Rossby Wave–Coastal Kelvin Wave Interaction in the Extratropics. Part I: Low-Frequency Adjustment in a Closed Basin

The interaction of open and coastal oceans in a midlatitude ocean basin is investigated in light of Rossby and coastal Kelvin waves. The basinwide pressure adjustment to an initial Rossby wave packet is studied both analytically and numerically, with the focus on the low-frequency modulation of the resulting coastal Kelvin wave. It is shown that the incoming mass is redistributed by coastal Kelvin waves as well as eastern boundary planetary waves, while the incoming energy is lost mostly to short Rossby waves at the western boundary. The amplitude of the Kelvin wave is determined by two mass redistribution processes: a fast process due to the coastal Kelvin wave along the ocean boundary and a slow process due to the eastern boundary planetary wave in the interior ocean. The amplitude of the Kelvin wave is smaller than that of the incident planetary wave because the initial mass of the Rossby wave is spread to the entire basin. In a midlatitude ocean basin, the slow eastern boundary planetary wave is the dominant mass sink. The resulting coastal Kelvin wave peaks when the peak of the incident planetary wave arrives at the western boundary. The theory is also extended to an extratropical–tropical basin to shed light on the modulation effect of extratropical oceanic variability on the equatorial thermocline. In contrast to a midlatitude basin, the fast mass redistribution becomes the dominant process, which is now accomplished mainly by equatorial Rossby and Kelvin waves, rather than the coastal Kelvin wave. The coastal Kelvin wave and the modulation of the equatorial thermocline peak close to the time when the wave trail of the incident Rossby wave arrives at the western boundary. Finally, the theory is also applied to the wave interaction around an extratropical island.