Ergodicity and spectral cascades in point vortex flows on the sphere

A.C.P. was supported under DOD (MURI) Grant No. N000141110087 ONR. The computations were supported by the CUNY HPCC under NSF Grants No. CNS-0855217 and No. CNS-0958379.We present results for the equilibrium statistics and dynamic evolution of moderately large [n = O (102 - 103)] numbers of interacting point vortices on the sphere under the constraint of zero mean angular momentum. For systems with equal numbers of positive and negative identical circulations, the density of rescaled energies, p(E), converges rapidly with n to a function with a single maximum with maximum entropy. Ensemble-averaged wave-number spectra of the nonsingular velocity field induced by the vortices exhibit the expected k-1 behavior at small scales for all energies. Spectra at the largest scales vary continuously with the inverse temperature of the system. For positive temperatures, spectra peak at finite intermediate wave numbers; for negative temperatures, spectra decrease everywhere. Comparisons of time and ensemble averages, over a large range of energies, strongly support ergodicity in the dynamics even for highly atypical initial vortex configurations. Crucially, rapid relaxation of spectra toward the microcanonical average implies that the direction of any spectral cascade process depends only on the relative difference between the initial spectrum and the ensemble mean spectrum at that energy, not on the energy, or temperature, of the system.Publisher PDFPeer reviewe

Ocean current estimation using a Multi-Model Ensemble Kalman Filter during the Grand Lagrangian Deployment experiment (GLAD)

In the summer and fall of 2012, during the GLAD experiment in the Gulf of Mexico, the Consortium for Advanced Research on Transport of Hydrocarbon in the Environment (CARTHE) used several ocean models to assist the deployment of more than 300 surface drifters. The Navy Coastal Ocean Model (NCOM) at 1km and 3km resolutions, the US Navy operational NCOM at 3km resolution (AMSEAS), and two versions of the Hybrid Coordinates Ocean Model (HYCOM) set at 4km were running daily and delivering 72-h range forecasts. They all assimilated remote sensing and local profile data but they were not assimilating the drifter’s observations. This work presents a non-intrusive methodology named Multi-Model Ensemble Kalman Filter that allows assimilating the local drifter data into such a set of models, to produce improved ocean currents forecasts. The filter is to be used when several modeling systems or ensembles are available and/or observations are not entirely handled by the operational data assimilation process. It allows using generic in situ measurements over short time windows to improve the predictability of local ocean dynamics and associated high-resolution parameters of interest for which a forward model exists (e.g. oil spill plumes). Results can be used for operational applications or to derive enhanced background fields for other data assimilation systems, thus providing an expedite method to non-intrusively assimilate local observations of variables with complex operators. Results for the GLAD experiment show the method can improve water velocity predictions along the observed drifter trajectories, hence enhancing the skills of the models to predict individual trajectories