Anisotropic Statistics of Lagrangian Structure Functions and Helmholtz Decomposition

Abstract

We present a new method to estimate second-order horizontal velocity structure functions, as well as their Helmholtz decomposition into rotational and divergent components, from sparse data collected along Lagrangian observations. The novelty compared to existing methods is that we allow for anisotropic statistics in the velocity field and also in the collection of the Lagrangian data. Specifically, we assume only stationarity and spatial homogeneity of the data and that the cross-covariance between the rotational and divergent flow components is either zero or a function of the separation distance only. No further assumptions are made and the anisotropy of the underlying flow components can be arbitrarily strong. We demonstrate our new method by testing it against synthetic data and applying it to the LASER data set. We also identify an improved statistical angle-weighting technique that generally increases the accuracy of structure function estimations in the presence of anisotropy.

Geostrophy Assessment and Momentum Balance of the Global Oceans in a Tide‐ and Eddy‐Resolving Model

“…Lastly, the numerical model study described here emphasized the importance of high‐frequency motions in determining ageostrophic levels. In the real ocean, Lagrangian observations such as surface drifters provide a unique opportunity to better estimate high‐frequency variability due to its high temporal resolution (approaching minutes with GPS tracking) and near‐global spatial coverage (Elipot et al., 2016), although wave‐vortex decomposition for Lagrangian data remains challenging (Wang & Bühler, 2021).…”