Multiple Oscillatory Modes of the Argentine Basin. Part II: The Spectral Origin of Basin Modes

Abstract

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.

Effects of rotation on stability of viscous stationary flows on a spherical surface

“…[5][6][7] The modeling of such moving air masses plays an important role in understanding the global climate control. 8 The inclusion of the Coriolis force creates a cyclonic rotation around the poles, i.e., west-to-east winds.…”

Conserved Vectors for a Model of Nonlinear Atmospheric Flows Around The Rotating Spherical Surface

“…The treatment of the geometric singularity in spherical coordinates has for many years been a difficulty in the development of analytic and numerical simulations for oceanic and atmospheric flows around the Earth ( [5], [6], [7], [9]). The common results on computational experiments (see e.g., [5]; [23]; [35] and [32]) seem to provide credible evidence to support the assertion that singular solutions to the shallow water equations may exist on a stationary sphere. They also suggest that singular solutions are less likely on a rotating sphere.…”

“…The value R 0 = 68.4932 has been chosen for the following reason; for a typical atmosphere, we can choose the characteristic velocity and length scale to be c 0 ∼ 10 m/s, and r 0 ∼ 10 3 (see also Table I in Ref. [35]) so that we have 1/R o ≈ 0.0146. A small Rossby number R 0 signifies a system which is strongly affected by Coriolis force while a large Rossby number signifies a system in which inertial and centrifugal forces dominate.…”

“…In almost all oceanographic applications, e.g., meteorology, the effects of rotation and the spherical shape of the Earth cannot be ignored and so the large-scale atmospheric dynamics is usually described by latitude-dependent Euler or Navier-Stokes three-and two-dimensional flows on a rotating spherical surface ( [6], [7]; [25], [26], [20], [18]) or within the theory of shallow water approximation (see e.g., [36], [31], [23]; [21] and [35]). In particular, since non-steady westerly winds in the southern hemisphere are an important force contributing to climate modulation ( [34], [1]), understanding of the large-scale atmospheric dynamics is the topic of current extensive research.…”

Stability of large-scale oceanic flows and the importance of non-local effects

“…Matching the real ocean basin oscillations with their theoretical counterpart is challenging since they are highly distorted by the bottom bathymetry. However, using numerical simulations it can be shown that at least some of the modes of variability identified be the statistical analysis are consistent with low-order barotropic basin modes (Weijer et al, 2007b).…”