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波の共鳴による不安定の理解
(通常のモードどうし)
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九州大学 応用力学研究所

伊賀 啓太

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iga@riam.kyushu-u.ac.jp


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(2003年夏 GFDセミナー, 2003/09/09 奈井江)          

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共鳴を起こす中立モードの特定のしかた(1)

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不安定モードが2つの中立波動の共鳴で理解できる場合が\
ありそうであることがわかった。
→具体的な手続きとしてはどのようにすればよいのか?

2つの中立波のうち片方のみが存在する「部分系」を作り、\
分散曲線・固有モードの構造などを比較する。
…2つの部分系の中立波の分散曲線が交わったところに\
不安定モードがあれば\
この不安定モードはこれらの中立波の共鳴として理解できる。

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シアー不安定の部分系解析

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基本場
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\begin{displaymath}
     U = \left\{ \begin{array}{cl}
                   U_0 & (y>L) \\
                   \displaystyle
                   \frac{U_0}{L} y & (-L<y<L) \\
                 - U_0 & (y<-L)
                 \end{array} \right.
\end{displaymath}
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\begin{displaymath}
     U = \left\{ \begin{array}{cl}
                   \displaystyle
                   \frac{U_0}{L} y & (y>-L) \\
                 - U_0 & (y<-L)
                 \end{array} \right.
\end{displaymath}
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\begin{displaymath}
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                   U_0 & (y>L) \\
                   \displaystyle
                   \frac{U_0}{L} y & (y<L)
                 \end{array} \right.
\end{displaymath}
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シアー不安定の部分系解析

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部分系の中立波の分散関係と\
全体系の分散関係

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%image "ncarg/zone-reso-c_1.eps" 0 120 120 1

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シアー不安定の部分系解析

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部分系の中立波の構造と\
不安定波の構造

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%image "ncarg/zone-phi.eps" 0 100 100 1

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前線不安定の部分系解析

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2層(多層)問題の不安定は、\
「各層を取り出す」という形で部分系を\
明確に作ることができるから、\
この解析方法が素直に適用できる。
両層ともに一様流からなる最も簡単な基本場に対する\
前線不安定に適用した例を示す。 (Iga 1993)
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Iga, 1993: J. Fluid. Mech., 255, 213, Fig.1
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前線不安定の部分系解析

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Orlanski (1969)の結果
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(Orlanski, 1968: J. Atmos. Sci., 25, 178, Fig.10)

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前線不安定の部分系解析

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Ri-Ro面に書いた、最も成長率の大きなモード(Iga 1993)
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(Iga, 1993: J. Fluid. Mech., 255, 213, Fig.3)

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前線不安定の部分系解析

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Ri=3.0の分散関係 (Iga 1993)
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(Iga, 1993: J. Fluid. Mech., 255, 213, Fig.6)

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前線不安定の部分系解析

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1層系の中立波の分類 (Iga 1993)
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(Iga, 1993: J. Fluid. Mech., 255, 213, Fig.9[left], Fig.10[right])

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前線不安定の部分系解析

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不安定モードと中立波の構造 (Iga 1993)
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(Iga, 1993: J. Fluid. Mech., 255, 213, Fig.10[left], Fig.12[right])

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前線不安定の部分系解析

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不安定モードの分類 (Iga 1993)
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(Iga, 1993: J. Fluid. Mech., 255, 213, Fig.11)
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不安定モードにつながる中立波の対を探す

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部分系が作りにくい場合でも\
分散曲線を書いた時に、\
不安定モードにつながる中立波の対の分散曲線\
を探せばよい。

←波数が多少変わっても同じ分散曲線上のモードの性質は\
大きくは変わらないはず。
不安定波は、そこにつながっている2つの中立波の
共鳴による解釈が可能となる。

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不安定モードにつながる中立波の対(浅水系)

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状況設定 (Hayashi and Young 1987)
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(Hayashi and Young, 1987: J. Fluid. Mech., 184, 477, Fig.1)

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不安定モードにつながる中立波の対(浅水系)

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分散曲線 (Hayashi and Young 1987)
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(Hayashi and Young, 1987: J. Fluid. Mech., 184, 477, Fig.2)

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不安定モードにつながる中立波の対(浅水系)

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不安定波と中立波の構造 (Hayashi and Young 1987)
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(Hayashi and Young, 1987: J. Fluid. Mech., 184, 477, Fig.4)

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不安定モードにつながる中立波の対(2次元系)

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部分系を作れたシアー不安定の場合も、\
この方法でも解析ができる。

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不安定モードにつながる中立波の対(2次元系)

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