Multiple oscillatory modes of the argentine basin. Part II: The spectral origin of basin modes

In this paper the spectrum of barotropic basin modes of the Argentine Basin is shown to be connected to the classical Rossby basin modes of a flat-bottom (constant depth), rectangular basin. First, the spectrum of basin modes is calculated for the Argentine Basin, by performing a normal-mode analysis of the barotropic shallow-water equations. Then a homotopy transformation is performed that gradually morphs the full-bathymetry geometry through a flat-bottom configuration into a rectangular basin. Following the eigenmodes through this transition establishes a connection between most of the basin modes and the classical Rossby basin modes of a rectangular geometry. In particular, the 20-day mode of the Argentine Basin is identified with the lowest-order mode of classical theory. Sensitivity studies show that the decay rate of each mode is controlled by bottom friction, but that it is insensitive to lateral friction; lateral friction strongly impacts the oscillation frequency. In addition, the modes are found to be only slightly sensitive to the presence of a background flow.