Wave packet solutions in a bounded equatorial ocean and its interannual and decadal variabilities
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Wave packet solutions in a bounded equatorial ocean and its interannual and decadal variabilities Dongling Zhang1, Juan Zhu2, 3, Xu Lu3, 4, Ming Zhang3* 1 Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China 2 Special Office of Marine Environment, National Marine Environment Forecasting Center, Ministry of Natural
Resources, Beijing 100081, China 3 Atmospheric Circulation and Short-term Climate Prediction Laboratory of Meteorology and Marine Institute,
National University of Defense Technology, Nanjing 211101, China 4 32021 Troop, People’s Liberation Army, Beijing 100094, China
Received 25 January 2018; accepted 6 March 2018 © Chinese Society for Oceanography and Springer-Verlag GmbH Germany, part of Springer Nature 2019
Abstract
Linearized shallow water perturbation equations with approximation in an equatorial β plane are used to obtain the analytical solution of wave packet anomalies in the upper bounded equatorial ocean. The main results are as follows. The wave packet is a superposition of eastward travelling Kelvin waves and westward travelling Rossby waves with the slowest speed, and satisfies the boundary conditions of eastern and western coasts, respectively. The decay coefficient of this solution to the north and south sides of the equator is inversely proportional only to the phase velocity of Kelvin waves in the upper water. The oscillation frequency of the wave packet, which is also the natural frequency of the ocean, is proportional to its mode number and the phase velocity of Kelvin waves and is inversely proportional to the length of the equatorial ocean in the east-west direction. The flow anomalies of the wave packet of Mode 1 most of the time appear as zonal flows with the same direction. They reach the maximum at the center of the equatorial ocean and decay rapidly away from the equator, manifested as equatorially trapped waves. The flow anomalies of the wave packet of Mode 2 appear as the zonal flows with the same direction most of the time in half of the ocean, and are always 0 at the center of the entire ocean which indicates stagnation, while decaying away from the equator with the same speed as that of Mode 1. The spatial structure and oscillation period of the wave packet solution of Mode 1 and Mode 2 are consistent with the changing periods of the surface spatial field and time coefficient of the first and second modes of complex empirical orthogonal function (EOF) analysis of flow anomalies in the actual equatorial ocean. This indicates that the solution does exist in the real ocean, and that El Niño-Southern Oscillation (ENSO) and Indian Ocean dipole (IOD) are both related to Mode 2. After considering the Indonesian throughflow, we can obtain the length of bounded equatorial ocean by taking the sum of that of the tropical Indian Ocean and the tropical Pacific Ocean, thus this wave packet can also explain the decadal variability (about 20 a) of the equatorial Pacific and Indian Oceans. Key words: bounded equatorial ocean, wave packet solutions, decadal
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