The advection effect of planetary vorticity on sea level slope in a western boundary current

Abstract

Western boundary currents, such as the Gulf Stream, are often modeled as flows in near cross‐stream geostrophic balance with paths that are straight or nearly straight. The effect of planetary vorticity advection on the downstream sea‐level slope in these rectilinear flows is re‐examined and found negligible. Instead, the re‐examination reveals a much greater effect of the ageostrophic component of the horizontal divergence in determining the downstream slope. Overlooked in previous studies is the geostrophic component of the horizontal divergence because of a hidden assumption of parallel flow. To avoid this pitfall, we employ a natural coordinate system to follow precisely the downstream direction. Further, we differentiate between weak geostrophic flows with small accelerations and flows in cross‐stream geostrophic balance where downstream acceleration might be appreciable. Two Rossby numbers are employed: a small cross‐stream number (≤0.01) to describe the near cross‐stream balance, and a large downstream number (≤0.1) to describe the large downstream accelerations that are found in western boundary flows. Finally, by means of a scale analysis we show that over the whole range of possible Rossby numbers, the advection effect of planetary vorticity on downstream sea level slope is negligible compared to the effect of the ageostrophic component of the horizontal divergence. Some new data on the nearshore gradient of the Reynolds stress are also included.