1.4.2 Stationary case: assumptions

Assumption: gravity in $\bgroup\color{DEFcolor}$z$\egroup$ direction (downward):

$\begin{displaymath} \Phi = g z \enspace . \end{displaymath}$

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Assumption: quasi-stationarity (no trends, fluctuations allowed)

Averaging over $\bgroup\color{DEFcolor}$t$\egroup$ , $\bgroup\color{DEFcolor}$x$\egroup$ , and $\bgroup\color{DEFcolor}$y$\egroup$ gives

$\begin{displaymath} \frac{\partial }{\partial t} = 0, \enspace \frac{\partial ... ...x} = 0, \enspace \frac{\partial }{\partial y} = 0 \enspace . \end{displaymath}$

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