Shearing-periodic boundary condition
= Shearing-periodic boundary condition
{title2=$f(L_x,y,z,t)=f(0,y+2AL_xt,z,t)$}
For background velocity $-2Ax\mathbf e_y$, opposite radial faces of a <shearing box> are identified after the displayed azimuthal shift, modulo $L_y$. Products and spatial derivatives inherit this condition. Their radial surface integrals cancel because a translation preserves an integral over a periodic azimuthal interval.