The Geometry of Lagrangian Accelerations in Geostrophic Eddies

Abstract:

Geostrophic turbulence is associated with the production of small-scale fronts and filaments, creating very sharp gradients of vorticity during the downscale cascade of potential enstrophy. A well-known method for studying similar dynamics in 2D turbulence is to partition the flow into strain- and vorticity-dominated regions via the Okubo-Weiss parameter, which indicates where vorticity gradients may undergo exponential growth. An alternative, complementary approach is to study the tendency for these gradients to align with the eigenvectors of the strain rate tensor. This talk will combine both of these viewpoints by studying the geometry of the tensors that govern the production of these gradients. In doing so, an extension of the Okubo-Weiss parameter will be introduced that is appropriate for quasigeostrophic flows. These results will be applied to both idealized and realistic numerical models to give perspective on how they might be used for eddy-tracking, or in developing improved eddy parameterizations for climate models.