On the role of domain aspect ratio in the westward intensification of wind-driven surface ocean circulation

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.

Ekman pumping on the β -plane

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Geostrophic adjustment on the midlatitude β plane

“…19). Nonetheless, their applicability to the ocean is well established (Gianchandani et al, 2021). In fact, all wave theories have to assume either the existence of boundaries or an infinite domain (i.e., L y → ∞).…”

Effects of paleogeographic changes and CO2 variability on northern mid-latitudinal temperature gradients in the Cretaceous

“…However, in the real ocean, the two do not necessarily coincide in general, and the extent of the surface gyres is constrained only by the latitudes corresponding to the vanishing wind-stress curl. Previous studies established that both ψ and the poleward heat transport ( ) associated with a surface gyre increase with the horizontal aspect ratio of the ocean basin containing the gyre 18 – 20 (hereafter referred to as the ‘gyral basin’). Thus, the aspect ratio of any gyral basin is governed by the curl of the overlying wind stress and the relative position of the zonal boundaries set by the continents.…”

“…Thus, the aspect ratio of any gyral basin is governed by the curl of the overlying wind stress and the relative position of the zonal boundaries set by the continents. Based on these first-order constraints, it was recently postulated that the large meridional SST gradients observed during some geologic periods may have resulted from the smaller ψ (and consequently a smaller ) associated with the surface gyres contained in basins with small aspect ratios 20 .…”