Abstract
Eigen modes of a linear shear flow in shallow water on an equatorial β-plane are obtained over a wide parameter range. High-order unstable modes, neutral modes, and continuous modes are examined based on the results of Taniguchi and Ishiwatari (2006) that investigates mainly the lowest order most unstable modes. It is found that some continuous modes have equatorial Rossby wave like structures, and that high-order zonally symmetric unstable modes are caused by resonance between eastward mixed Rossby-gravity modes and continuous modes or by resonance between eastward inertial gravity modes and continuous modes. Neutral modes whose dispersion curves intersect with nearby dispersion curves of other neutral modes are also examined. Behaviors of dispersion curves of equatorial Kelvin modes and westward mixed Rossby-gravity modes are observed in cases that the two curves come closer.
