Beta-Plane Arrested Topographic Wave as a Linkage of Open Ocean Forcing and Mean Shelf Circulation

Abstract

Pressure anomaly set by the open ocean affects the dynamic topography and associated circulation over the continental shelf, which is explored here on a linearized β -plane arrested topographic wave framework that considers the variation in Coriolis parameter with latitude. It was found that on a meridional shelf, a nondimensional parameter Pe β , termed the β Péclet number, signifies the characteristics of open ocean–shelf interaction. The Pe β ≡ D β / α is determined by the ratio of long-wave-limit planetary to topographic Rossby wave speeds, i.e., the β drift D β , and the linear Ekman number α . On the western boundary shelf, due to the westward planetary Rossby wave, open ocean pressure propagates shoreward as Pe β > 1, and shelf circulation peaks where Pe β drops to 1. At this location, the planetary β effect is balanced by the bottom friction. The Pe β = 1 must occur either on the shelf or on the coastal wall when Pe β > 1 is observed at the shelf edge. On the eastern boundary shelf, however, Pe β < 0, the pressure anomaly is removed from the shelf, and hence the inductive circulation decays rapidly from the shelf edge. This β effect is robust on gently sloping meridional shelves. For zonal shelves, the planetary β increases the effective bottom slope on the northern boundary shelf but decreases it on the southern one, in a sense of potential vorticity conservation. However, this effect could be less significant in reality, given the complex dynamics involved. The above mechanism can explain the dynamics driving the Taiwan Warm Current in the East China Sea and its bifurcation around 28°N.