Spectral gap of a shearing-periodic box
= Spectral gap of a shearing-periodic box
{title2=$\langle|\nabla f|^2\rangle\ge(2\pi/L)^2\langle|f|^2\rangle$}
For zero-mean fields in a <shearing box>, <Fourier modes> have wavevectors $(2\pi n/L_x+2At\,2\pi m/L_y,2\pi m/L_y,2\pi p/L_z)$. A nonzero azimuthal or vertical index supplies at least $2\pi/L$, where $L$ is the largest box side; otherwise the nonzero radial index does. <Parseval identity> gives the displayed <Poincaré inequality> uniformly in time.