%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% 表題: 2001 年 月・惑星シンポジウム 発表原稿 %%% %%% 履歴: 2001/05/03 杉山耕一朗 %%% 2001/05/08 杉山耕一朗 %%% 2001/06/03 杉山耕一朗 %%% 2001/07/31 杉山耕一朗 %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% %%deffont "standard" xfont "comic sans ms-medium-r" %%deffont "thick" xfont "arial black-medium-r" %%deffont "typewriter" xfont "courier new-bold-r" %%deffont "type2writer" xfont "arial narrow-bold-r" %% %% Default settings per each line numbers. %% %%%default 1 leftfill, size 2, fore "darkgreen", back "lemonchiffon" %default 1 leftfill, size 2, fore "darkgreen", back "white" %default 2 size 7, vgap 10, prefix " " %%%default 3 size 2, image "brush-lemonchiffon.jpg", vgap 20 %default 3 size 2, bar "grey70", vgap 20 %default 4 size 5, fore "navyblue", vgap 30, prefix " " %% %% Default settings that are applied to TAB-indented lines. %% %tab 1 size 4, vgap 35, prefix " ", icon arc "tomato" 40 %tab 2 size 4, vgap 20, prefix " ", icon box "seagreen" 40 %tab 3 size 3, vgap 20, prefix " ", icon delta3 "blue" 40 %% %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %page %nodefault %%%size 7, fore "darkblue", vgap 20, back "lemonchiffon" %size 7, fore "darkblue", vgap 20, back "white" %center, size 7 木星型惑星大気の熱力学計算 %image "ps/jupiter.ps" 0 70 70 1 %size 4 杉山耕一朗 (北大・理) 小高正嗣 (東大・数理) 倉本圭 (北大・理) 林祥介 (北大・理) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %page 目次 はじめに 研究の背景 本研究の目標 熱力学モデルの開発 本研究の計算手法 計算結果 まとめ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %page はじめに: 木星型惑星の雲対流構造とは? %mark 光学観測 表層のアンモニア雲のみ観測可能 深部の対流をとらえることはできない ガリレオプローブ 雲の無い領域に落下 雲対流に関する情報があまり取れなかった モデル計算 地球の雲対流モデルを適用 水の凝縮しか考慮されていない 大気全体を覆うような雲分布を再現できず %again %right %fore "black", image "ps/nakajima.eps" 0 90 90 1 %size 3 Nakajima et al (2000) の雲対流モデルの結果 左上: 降水量, 左下: 温位 右上: 鉛直流速, 右下: 水蒸気圧 %pause, left, fore "red", size 5 水以外の凝縮物質によって対流構造はどのような影響を受けるか? 数値シミュレーションによって考察 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %page はじめに: 雲対流構造を考えるために %mark 鉛直 1 次元構造の把握 対流平衡 (熱力学) 断熱温度減率 凝縮物分布 放射対流平衡 (熱力学 + 放射) 加熱率分布 対流構造の把握 雲対流計算 (熱力学 + 放射 + 流体力学) 流れ場 温度場 凝縮物分布 運動量輸送 %pause, again, right, fore "black" %image "ps/AW1999.ps" 0 80 80 1 %cont %size 3 熱平衡を仮定した場合の雲密度・温度分布 (Atreya et al 1999) %pause, left, size 5, fore "red" 対流平衡ですら必要な情報がまとめられていない. 温度分布は? %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %page 本研究の目標 %fore "red", size 5 木星型惑星大気の対流平衡状態を記述するための熱力学コードの開発 %fore "navyblue" 断熱線に沿った温度・化学組成を計算 断熱温度減率 気体成分の組成の鉛直変化 系の物質の変更が容易な熱力学コード開発 従来の熱力学コードでは, どのような化学反応が生じているか把握していないと計算できない 新しい物質の追加 %fore "red", cont → %fore "navyblue", cont 必要となる化学反応式の再考 %fore "red", cont → %fore "navyblue", cont アルゴリズムの変更 %fore "darkgreen", size 4 → 化学反応式を考慮しなくても済む熱力学コードを開発する %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %page 本研究の計算手法 %fore "red", size 5 大気の熱平衡状態 → 断熱線を計算 %fore "navyblue" 温度・圧力固定, 元素保存の条件のもとギブスの自由エネルギー G を最小化 %fore "red" → 平衡化学組成 %fore "navyblue" 物質の化学ポテンシャルが計算できればわかれば OK. → 化学反応式の情報は必要なし %size 3 温度・圧力空間での平衡組成 %cont, fore "red" → エントロピー S %fore "navyblue" %size 3 温度・圧力空間でのエントロピー S %cont, fore "red" → 断熱曲線 dS = 0 %fore "navyblue" 大気の擬湿潤断熱(pseudo moist adiabat)変化を仮定 凝縮性成分気体が凝縮 → 空気塊から離脱(降水) 離脱した凝縮物質を含めた全エントロピーが保存 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %page 計算手順 1: 平衡状態の求め方 %fore "red" ギブスの自由エネルギー G の式 %fore "navyblue" %filter "platex2eps.sh gibbs" \begin{eqnarray} G(T, p, n^{\phi}_{i}) &=& \sum \mu_{i}^{\phi}(T, p, n^{\phi}_{i}) n_{i}^{\phi} \nonumber \\ &=& \sum \left\{ {\mu_{i}^{\circ}}^{\phi}(T) + RT \ln \frac{n_{i}^{\phi}}{\sum n_{i}^{\phi}} + \alpha RT \ln{\frac{p}{p_0}} \right\} n_{i}^{\phi} \nonumber \end{eqnarray} %endfilter %cont, fore "red", image "gibbs.eps" 0 250 250 1 %fore "navyblue" 必要なパラメータ 温度 圧力 標準化学ポテンシャル 計算から得られる量 平衡化学組成 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %page 計算手順 2: エントロピーの求め方 %fore "red" Maxwell の関係式 %fore "navyblue" %filter "platex2eps.sh entropy" \begin{eqnarray} S &=& - \left( \DP{G}{T} \right)_{p, n_{i}} \nonumber \\ &=& - \sum_{i} \left\{ \DP{{\mu_i^{\circ}}^{\phi}(T)}{T} + R \ln \left( \frac{n_i^{\phi}}{\sum n_i^{\phi}}\right) + \alpha R \ln p \right\} n_{i}^{\phi} \nonumber \end{eqnarray} %endfilter %cont, fore "red", image "entropy.eps" 0 250 250 1 %fore "navyblue" 必要なパラメータ 温度 圧力 標準化学ポテンシャル 平衡化学組成 計算から得られる量 エントロピー %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %page 計算手順 3: 断熱曲線の求め方 %mark %center, image "ps/pseudo3-1.eps" 0 250 250 1 %center, image "ps/pseudo3-1-info.eps" 0 200 200 1 %pause, again %mark %center, image "ps/pseudo3-2.eps" 0 250 250 1 %center, image "ps/pseudo3-2-info.eps" 0 200 200 1 %pause, again %mark %center, image "ps/pseudo3-3.eps" 0 250 250 1 %center, image "ps/pseudo3-3-info.eps" 0 200 200 1 %pause, again %center, image "ps/pseudo3-4.eps" 0 250 250 1 %center, image "ps/pseudo3-4-info.eps" 0 200 200 1 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %page 計算結果の紹介の概要 %fore "red" 開発したモデルが正しく動いていることの確認. 基本的な物理量の値の提示 %fore "navyblue" 計算設定 パフォーマンスチェックのため, 従来の研究と同一条件に パフォーマンスチェック 凝縮物分布 従来の研究(Atreya et al, 1999)との比較 蒸気圧と飽和蒸気圧の関係 計算結果 温度分布 断熱温度減率 大気の静的安定度 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %page 計算設定 %fore "red", size 5 Atreya et al (1999) の木星条件での計算と同一 %fore "navyblue" 基準面での温度・圧力 初期温度: 345 K 初期圧力: 12 bar 計算終了圧力: 0.3 bar 圧力刻み幅: 1000 点 元素存在度と物質の種類(下表) 太陽系元素存在度 (Anders and Grevesse, 1989) 物質の標準化学ポテンシャル %filter "platex2eps.sh genso" \begin{tabular}{|r|r|}\hline 元素 & 存在比 \\ \hline \hline He/H & 0.095 \\ O/H & 8.51 $\times 10^{-4}$ \\ C/H & 3.62 $\times 10^{-4}$ \\ N/H & 1.12 $\times 10^{-4}$ \\ S/H & 1.62 $\times 10^{-5}$ \\ \hline \end{tabular} %endfilter %filter "platex2eps.sh sosei" \begin{tabular}{|l|}\hline 物質名 \\ \hline \hline H$_2$(g), He(g), H$_2$O(g), CH$_4$(g), NH$_3$(g), H$_{2}$S(g) \\ H$_2$O(l), CH$_4$(l), NH$_3$(l), H$_{2}$S(l) \\ H$_2$O(s), NH$_3$(s), NH$_{4}$SH(s) \\ \hline \end{tabular} %endfilter %size 5, fore "black" %cont, size 3 表1: 太陽系元素存在度 表2: 計算に利用した物質の種類 %center %image "genso.eps" 0 200 200 1 %cont %cont, image "sosei.eps" 0 200 200 1 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %page パフォーマンスチェック (その 1) 鉛直雲密度・温度分布 過去の大気研究と整合的 %fore "black" %mark %cont, image "ps/cloud-t.gif" 0 100 100 1 %size 3 本研究での雲密度・温度分布 %again, right %image "ps/AW1999.ps" 0 60 60 1 %cont %size 2 %size 3 過去の研究での雲密度・温度分布 (Atreya et al 1999) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %page パフォーマンスチェック (その 2) 蒸気圧と飽和蒸気圧の関係 持ち上げ凝縮高度より上で, 飽和蒸気圧と蒸気圧が一致 %fore "black" %center %image "ps/vaper-H2O-edit.gif" 0 100 100 1 %cont %image "ps/vaper-NH3-edit.gif" 0 100 100 1 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %page 計算結果 (その 1) %fore "red", size 5 断熱温度分布 %fore "navyblue" 対流性の雲付近での温度分布 %fore "black" %center %image "ps/therm.gif" 0 100 100 1 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %page 計算結果 (その 2) %fore "red", size 5 断熱温度減率 %fore "navyblue" 平均: -2.0 k/km (下層), -2.4 K/km(上層) 凝縮物質の潜熱の影響によって値が変化 %mark %fore "black" %cont, image "ps/gamma-edit.gif" 0 100 100 1 %again %fore "black" %right %filter "platex2eps.sh dannetu" \begin{tabular}{|l|l|}\hline 物質名 & 断熱温度減率 \\ \hline \hline NH$_3$ & -2.0 K/km \\ \hline NH$_4$SH & -2.0 K/km \\ \hline H$_2$O & -1.7 K/km \\ \hline \end{tabular} %endfilter %image "dannetu.eps" 0 250 250 1 %cont %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %page 計算結果 (その 3) %fore "red", size 5 大気の静的安定度: 重力を復元力とする振動数の大きさ %fore "navyblue" 凝縮の潜熱によって大気が安定成層に H2O による成層が最も強い. NH3, NH4SH による寄与は H2O の 1/3, 1/6 程度 地球大気 = 約 10^-4 [s^-2] よりは弱い %mark %fore "black" %left %cont, image "ps/stability-new3.gif" 0 100 100 1 %again %fore "black" %right %filter "platex2eps.sh N2" \begin{tabular}{|l|l|}\hline 物質名 & 静的安定度 (N$^2$) \\ \hline \hline NH$_3$ & $8.0 \times 10^{-6}$ \\ \hline NH$_4$SH & $4.0 \times 10^{-6}$ \\ \hline H$_2$O & $2.5 \times 10^{-5}$ \\ \hline \end{tabular} %endfilter %image "N2.eps" 0 250 250 1 %cont %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %page まとめ 木星大気の熱力学状態を計算するための熱力学コードを開発し, 実際の計算を行った 本研究の計算手法の利点 物質の種類を変更することが容易 大気中の化学反応の情報を知らなくて良い. 大気中の物質の種類を変えても数値コード自体を変更する必要がない パフォーマンスチェック 凝縮物質の分布 Atreya et al (1999) と整合的 気相の分圧 凝縮高度より上で飽和蒸気圧に一致 温度構造の計算 温度分布, 断熱減率, 静的安定度を定量的に求めた 凝縮物質の潜熱によって大気が安定成層する. H2O による成層が最も強い 地球よりは成層が弱い %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%page %%% %%%これからの予定 %%% %%% 物質量を変化させた時の振るまいを調べる %%% 断熱温度減率 %%% 静的安定度 %%% %%% 大気の安定成層度からロスビー変形半径を見積もる %%% 実際の木星渦との比較