Comments on "on the steadiness of separating meandering currents"

Using integration constraints and scale analysis, van Leeuwen and De Ruijter focused on the steady aspect of the downstream flow in the momentum imbalance articles of Nof and Pichevin appearing in the 1990s and later on. They correctly pointed out that when the steady downstream flow is exactly geostrophic then it must obey the additional downstream (critical) condition u² = g'h (where u is the speed, g' is the reduced gravity, and h is the thickness). They then further argue that this additional condition provides "a strong limitation on the generality of their results."These results for steady flows have been incorrectly generalized by the typical reader to eddy generating unsteady flows, which was the focus of Nof and Pichevin. The current authors argue that, although the van Leeuwen and De Ruijter condition of u² =g'h is valid for a purely geostrophic and steady flow downstream, it is inapplicable even for the steady aspect of the Nof and Pichevin solutions because the assumption of a purely geostrophic flow (i.e., fu=-2g'h_Y and ν=0) was never made at any downstream cross section in Nof and Pichevin. Instead, the familiar assumption of a cross-stream geostrophic balance in a boundary current, which is slowly varying in the downstream direction, as well as time, has been made (i.e., fu ≃ -g'h_Y, ν ≪ u, and small ∂/∂t but nonzero). Perhaps the current authors originally were not as clear about that as they should have been, but this implies that the basic state around which van Leeuwen and De Ruijter expanded their steady Taylor series does not exist in Nof and Pichevin; consequently, their expansion fails to say anything about both the time-dependent and the time-independent Nof and Pichevin. In the current authors' view, the "strong limitation"that they allude to does not exist.