On the modeling of nonlinear wind-induced ice-drift ocean currents at the North Pole

The paper constructs a Lagrangian solution for ice–drift currents at the North Pole, verifies it solves the leading-order horizontal momentum and continuity equations, derives the dispersion relation kc = f + 2AV k^2, obtains the time-mean drift and depth-integrated Ekman transport, and uses the ice–ocean stress law to show the surface non-geostrophic drift is uniquely determined; these appear as equations (19)–(21), (52), (72)–(76), and (61)–(67) in the PDF. The candidate solution reproduces the same structure using complex notation: it checks DU/Dt + i f U = AV ∂z^2 U after separating the geostrophic pressure, obtains the same dispersion relation and trochoidal particle paths, recovers the mean drift (73) and transport (76), and derives the quartic with a uniqueness argument essentially equivalent to the paper’s convexity argument. Minor differences are present: the candidate’s monotonicity proof for the quartic uses P′(R)>0, while the paper uses strict convexity; the candidate implicitly takes s = λ (as the paper eventually does for the final closed-form solution), and it asserts decay of kinetic energy with depth more informally than the paper’s boundary condition (33). Otherwise, the steps are consistent with and essentially the same as the paper’s derivations and results (governing system and continuity: ; Lagrangian map, Jacobian, and constant vorticity: , ; dispersion relation: ; Ekman profile and time mean: , ; surface stress law and quartic uniqueness: , , ).