Anisotropic Helmholtz Decomposition of Lagrangian Tracer Data and its Dynamical Implications

Lagrangian velocity measurements in the ocean have played an important role in furthering our understanding of submesoscale dynamics. The Helmholtz decomposition of this data, which separates the divergent and rotational components of velocity spectra or structure functions, can indicate the robustness of geostrophic balance at different scales, and serves as a building block for analysis of scale-dependent energy distributions.

Previous Helmholtz decomposition algorithms relied on horizontal homogeneity as well isotropy, in a statistical sense. We develop a new Helmholtz decomposition method that still relies on horizontal homogeneity, but now allows for arbitrary horizontal anisotropy. To achieve this, the structure functions are expanded into azimuthal Fourier coefficients, and in principle our algorithm can identify any of these Fourier coefficients using the same data as the previous isotropic algorithms.

Also, using an expansion into vertical normal modes, we investigate the possibility of estimating internal wave energy spectra directly from the Lagrangian surface data, thus exploring the dynamical implications of our new Helmholtz decomposition method. Illustrations with synthetic data sets, as well as observational data sets such as GLAD and LASER will be provided.