2026/07/31 by Christian Puntini, Luigi Roberti
Physics and Astronomy · Mathematics · #physics.flu-dyn #math-ph #math.AP #math.MP #physics.ao-ph #msc:35Q35 #msc:76U60 #msc:86A05
6 pages, 4 figures
arxiv created 2026/07/31 · arxiv updated 2026/08/03
We show that the assumption of a stress-free boundary condition at a finite intermediate depth, namely, at the bottom of the Ekman layer, in the analysis of wind-driven ocean flows necessarily leads to an unphysical current profile. Indeed, if the z-derivative of the fluid velocity vanishes at a given depth, then this depth necessarily corresponds to a minimum of the velocity profile, with the velocity increasing beneath it. Using a WKB ansatz based on the small variations of the ocean's water density at great depths, we also argue that a no-slip condition at the bottom of the ocean, if sufficiently deep, still effectively implies (up to a very small error) the orthogonality of the Ekman transport and the wind-stress.