= Particle ellipses for rotating shallow-water waves
{title2=$\xi=-U\sin\theta/\omega,\quad\upsilon=V\cos\theta/\omega$}
For a plane <inertia-gravity wave> on a resting layer, $\eta=\eta_0\cos(kx-\omega t)$, the horizontal velocities are $u=U\cos\theta$ and $v=V\sin\theta$, where $U=\omega\eta_0/(kh_0)$ and $V=f\eta_0/(kh_0)$. First-order integration at a fixed equilibrium coordinate gives $\xi=-U\sin\theta/\omega$, $\upsilon=V\cos\theta/\omega$. The particle trajectory is an <ellipse> with axis ratio $|f|/\omega$. For positive $f$, the orbit is clockwise in the $(x,y)$ plane.
Back to article page
