%$BI=Bj(B	2 $B<!85I9>2%b%G%k$N?tCM7W;;(B
%
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%$BMzNr(B   2001-11-06 $BB<EDBYMN(B

\documentclass[a4j,12pt]{jarticle}
\usepackage{Dennou6}

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\Dtitle{ 2 $B<!85I9>2%b%G%k$N?tCM7W;;(B}
\Ddate{2001 $BG/(B 11 $B7n(B 06 $BF|(B}
\Dauthor{$BB<ED(B $BBYMN(B}
\Dchargrad


\def\thefigure{\thesection.\arabic{figure}}
\def\theequation{\thesection.\arabic{equation}}
\def\thetable{\thesection.\arabic{table}}

\begin{document}
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%\renewcommand{\thefigure}{\thesection.\arabic{figure}}
%$B$H$$$&MM$K:FDj5A$9$k(B

% $B%?%$%H%k(B-------------------------------------
\maketitle
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%$BL\<!(B -----------------------------------------
\tableofcontents
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%----------------------------------------------
\Dparskip
\section{2 $B<!85I9>2%b%G%k$N?tCM7W;;(B}

\subsection{$B4pACJ}Dx<0$+$i$NCV$-49$((B}

$B@uI96a;w2<$G$N(B 2 $B<!85I9>2(B
$B$N2r$/$Y$-4pACJ}Dx<0$H6-3&>r7o$rM?$($?(B. 

$B$3$3$+$iF3$-=P$5$l$kI9>2$NCO7A(B $h$, $BB.EY>l(B$u, w$, $B29EY>l(B$T$
$B$r5a$a$k$?$a$K<!$N7A<0$KCV$-49$($k(B.

\subsubsection{$B1tD>J}8~$N:BI8JQ49(B}

$B1tD>J}8~$OI98|$G5,3J2=$7$?:BI8$rMQ$$$k(B.
$B$3$l$K$h$C$FI9>2$N>eIt$*$h$S2<It6-3&$K$*$1$k(B
$B?tCM8m:9$r8:$i$;$k(B.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% $B5,3J2=$7$?:BI8$rMQ$$$k0UL#(B ref Jennsen 1977
%
%
%
\begin{equation}
\zeta = \frac{h - z}{h}
\end{equation}

$B$3$l$K$h$j4pACJ}Dx<0$O<!$N$h$&$K=q$-49$($i$l$k(B.

\begin{eqnarray}
\left. \DP{u}{x} \right|_z- \frac{1}{h}\DP{w}{\zeta} &=& 0	\label{continity}\\
0 &=& -\rho g \DP{h}{x} - \frac{1}{h}\DP{\sigma_{xz}}{\zeta}
	\label{moment}\\
D &=& A(T) \sigma^n_{xz} \label{gren}\\
\DP{T}{t} + \DP{T}{\zeta} \frac{1}{h}
	\left\{ u(1 - \zeta)\DP{h}{x} - w\right\}
	&=& 
-u \DP{T}{x} 
	+ \frac{k}{\rho c_p}\frac{1}{h^2}\DP[2]{T}{\zeta}
	+ \frac{2}{\rho c_p}D \sigma^n_{xz}
	\label{energy}\\
D &=& -\frac{1}{2h}\DP{u}{\zeta} \label{hizumi}
\end{eqnarray}

$B6-3&>r7o$O1?F03XE*6-3&>r7o(B
\begin{eqnarray}
w(\zeta = 1) &=& 0\\
w(\zeta = 0) &=& \DP{h}{\zeta} + u \DP{h}{x} - \frac{M_s}{\rho}
\end{eqnarray}
$B$G$"$k(B.
$BNO3XE*6-3&>r7o$O(B
\begin{eqnarray}
\sigma_{xz}(\zeta = 0) &=& 0\\
u(\zeta =1) &=& 0
\end{eqnarray}

$BG.NO3XE*6-3&>r7o$O(B
\begin{eqnarray}
\left. -k \DP{T}{\zeta} \right|_{\zeta = 1} &=& - \gamma \\
T_s &=& T_s(h)
\end{eqnarray}
$B$G$"$k(B.



\subsubsection{$BI98|$N<0(B}
$BI9>2$N7A(B $h$ $B$r5a$a$k$?$a$K(B 
$BO"B3$N<0(B(\ref{continity})$B$r(B $\zeta$ $BJ}8~(B 0 $B$+$i(B 1 $B$^$G@QJ,$7(B, 
$B1?F03XE*6-3&>r7o$+$i(B
$BI98|$N;~4VH/E8$N<0$K$9$k(B
\footnote{$B<B:]$K$OLLE]$J$N$G(B$z$ $B:BI87O$G=q$+$l$?(B 
$F$ $B$r(B $\zeta$ $B$K:BI8JQ49$7$?(B.  }.

\begin{equation}
\DP{h}{t} = -\DP{F}{x} + \frac{M_s}{\rho}\label{thick}
\end{equation}

$B$3$3$G(B $F$ $B$O8e=R$NB.EY(B $u$ $B$N<0$+$i(B
\begin{eqnarray}
F &=& h \int^{1}_{0} u \Dd \zeta \\
  &=& 2 (\rho g)^n \left| \DP{h}{x} \right|^{n-1} 
	\DP{h}{x} h^{n+2} 
	\int^{1}_{0} \Dd \zeta 	\int^{\zeta}_{1} A(T) \zeta^{n} \Dd \zeta
\end{eqnarray}
$B$H$J$k(B.

\subsubsection{$BB.EY>l(B}
$B<!$K1?F0NLJ]B8B'(B(\ref{moment}), $B9=@.J}Dx<0(B(\ref{gren}), 
$BOD$_B.EY$NDj5A<0(B(\ref{hizumi})
$B$+$iB.EY>l(B $u$ $B$O(B$A(T), h, \zeta$ $B$N4X?t$H$7$F<!$N$h$&$K5a$^$k(B.

\begin{equation}
u =  2 (\rho g)^n h^{n+1}\left| \DP{h}{x} \right|^{n-1}\DP{h}{x}
	\int^{\zeta}_{1}A(T) \zeta^n \Dd \zeta \label{u}
\end{equation}

$w$ $B$O(B $u$ $B$HO"B3$N<0$+$i5a$^$k(B.

\begin{eqnarray}
w(\zeta) &=& h\int^{\zeta}_{1} 
		\left.\DP{u}{x}\right|_z \Dd \zeta \nonumber\\
     &=& h\int^{\zeta}_{1} 
		\left.\DP{u}{x}\right|_\zeta \Dd \zeta 
	+ \DP{h}{x} \int^{\zeta}_{1}\DP{u}{\zeta}(1 - \zeta) \Dd \zeta
\end{eqnarray}

\subsection{$B29EY>l(B}
$B%(%M%k%.!<J]B8B'$+$i29EYJ,I[$r5a$a$k(B.

\subsection{$B<B83@_Dj(B}

$B@5L#$N<ANL<};YNL(B $M_s$, $B$*$h$SI9>2I=LL29EY(B$T_s$ $B$O(B
$B<!$N$b$N$r<h$jF~$l$k(B.

%\begin{itemize}
%   \item $B8GDj$5$l$?1o<B83(B
%   \item  $B0\F0$9$k1o<B83(B
%\end{itemize}

\begin{eqnarray}
M_s = \mathmc{min}[0.5 ,s(R_{el} - d)] \\
T_s = 270 K -0.01 h 
\end{eqnarray}
$s$ $B$O<ANL<};Y4X?t$N8{G[(B, 
$R_{el}$$B$O^>M\0h$H>CLW0h$N6-3&$+$iI9>2Cf?4$^$G$N5wN%(B, 
$d$ $B$OI9>2Cf?4$+$i$N5wN%$G$"$k(B.

\subsection{$BJ,2rG=(B $B$H7W;;NN0h(B}

$B7W;;$9$kNN0h$O?eJ?J}8~$K(B 750 km $B$G3J;R4V3V$O(B 50 km $B$H$9$k(B.
$B1tD>J}8~$O(B 10 $BAX$H$j(B, $\zeta = 
0, 0.15, 0.30, 0.45, 0.60, 0.75, 0.83, 0,90, 0.95, 0.98, 1 $
$B$H$$$&CM$r<h$k(B
\footnote{$B<B:]$K$O6u4V3J;RE@$O$^$@L$Dj(B. 
$B:XF#$5$s$NOC$@$H1tD>J}8~$OB?$a$K<h$C$F(B 50 $BAX(B
$B$0$i$$$G$bNI$$$s$8$c$J$$$H$N$3$H(B.}. 

$B;~4V9o$O(B CFL $B>r7o$+$i7h$^$k;~4V9o$_$G$"$k?tG/(B
\footnote{$B$^$@=P$7$F$J$$$G$9(B}
$B$H$9$k(B.


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%$BI9>2%b%G%k$N<B83@_Dj$NNc(B
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\begin{table}[h]
%\begin{center}
%\begin{tabular}{|l|l|l|l|}
%\hline
%$BO@J8(B	& $B?eJ?%9%1!<%k(B	& $B1tD>%9%1!<%k(B	& $B;~4V%9%1!<%k(B\\
%\hline
%EISMINT	& 50 km x 50 km	& ?		& --	\\
%(1996)	& 31 x 31 grid	& 10 $BAX(B		&\\
%\hline
%saito	& 40 km x 40 km & --		& 		\\
%(1996)	& 141 x 141 grid& 26 $BAX(B		&5 $BK|G/0J>e(B 	\\
%%\hline
%abe-ouchi & 10 km $B0J2<(B  & --		& 1 $BG/(B($BB.EY>l(B), 5 $BG/(B($B29EY(B)\\
%(1993)	  & 50 grid	& 50 --100 $BAX(B	& \\
%\hline
%\end{tabular}
%%%\end{center}
%\end{table}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



\subsection{$BN%;62=(B}

$BI98|$N<0$O(B 3 $B<!85I9>2%b%G%k$N:](B, ADI $BK!$,MQ$$$i$l$k(B.
$B$7$+$7(B ADI $BK!$r(B 3 $B<!85$+$i(B 2 $B<!85$X$N>FD>$7$O$?$@$J$,$a$F$$$F$b(B
$B$o$+$i$J$+$C$?$N$GC1=c$K(B $y$ $BJ}8~@.J,$r9M$($J$$$G:9J,2=$9$k(B
\footnote{ 
2 $B<!85I9>2%b%G%k$N(B abe-ouchi(1993)$B$N?tCME*$J<jK!$O(B
\begin{itemize}
\item $BI98|$N<0(B: $B6u4V:9J,$OCf?4:9J,$rMQ$$$?M[2rK!(B
\item $BB.EY>l(B: $B%9%?%C%,!<3J;R$G@QJ,(B
\item $B29EY>l(B: $B;~4V$KBP$7$FA0?J:9J,$N1"2rK!(B
\end{itemize}
$B$H=q$$$F$"$k$@$1$G$h$/$o$+$i$J$$(B.
Jensenn(1977)$B$H(B Huybrechs(1990,1992)$B$r85$K$7$F$$$k$H$O(B
$B=R$Y$F$$$k$,(B 3 $B<!85$J$N$G(B ADI $BK!$K$J$C$F$$$k(B.}

\subsubsection{$BI98|$N<0(B}

\begin{equation}
\frac{h^{t+1}_{i} - h^{t}_{i}}{\Delta t} = 
	- \frac{F^{t}_{i + \frac{1}{2}} - F^{t}_{i - \frac{1}{2}}}{\Delta x} 
	+ M^{t}_{i}
\end{equation}

$B$3$3$G(B$F^{t}_{i + \frac{1}{2}}$$B$O(B $h$ $B$N8{G[$H$=$l0J30$NItJ,$K$o$1$F(B

\begin{equation}
F_{i + \frac{1}{2}} = D_{i + \frac{1}{2}} \frac{h_{i + 1} - h_{i}}{\Delta x}
\end{equation}
$B$H$7$F(B $D_{i + \frac{1}{2}}$ $B$rJL$G7W;;$9$k(B.

\subsubsection{$BB.EY>l(B}

\subsubsection{$B29EY>l(B}


\end{document}









