Document Type

Article

Version Deposited

Accepted for publication (PostPrint)

Publication Date

5-19-2025

Publication Title

Physics of Fluids

DOI

https://doi.org/10.1063/5.0276584

Abstract

Observations from recent large submesoscale drifter deployments in the ocean exhibit complicated time series of the kinematic properties (KP) — divergence, vorticity, shear and normal strain rates. These are challenging to interpret in the complex ocean-atmosphere system. The evolution equations for the four KP are derived from the two-dimensional momentum conservation equations on the f -plane. The resulting equations capture the submesoscale motion of drifters along fixed ocean surfaces, with time and space scales on the order of days and kilometers. They are linearly coupled through the Coriolis term and nonlinearly coupled through the horizontal divergence. The solution space, even under steady forcing, is found to be enormously rich. The present study summarizes the KP’s responses to various generic forcing scenarios, providing a basis for disentangling different effects in the observed time series. Generally, the system permits two to six equilibrium solutions; in most cases, they are characterized by positive and negative absolute vorticity and/or positive and negative divergence. Stable solutions either oscillate with periods that can be inertial, super-, or subinertial, or converge to a steady state with positive divergence. Some stable solutions take on unrealistically large values. In the unforced case, solution stability depends on the balance between the total strain rate and the absolute vorticity. No such simple stability criterion exists for nonzero forcing. Traditional diagnostics, such as the Okubo criterion or the relative magnitude of forcing parameters, are shown to be unreliable indicators of stability in the most general case.

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