Volume averages in a shearing box
= Volume averages in a shearing box
{title2=$\langle\partial_xQ\rangle=\langle\partial_yQ\rangle=\langle x\partial_yQ\rangle=\langle\partial_zQ\rangle=0$}
Periodic azimuthal and vertical boundary terms vanish. Radial boundary terms cancel after the azimuthal translation prescribed by the <shearing-periodic boundary condition>. Consequently the <volume average> of a divergence is zero, enabling integration by parts for the smooth shearing-periodic fields.