\contentsline {chapter}{\numberline {1}浅水系の赤道波の定式化と無次元化}{1}
\contentsline {section}{\numberline {1.1}定式化}{1}
\contentsline {section}{\numberline {1.2}無次元化}{1}
\contentsline {section}{\numberline {1.3}$ v$ の式の導出}{3}
\contentsline {section}{\numberline {1.4}境界条件}{4}
\contentsline {chapter}{\numberline {2}赤道波の固有値問題とその解}{5}
\contentsline {section}{\numberline {2.1}固有値問題の定式化}{5}
\contentsline {section}{\numberline {2.2}$\mathaccent "705E {v}\not =0$ の場合}{6}
\contentsline {subsection}{\numberline {2.2.1}$n=0$ の場合}{7}
\contentsline {subsection}{\numberline {2.2.2}$n\ge 1$ の場合}{9}
\contentsline {section}{\numberline {2.3}$\mathaccent "705E {v}=0$ の場合}{12}
\contentsline {subsection}{\numberline {2.3.1}$\omega = -k (\not =0)$ の場合}{12}
\contentsline {subsection}{\numberline {2.3.2}$\omega = k$ の場合}{13}
\contentsline {section}{\numberline {2.4}固有値, 固有関数のまとめ}{13}
\contentsline {subsection}{\numberline {2.4.1}$ \mathaccent "705E {v}\not =0$ の解}{13}
\contentsline {subsection}{\numberline {2.4.2}$ \mathaccent "705E {v}=0$ の解}{14}
\contentsline {section}{\numberline {2.5}位相速度のまとめ}{15}
\contentsline {subsection}{\numberline {2.5.1}$ \mathaccent "705E {v}\not =0$ の解}{15}
\contentsline {subsection}{\numberline {2.5.2}$ \mathaccent "705E {v}=0$ の解}{16}
\contentsline {chapter}{\numberline {3}赤道波の分散関係式と水平構造}{17}
\contentsline {section}{\numberline {3.1}赤道波の分散曲線}{17}
\contentsline {section}{\numberline {3.2}$n=-1$ の場合の水平構造}{18}
\contentsline {section}{\numberline {3.3}$n=0$ の場合の水平構造}{19}
\contentsline {section}{\numberline {3.4}$n\ge 1$ の場合の水平構造}{20}
\contentsline {section}{\numberline {3.5}$k=0$ のモードの水平構造に関する注釈}{23}
\contentsline {chapter}{\numberline {4}慣性重力波の水平伝播のメカニズム}{25}
\contentsline {section}{\numberline {4.1}$ n=1, k=0$ の慣性重力波}{26}
\contentsline {subsection}{\numberline {4.1.1}$n=1, k=0$ の慣性重力波の特徴}{26}
\contentsline {subsection}{\numberline {4.1.2}$n=1, k=0$ の慣性重力波の構造を決める物理量}{27}
\contentsline {subsection}{\numberline {4.1.3}$n=1, k=0$ の慣性重力波の構造}{28}
\contentsline {section}{\numberline {4.2}$ n=1, k\not =0$ の東進慣性重力波}{35}
\contentsline {subsection}{\numberline {4.2.1}$ 0 < k \le 1.2$ (低波数)の東進慣性重力波の特徴}{35}
\contentsline {subsection}{\numberline {4.2.2}$ k > 1.2$ (高波数)の東進慣性重力波の特徴}{45}
\contentsline {section}{\numberline {4.3}$ n=1, k\not =0$ の西進慣性重力波}{47}
\contentsline {subsection}{\numberline {4.3.1}$ 0 < k \le 1.1$ (低波数)の西進慣性重力波の特徴}{47}
\contentsline {subsection}{\numberline {4.3.2}$ k > 1.1$ (高波数)の西進慣性重力波の特徴}{51}
\contentsline {section}{\numberline {4.4}$ n=2, k=0$ の慣性重力波}{53}
\contentsline {subsection}{\numberline {4.4.1}$n=2, k=0$ の慣性重力波の特徴}{53}
\contentsline {subsection}{\numberline {4.4.2}$n=2, k=0$ の慣性重力波の構造}{54}
\contentsline {section}{\numberline {4.5}$ n=2, k\not =0$ の東進慣性重力波}{60}
\contentsline {section}{\numberline {4.6}$ n=2, k\not =0$ の西進慣性重力波}{64}
\contentsline {chapter}{\numberline {5}赤道ロスビー波の水平伝播のメカニズム}{68}
\contentsline {section}{\numberline {5.1}$ n=1, k=0$ の赤道ロスビー波}{69}
\contentsline {section}{\numberline {5.2}$ n=1, k\not =0$ の赤道ロスビー波}{69}
\contentsline {subsection}{\numberline {5.2.1}$ 0 < k \le 2.0$ (低波数)の赤道ロスビー波の特徴}{69}
\contentsline {subsection}{\numberline {5.2.2}$ k > 2.0$ (高波数)の赤道ロスビー波の特徴}{75}
\contentsline {section}{\numberline {5.3}$ n\ge 2, k\not =0$ の赤道ロスビー波}{78}
\contentsline {chapter}{\numberline {6}混合ロスビー重力波の水平伝播のメカニズム}{83}
\contentsline {section}{\numberline {6.1}$n=0, k=0$ の混合ロスビー重力波}{83}
\contentsline {subsection}{\numberline {6.1.1}$n=0, k=0$ の混合ロスビー重力波の特徴}{84}
\contentsline {subsection}{\numberline {6.1.2}$n=0, k=0$ の混合ロスビー重力波の構造}{84}
\contentsline {section}{\numberline {6.2}$ n=0, k\not =0$ の東進混合ロスビー重力波}{90}
\contentsline {subsection}{\numberline {6.2.1}$ 0 < k \le 0.7$ (低波数)の東進混合ロスビー波の特徴}{90}
\contentsline {subsection}{\numberline {6.2.2}$ k > 0.7$ (高波数)の東進混合ロスビー波の特徴}{95}
\contentsline {section}{\numberline {6.3}$ n=0, k\not =0$ の西進混合ロスビー重力波}{98}
\contentsline {subsection}{\numberline {6.3.1}$ 0 < k \le 2.5$ (低波数)の西進混合ロスビー波の特徴}{98}
\contentsline {subsection}{\numberline {6.3.2}$ k > 2.5$ (高波数)の西進混合ロスビー波の特徴}{103}
\contentsline {chapter}{\numberline {7}赤道ケルビン波の水平伝播のメカニズム}{109}
\contentsline {chapter}{\numberline {A}赤道波の固有値・固有関数(有次元系)}{113}
\contentsline {section}{\numberline {A.1}固有値問題の定式化}{113}
\contentsline {section}{\numberline {A.2}固有値, 固有関数のまとめ}{114}
\contentsline {subsection}{\numberline {A.2.1}$ \mathaccent "705E {v}\not =0$ の解}{114}
\contentsline {subsection}{\numberline {A.2.2}$ \mathaccent "705E {v}=0$ の解}{115}
\contentsline {chapter}{\numberline {B}$n\ge 1$ の分散関係式の解}{116}
\contentsline {section}{\numberline {B.1}$ n\ge 1$ の場合の分散関係式の厳密解}{116}
\contentsline {section}{\numberline {B.2}$ n\ge 1$ の場合の分散関係式の近似解}{121}
\contentsline {subsection}{\numberline {B.2.1}Matsuno(1966)の方法}{121}
\contentsline {subsection}{\numberline {B.2.2}厳密解から近似解を導く方法}{122}
\contentsline {chapter}{\numberline {C}赤道波方程式の各項のモード展開}{125}
\contentsline {chapter}{\numberline {D}渦度方程式の各項のモード展開}{128}
\contentsline {chapter}{\numberline {E}回転の無い浅水系の重力波}{131}
\contentsline {section}{\numberline {E.1}1次元の非回転浅水系重力波}{131}
\contentsline {section}{\numberline {E.2}2次元の非回転浅水系重力波}{132}
\contentsline {chapter}{\numberline {F}$ n=1, k\not =0$ の慣性重力波の物理量}{141}
\contentsline {chapter}{\numberline {G}$ n=2, k=0$ の慣性重力波の物理量}{144}
\contentsline {chapter}{\numberline {H}$ n=0, k=0$ の混合ロスビー重力波の物理量}{146}
\contentsline {chapter}{\numberline {I}中緯度ロスビー波}{148}
\contentsline {section}{\numberline {I.1}準地衝流渦度方程式}{148}
\contentsline {section}{\numberline {I.2}ロスビー波の分散関係式}{149}
\contentsline {section}{\numberline {I.3}速度ベクトル, ジオポテンシャルの位相伝搬のメカニズム}{151}