Linear planetary wave dynamics in a 2.5-layer ventilated thermocline model is investigated by a local eigenvalue analysis and simple numerical computations. It is known that there are two types of waves in this system; we refer to one of them as the N-mode (Non-Doppler shift mode), which propagates almost westward, and the other as the A-mode (Advection mode), which propagates almost along the second layer basic current. First, we study the local longwave dynamics, assuming that the wavelength is much longer than the deformation radius and shorter than the gyre scale. It is shown that the N-mode and the A-mode cannot neatly be separated in the ventilated zone, and even in the Rhines and Young pool, a compact A-mode disturbance cannot exist by itself. When anomalous Ekman pumping is applied in the ventilated zone, the N-mode is generated in the forcing region, and the A-mode is generated at the wave front of the N-mode. For diabatic forcing, a similar phenomenon occurs. It is also found that the shadow zone is unstable to longwave disturbances. Secondly, the wave behavior in the linear planetary geostrophic model is numerically investigated. The main features can be interpreted by the local wave dynamics, and the disturbances around the maximum amplitudes are dominated by the waves whose wavenumber vectors are perpendicular to the second layer potential vorticity contours. The amplitude changes during the wave propagation are also discussed. Finally, the effects of the finite wavelength are studied. The N-mode is strongly dispersive at the scale of the Rossby deformation radius, while the A-mode is weakly dispersive. It is also shown that the ventilated zone is unstable to shortwave disturbances, although it is stable to longwave disturbances.
Kubokawa, Atsushi, and Maki Nagakura. 2002. "Linear planetary wave dynamics in a 2.5-layer ventilated thermocline model." Journal of Marine Research 60, (3). https://elischolar.library.yale.edu/journal_of_marine_research/2436