= Hydrostatic response to a localized horizontal force
{title2=$\psi_{tt}-c^2\psi_{xx}=-if_t/m,\quad c=N/|m|$}
For a weak horizontal forcing proportional to $e^{imz}$ in an ideal uniformly stratified nonrotating fluid, the low-frequency <hydrostatic approximation> gives the displayed one-dimensional <wave equation> for the <streamfunction> amplitude. Two oppositely propagating characteristic integrals determine the response. A source confined to $|x|\leq a$ and switched on at time zero produces no response beyond $|x|\leq ct+a$ in this reduced equation. The bound on mixed forcing derivative $|f_{xt}|\ll |mNf_{\max}|$ controls the neglected vertical acceleration in characteristic magnitude.
Back to article page
