= Acoustic eikonal equation in a shear flow
{title2=$(\omega-Uk_x)^2=c_0^2|\mathbf k|^2$}
For a slowly varying parallel <shear flow> $U(y)\mathbf e_x$, the leading <WKB method> neglects mean-velocity gradients while retaining local advection. The <continuity equation> and <linearized Euler equations> then give the displayed acoustic <dispersion relation>. On the positive intrinsic-frequency branch, $\omega=Uk_x+c_0|\mathbf k|$ and the <group velocity> is $U\mathbf e_x+c_0\mathbf k/|\mathbf k|$. A <wavefront> normal is parallel to $\mathbf k$; the acoustic energy-ray direction generally differs because of the advection term.
Back to article page
