vee\overline{\iota}’5$$\subset \mathrm{t}_{\vee}^{\rho}\S \mathrm{c}\iota\{19\overline{\mathit{1}}1.\mathrm{J}$$\backslash _{\backslash }.$.$\underline{\rho},?^{11\mathrm{f}31\mathrm{t}\mathrm{r}11\mathrm{f}\mathrm{J}\mathfrak{n}}\mathrm{J}$ ltro$\Leftrightarrow \mathrm{q}\vee\iota \mathrm{i}\mathrm{l}\mathrm{l}\mathrm{t}\mathrm{t}\mathrm{j}\mathfrak{U}1.\mathrm{I}fl|$ s r.:7)e $1i\}\mathfrak{i}\mathrm{k}^{\triangleright}\mathrm{q}\mathrm{u}11_{\mathrm{t}}^{r}\mathrm{b}\mathrm{r}\{\mathrm{U}\hslash 1\backslash \backslash \{\prime 0$$\backslash \mathrm{t}^{\dot{\mathrm{k}}’}.\mathrm{J}_{\mathrm{v}}$. $1_{\vee\sim d}^{t_{\gamma j^{\neg}}’r_{d}}’\cdot \mathrm{J}$ $fJ\simeq\beta_{r}$ $\mathrm{f}^{-}i|||$$\text{ }\mathrm{b}\mathfrak{l}_{\mathrm{t}^{1})}\mathrm{t}\int_{\mathrm{g}_{\backslash \backslash }^{12}}.\overline{\sim}\mathrm{f}1*$1 $l1$$\.-\mathrm{j}$$-F1\cdot f\mathrm{t}^{\frac{\cot\beta}{\cot\gamma_{\mathit{1}_{t}}}}-1)\ldots\ldots(1)$(b) steep slopecol $\beta$.$\overline{-}-\underline{d1^{f}}\ldots\ldots\ldots(_{\wedge}^{\gamma})$$(\mathrm{d}\mathrm{o}4^{\wedge\prime}.\mathrm{n}\mathrm{b}.,l\S t\mathrm{d}\}ff_{\grave{\prime}}fl\mathit{1}J_{i}^{<\mathrm{t}1}]|\mathrm{i}_{\mathcal{A}\wedge-}\mathrm{t}_{!}\mathrm{i}||\ldots.$.$d_{\overline{4}}$$\mathrm{V}l\overline{\kappa}t\vee\overline{\iota}’5$\inf y_{\cap}$$f$ {{ . . $\cdot$$]^{r}$.$/\lrcorner$$\wedge J1\wedge$1I$\gamma_{r_{\theta}}\mathrm{t}\mathrm{h}_{\dot{\mathrm{c}}}i3\mathrm{I}\iota\underline{\mathrm{g}}1^{p}$. $r \backslash \zeta d\dagger \mathrm{h}rightarrow\bigvee_{\acute{\mathrm{t}}}\mathit{1}\dagger 1\vee- 11\mathrm{i}^{f}\mathrm{J}\mathrm{r}\downarrow \mathrm{f}\mathit{3}\mathrm{I}Y1\mathrm{t}_{\vee}\lrcorner \mathrm{a}\mathrm{c}]_{\mathrm{J}}- 1\sim^{\wedge}\grave{s}j\mathrm{i}^{\tilde{\mu}}$. (c) $\{f^{8\hslash \mathrm{t}1\mathrm{e}\mathrm{s}1\theta \mathrm{p}\epsilon_{\wedge}}$$.l\iota x\theta.\mathrm{P}^{\wedge}\mathrm{i}’ \mathrm{t}11\mathrm{J}\mathrm{l}\overline{\mathrm{k}}\underline{\backslash }\cdot\iota \mathrm{I}\mathrm{I}\iota \mathrm{s}1/a\iota\iota \mathrm{r}]^{\mathrm{J}\mathrm{U}l\mathrm{L}}\cdot*l_{L}$$\underline{\rho},?\iota\iota:3$ ltJf IlfJn $\xi^{1}\mathrm{r}1\supset \mathrm{f}\mathrm{i}1\overline{\prime-}$$t\angle\sim-F1\cdot f\mathrm{t}^{\frac{\cot\beta}{\cot\ga ma_{\mathit{1}_{t }-1)\ldots\ldots(1)$erline{-}-\underline{d1^{f}}\ldots\ldots\ldots(_{\wedge}^{9})$$\mathrm{c}J_{i}^{<\{\}}$amma_{r_{\theta}}$the$\mathfrak{j}\underline{\mathrm{g}}$]$p.\cdot r\backslash [\backslash \mathrm{t}_{\backslash }\mathrm{z}_{d\mathrm{f}\dagger \mathrm{h}_{\vee-}’}\dot{*}’\mathrm{J}_{\mathrm{v}}.\underline{\prime}\tau_{d_{\overline{4}}}\zeta 1^{t_{\gamma j^{\neg}}’r_{d}}.$}$rightarrow\vee\acute{(}\mathit{1}^{1111\mathrm{i}\dagger \mathrm{y}\mathrm{r}\downarrow \mathrm{f}\mathit{3}\mathrm{I}Y1\mathrm{t}_{\vee}^{d}\mathrm{a}\mathrm{c}1)_{\sim}^{-}arrow 1\grave{s}}.j\mathrm{i}^{\tilde{\mu}}\Leftrightarrow \mathrm{q}\mathrm{c}_{\vee\sim d}\iota \mathrm{i}11\mathrm{t}\mathrm{t}\mathrm{j}\mathfrak{U}1\mathrm{I}\mathfrak{n}\iota \mathrm{s}\downarrow l_{\mathrm{r}}\mathrm{t}\mathrm{r}_{-r}^{l}3${$\mathrm{f}^{\mathrm{e}\mathfrak{n}l1\mathrm{g}\{\theta \mathrm{r}_{1}\epsilon_{\wedge}}*\overline{\sim}\mathrm{r}1_{\backslash }’\mathrm{i}1|||...\cdot.\cdot...’,\acute{\{}\backslash \{0|\iota_{\mathrm{i}}\dot{\mathrm{L}}--^{1}.‘.\cdot.\cdot.,\cdot.’\backslash _{\frac{f1_{\iota-}}{}}\ovalbox{\tt\small REJECT}\underline{\sigma}_{\sim\dot{\mathrm{i}}}’..@\mathrm{f}-\simarrowarrow’..\cdot.\sim‘\tilde{\backslash },\cdot \mathrm{m}\sim,-"-\cdot\sim.*\cdot..‘.".- \mathrm{J}_{\mathrm{r}}\acute{\tau}--\wedge \mathrm{v}--+-\cdot.\sim\cdot-$ ( $\sim \mathrm{r}_{\mathrm{L}1_{\sim}}.\cdot.\overline{‘}!_{\mathrm{s}_{\vee}\backslash \mathrm{t}}^{\mathrm{v}\mathrm{t}.}\sim \mathrm{c}\mathrm{c}.\cdot\frac{\ovalbox{\tt\small REJECT}_{\mathrm{v}}}{\ovalbox{\tt\small REJECT}\sim \mathrm{v}}t..1\mathrm{t}1\mathrm{v}_{\epsilon_{\vee}^{\wedge}}\mathrm{c}\backslash \iota\overline{4}\mathrm{L}\mathrm{t}.1\mathrm{v}_{\vee}.\mathfrak{l}\iota \mathrm{v}\forall\dot{t}\mathrm{t}\frac{\mathrm{t}}{}\mathrm{t}\mathrm{i}\dot{\mathrm{J}}J\}\mathrm{t}\gamma\#\dot{\Delta}\mathrm{d}\mathrm{L}\mathrm{r}l.\mathrm{r}\backslash$}$\overline{\mathfrak{n}}\mathrm{f}\mathrm{f}\mathrm{c}_{1}11.\dot{\mathrm{y}}\mathrm{t}1_{1}31^{\underline{\mathrm{r}}\mathfrak{j}}\}rightarrow \mathrm{n}$$fI$ $\mathrm{t}\mathrm{h}\mathrm{e}.\cdot\sim \mathrm{n}r1_{\sim}^{p_{1\}}}\mathrm{f}\mathrm{t}\mathrm{h}_{-\sim}\mathrm{P}\mathrm{V}_{-\S\}_{--\mathrm{f}}}. h|i$. slope$\eta_{\vee\dot{\acute{\vee}}}-1\mathrm{n}\mathrm{t}011\mathrm{r}$ $1\ddagger\dagger \mathfrak{l}_{*}^{\dot{\mu}}\mathrm{r}\mathrm{v}\mathrm{a}1$$\int \mathrm{J}.<f\mathrm{J}{}^{t}t_{-}^{>}(\mathrm{j}$$\mathrm{Y}^{\cdot}\iota\ell_{1\mathrm{f}\dot{\mathrm{f}}^{\mathrm{I}^{\neg}}.\mathrm{f}\mathrm{f}_{\iota>}\mathrm{f}:\mathrm{O}\mathrm{f}_{\vee}^{\dot{\mu}}\theta\iota_{\backslash ^{\backslash }}^{n}\mathrm{t}_{\mathrm{d}\mathrm{J}1\mathrm{C}^{\urcorner}\mathrm{e};\circ \mathfrak{s}1\iota,\mathrm{c}\mathrm{o}:;\mathrm{t}\mathrm{O}\aleph 1];\mathrm{B}_{\vee}^{\prime>}}^{\mathcal{X}}},|\urcorner\cdot \mathrm{I}^{\dot{\mathrm{J}}}$$(1\mathrm{J}\mu_{\iota}\mathrm{v}*1\mathrm{f}T4)$-39\dashv-5-6-710-9(a)$250..\cdot\neg..---.----\cdot--\cdot--\cdot.-\cdot\cdot\sim\cdot-$ $r\cdot--$$\succ\vee\wedge\in 100- 50500^{\cdot}..\cdot--.\cdot.\cdot.\vee\iota-\mathrm{i}_{-}\backslash \cdot$$...\cdots.\cdot.\vdash^{7\mathrm{G}\mathrm{m}}-.\cdot\sim--\mathrm{c}N^{\cdot}t.---.\cdot..\cdot-,--.S_{--}--.--.\cdot"’\cdot--\cdot----r3-----------$.$.——?5\mathfrak{m}- 2\mathrm{I}$}$m\backslash \triangleright m\{.\lambda 9\mathrm{j}^{\backslash }R\hslash-\cdot.\cdot-\cdot--\cdot.\cdot....\cdot\ldots\cdot$.$-\cdot-$“2001 $\mathrm{S}0.\cdot$.i $=$ $1/10$-10$\iota$ . , $\mathrm{A}$ $’$ ... $arrow$0 100 200 300 400 500$\mathrm{X}(’\iota\iota)$(b)$\mathrm{Z}50\overline{.\tau}-\cdot-\cdot---$ .-$\cdot$ $\cdot.-$‘4 $.2\mathrm{C}m\dagger$ \lambda n^$u$.200 , -. $m.$.—,.$.’\vdash$150 $\cdot\overline{\cdot\rceil \mathrm{s}-}$:$\hat{\frac{\in}{\succ}}100$$.t0$ ...50 $|$.. $\cdot$ -,$\cdot$ .$\cdot$ ..-. .:. .’0 . $—\cdot.\sim--$.$\cdot$. ..—– –.5– -.- $\cdot$ .$.\cdotarrow$ :.– .$\sim$ , $\cdot$-\={o} - . $’-arrow-\sim$ ..$\sim\cdot\cdot\cdot$ .$.50$ : -.– . .$*,\cdot \mathrm{R}\neg\dot{\mathrm{t}}7\dot{4}.\mathrm{k}$.1OO$.-\text{ _{}\hat{0}100\overline{2003004\mathrm{o}\mathrm{o}}\mathrm{s}\overline{\mathrm{o}}\mathrm{o}}---\cdot\cdot-arrow-\cdot--------\cdot--\cdot\cdot----\cdot"\sim\cdot-\sim$$\mathrm{X}\{\mathrm{m}\mathrm{I}$. - .- $-\wedge\vee l\cdot$ . -. $\wedge$..\overline{\cdot \mathrm{I} S }-... ’’$-’.\cdot$.$\cdot.-$. $.:$. $.$ ’.-$-.-\cdot.\cdotarrow$..- /.$:_{-}.-$$’$.$\vee\cdot$. .$—\sim$ $\sim\cdot\cdot\cdot..$: $-’.\overline{0.}.-\wedgearrow\sim...\cdot\wedge\sim$ -,$ $arrow-\sim$ . $’$ .$-.\llcorner$$-\cdot-$ . .. .-10

数値シミュレーションによる海浜変形の予測(複雑流体の数理とその応用)

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数値シミュレーションによる海浜変形の予測(複雑流体の数理とその応用)

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