Комплексный потенциал

Комплексный потенциал — функция двух переменных $x$ и $y$ , использующаяся в гидродинамике для описания плоского стационарного безвихревого движения несжимаемой жидкости вида $f(z)=u(x,y)+iv(x,y)$ . Действительная часть $u(x,y)$ называется потенциальной функцией, мнимая часть $v(x,y)$ называется функцией тока. Линии $u(x,y)={\rm {const}}$ называются эквипотенциальными линиями, или линиями уровня. Линии $v(x,y)={\rm {const}}$ называются линиями тока. Каждая частица жидкости движется по линии тока. Величина скорости течения жидкости равна модулю производной комплексного потенциала $V=|f'(z)|$ . Направление скорости течения жидкости образует с положительным направлением оси $Ox$ угол $\varphi =-\arg f'(z)$ . Пользуясь условиями Коши-Римана, можно из уравнения эквипотенциальных линий восстановить вид комплексного потенциала.

См. также

Потенциальное течение

Литература

Краснов М. Л., Киселев А. И., Макаренко Г. И. Функции комплексного переменного. Операционное исчисление. Теория устойчивости.. — 2-е. — М., 1981.

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