Waves on the β-planes in the presence of a mean zonal flow: Beyond the Doppler shift

Yair De-Leon (HU of Jerusalem)

May 24. 2023, 14:00 — 14:45

Numerical solutions of the eigenvalue equation associated with zonally propagating waves of the Linearized Rotating Shallow Water Equations are derived in a channel on either the equatorial β-plane or the mid-latitudes β-plane in the presence of a uniform mean zonal flow. The meridionally varying mean height field is in geostrophic balance with the prescribed mean zonal flow. In addition to the trivial Doppler shift of the free waves’ phase speeds, the uniform mean state causes the dispersion curves of each of the free Rossby and Poincaré waves to coalesce in pairs of modes when the zonal wavenumber increases. However, there is no instability. When the mean flow is not uniform but meridionally varying as a Gaussian jet, there is an instability for some values of the jet's amplitude and its width. We show that such an instability can occur only if the mean flow is  meridionally varying. In contrast to classical free Kelvin waves, in the presence of a mean flow the meridional velocity component of these waves does not vanish identically.

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
The Dynamics of Planetary-scale Fluid Flows (Thematic Programme)
Adrian Constantin (U of Vienna)
David Dritschel (U of St Andrews)
Nathan Paldor (HU of Jerusalem)