Abstract
Abstract. The two seminal studies on westward intensification, carried out by Stommel and Munk over 70 years ago, are revisited to elucidate the role of the domain aspect ratio (i.e., meridional to zonal extents of the basin) in determining the transport of the western boundary current (WBC). We examine the general mathematical properties of the two models by transforming them to differential problems that contain only two parameters – the domain aspect ratio and the non-dimensional damping (viscous) coefficient. Explicit analytical expressions are obtained from solutions of the non-dimensional vorticity equations and verified by long-term numerical simulations of the corresponding time-dependent equations. The analytical expressions as well as the simulations imply that in Stommel's model both the domain aspect ratio and the damping parameter contribute to the non-dimensional transport of the WBC. However, the transport increases as a cubic power of the aspect ratio and decreases linearly with the damping coefficient. On the other hand, in Munk's model the WBC's transport increases linearly with the domain aspect ratio, while the damping coefficient plays a minor role only. This finding is employed to explain the weak WBC in the South Pacific. The decrease in transport of the WBC for small-domain aspect ratio results from the decrease in Sverdrup transport in the basin's interior because the meridional shear of the zonal velocity cannot be neglected as an additional vorticity term.
Highlights
As was noted by Henry Stommel, in the opening sentence of his seminal 1948 study, “Perhaps the most striking feature of the general oceanic wind-driven circulation is the intense crowding of streamlines near the western borders of the oceans”
A better alternative is to combine several dimensional parameters to yield a system with fewer non-dimensional parameters as was employed by, for example, Welander (1976) to identify a zonally uniform regime in ocean circulation and by Bye and Veronis (1979) to identify the correction to the Sverdrup transport in the context of S48’s original model
We address the issue raised by Bye and Veronis (1979) regarding the effect of domain aspect ratio on the western boundary current (WBC)’s transport by providing explicit expressions of the non-dimensional transport in both S48’s and M50’s models
Summary
As was noted by Henry Stommel, in the opening sentence of his seminal 1948 study, “Perhaps the most striking feature of the general oceanic wind-driven circulation is the intense crowding of streamlines near the western borders of the oceans”. As in S48 and M50, a large number of these subsequent studies employed the dimensional form of the governing equations which are the time-independent rotating linearized shallow water equations compounded by friction and forcing These dimensional models include numerous parameters: the zonal and meridional extents of the basin; either the coefficient of linear drag (i.e., the coefficient in the Rayleigh frictional term) or the kinematic eddy viscosity (i.e., the coefficient in parameterization of the viscous term); the amplitude (and possibly meridional structure) of the wind stress; the gradient of Coriolis frequency (β effect). These typos do not change the scientific conclusions drawn in S48
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