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LL_6_main.tex
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Преамбула
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\documentclass[12pt,a4paper]{book}
\usepackage{amsmath,amstext,amssymb} % AMS Math Package
% Bold Math. Иначе XeTeX некорекктно отображает жирные греческие символы
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%% L/C/R denote left/center/right header (or footer) elements
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%\fancyfoot[LO,LE]{\slshape Short Course on Asymptotics}
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\input{macros} % Макросы для формул
%\includeonly{LL_6_09.03}
\pagestyle{plain}
\title{Гидродиамика}
\author{Ландау Л.Д., Лифшиц Е.М.}
\date{1984 г.}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Основной документ
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{document}
\maketitle % заголовок
\frontmatter
\tableofcontents % Оглавление
\include{LL_6_0} % Предисловие
\mainmatter
\pagestyle{fancy}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Идеальная жидкость}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\include{LL_6_01.01} % Уравнение непрерывности
\include{LL_6_01.02} % Уравнение Эйлера
\include{LL_6_01.03} % Гидростатика
\include{LL_6_01.04} % Условие отсутствия конвекции
\include{LL_6_01.05} % Уравиеиие Бернулли
\include{LL_6_01.06} % Поток энергии
\include{LL_6_01.07} % Поток импульса
\include{LL_6_01.08} % Сохранение циркуляции скорости
\include{LL_6_01.09} % Потенциальное движение
\include{LL_6_01.10} % Несжимаемая жидкость
\include{LL_6_01.11} % Сила сопротивления при потенциальном обтекании
\include{LL_6_01.12} % Гравитационные волны
\include{LL_6_01.13} % Внутренние волны в несжимаемой жидкости
\include{LL_6_01.14} % Волны во вращающейся жидкости
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Вязкая жидкость}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Уравнения движения вязкой жидкости}\label{sec:p15}
\section{Диссипация энергии в несжимаемой жидкости}\label{sec:p16}
\section{Течение по трубе}\label{sec:p17}
\section{Движение жидкости между вращающимися цилиндрами}\label{sec:p18}
\section{Закон подобия}\label{sec:p19}
\section{Течение при малых числах Рейиольдса}\label{sec:p20}
\section{Ламинарный след}\label{sec:p21}
\section{Вязкость суспензий}\label{sec:p22}
\section{Точные решения уравнений движения вязкой жидкости}\label{sec:p23}
\section{Колебательное движение в вязкой жидкости}\label{sec:p24}
\section{Затухание гравитационных волн}\label{sec:p25}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Турбулентность}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Устойчивость стационарного движения жидкости}\label{sec:p26}
\section{Устойчивость вращательного движения жидкости}\label{sec:p27}
\section{Устойчивость движения по трубе}\label{sec:p28}
\section{Неустойчивость тангенциальных разрывов}\label{sec:p29}
\section{Квазипериоднческое движение и синхронизация частот}\label{sec:p30}
\section{Странный аттрактор}\label{sec:p31}
\section{Переход к турбулентности путем удвоения периодов}\label{sec:p32}
\section{Развитая турбулентность}\label{sec:p33}
\section{Корреляционные функции скоростей}\label{sec:p34}
\section{Турбулентная область и явление отрыва}\label{sec:p35}
\section{Турбулентная струя}\label{sec:p36}
\section{Турбулентный след}\label{sec:p37}
\section{Теорема Жуковского}\label{sec:p38}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Пограничный слой}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Ламинарный пограничный слой}\label{sec:p39}
\section{Движение вблизи линии отрыва}\label{sec:p40}
\section{Устойчивость движения в ламинарном пограничном слое}\label{sec:p41}
\section{Логарифмический профиль скоростей}\label{sec:p42}
\section{Турбулентное течение в трубах}\label{sec:p43}
\section{Турбулентный пограничный слой}\label{sec:p44}
\section{Кризис сопротивления}\label{sec:p45}
\section{Хорошо обтекаемые тела}\label{sec:p46}
\section{Индуктивное сопротивление}\label{sec:p47}
\section{Подъемная сила тонкого крыла}\label{sec:p48}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Теплопроводность в жидкости}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Общее уравнение переноса тепла}\label{sec:p49}
\section{Теплопроводность в несжимаемой жидкости}\label{sec:p50}
\section{Теплопроводность в неограниченной среде}\label{sec:p51}
\section{Теплопроводность в ограниченной среде}\label{sec:p52}
\section{Закон подобия для теплопередачи}\label{sec:p53}
\section{Теплопередача в пограничном слое}\label{sec:p54}
\section{Нагревание тела в движущейся жидкости}\label{sec:p55}
\section{Свободная конвекция}\label{sec:p56}
\section{Конвективная неустойчивость неподвижной жидкости}\label{sec:p57}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Диффузия}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Уравнения гидродинамики для жидкой смеси}
\section{Коэффициенты диффузии и термодиффузии}
\section{Диффузия взвешенных в жидкости частиц}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Поверхностные явления}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Формула Лапласа}\label{sec:p61}
\section{Капиллярные волны}\label{sec:p62}
\section{Влияние адсорбированных пленок на движение жидкости}\label{sec:p63}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Звук}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Звуковые волны}\label{sec:p64}
\section{Энергия и импульс звуковых волн}\label{sec:p65}
\section{Отражение и преломление звуковых волн}\label{sec:p66}
\section{Геометрическая акустика}\label{sec:p67}
\section{Распространение звука в движущейся среде}\label{sec:p68}
\section{Собственные колебания}\label{sec:p69}
\section{Сферические волны}\label{sec:p70}
\section{Цилиндрические волны}\label{sec:p71}
\section{Общее решение волнового уравнения}\label{sec:p72}
\section{Боковая волна}\label{sec:p73}
\section{Излучение звука}\label{sec:p74}
\section{Возбуждение звука турбулентностью}\label{sec:p75}
\section{Принцип взаимности}\label{sec:p76}
\section{Распространение звука по трубке}\label{sec:p77}
\section{Рассеяние звука}\label{sec:p78}
\section{Поглощение звука}\label{sec:p79}
\section{Акустическое течение}\label{sec:p80}
\section{Вторая вязкость}\label{sec:p81}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Ударные волны}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\include{LL_6_09.01} % Распространение возмущений в потоке сжимаемого газа
\include{LL_6_09.02} % Стационарный поток сжимаемого газа
\include{LL_6_09.03} % Поверхности разрыва
\include{LL_6_09.04} % Ударная адиабата
\include{LL_6_09.05} % Ударные волны слабой интенсивност
\include{LL_6_09.06} % Направление изменении величии в ударной волне
\include{LL_6_09.07} % Эволюционность ударных волн
\include{LL_6_09.08} % Ударные волны в политропном газе
\include{LL_6_09.09} % Гофрировочная неустойчивость ударных волн
\include{LL_6_09.10} % Распространение ударной волны по трубе
\section{Косая ударная волна}\label{sec:p92}
\section{Ширина ударных волн}\label{sec:p93}
\section{Ударные волны в релаксирующей среде}\label{sec:p94}
\section{Изотермический скачок}\label{sec:p95}
\section{Слабые разрывы}\label{sec:p96}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Одномерное движение сжимаемого газа}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Истечение газа через сопло}\label{sec:p97}
\section{Вязкое движение сжимаемого газа по трубе}\label{sec:p98}
\section{Одномерное автомодельное движение}\label{sec:p99}
\section{Разрывы в начальных условиях}\label{sec:p100}
\section{Одномерные бегущие волны}\label{sec:p101}
\section{Образование разрывов в звуковой волне}\label{sec:p102}
\section{Характеристики}\label{sec:p103}
\section{Инварианты Римана}\label{sec:p104}
\section{Произвольное одномерное движение сжимаемого газа}\label{sec:p105}
\section{Задача о сильном взрыве}\label{sec:p106}
\section{Сходящаяся сферическая ударная волна}\label{sec:p107}
\section{Теория мелкой воды}\label{sec:p108}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Пересечение поверхностей разрыва}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Волна разрежения}\label{sec:p109}
\section{Типы пересечений поверхностей разрыва}\label{sec:p110}
\section{Пересечение ударных волн с твердой поверхностью}\label{sec:p111}
\section{Сверхзвуковое обтекание угла}\label{sec:p112}
\section{Обтекание конического острия}\label{sec:p113}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Плоское течение сжимаемого газа}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Потенциальное движение сжимаемого газа}\label{sec:p114}
\section{Стационарные простые волны}\label{sec:p115}
\section{Уравнение Чаплыгина (общая задача о двухмерном стационарном движении сжимаемого газа)}\label{sec:p116}
\section{Характеристики плоского стационарного течении}\label{sec:p117}
\section{Уравнение Эйлера - Трикоми. Переход через звуковую скорость.}\label{sec:p118}
\section{Решения уравнения Эйлера - Трикоми вблизи неособых точек звуковой поверхности}\label{sec:p119}
\section{Обтекание со звуковой скоростью}\label{sec:p120}
\section{Отражение слабого разрыва от звуковой линии}\label{sec:p121}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Обтекание конечных тел}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Образование ударных волн при сверхзвуковом обтекании тел}\label{sec:p122}
\section{Сверхзвуковое обтекание заостренного тела}\label{sec:p123}
\section{Дозвуковое обтекание тонкого крыла}\label{sec:p124}
\section{Сверхзвуковое обтекание крыла}\label{sec:p125}
\section{Околозвуковой закон подобия}\label{sec:p126}
\section{Гиперзвуковой закон подобия}\label{sec:p127}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Гидродинамика горения}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Медленное горение}\label{sec:p128}
\section{Детонация}\label{sec:p129}
\section{Распространение детонационной волны}\label{sec:p130}
\section{Соотношение между различными режимами горения}\label{sec:p131}
\section{Конденсационные скачки}\label{sec:p132}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Релятивистская гидродинамика}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Тензор энергии-импульса жидкости}\label{sec:p133}
\section{Релятивистские гидродинамические уравнения}\label{sec:p134}
\section{Ударные волны в релятивистской гидродинамике}\label{sec:p135}
\section{Релятивистские уравнения движения вязкой и теплопроводной среды}\label{sec:p136}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Гидродинамика сверхтекучей жидкости}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Основные свойства сверхтекучей жидкости}\label{sec:p137}
\section{Термомехаяический эффект}\label{sec:p138}
\section{Уравнения гидродинамики сверхтекучей жидкости}\label{sec:p139}
\section{Диссипативные процессы в сверхтекучей жидкости}\label{sec:p140}
\section{Распространение звука в сверхтекучей жидкости}\label{sec:p141}
\end{document}