Oceanic eddies, which are highly mass-coherent vortices traveling through the earth's waters, are of special interest for their mixing properties. Therefore, large-scale ensemble simulations are performed to approximate their possible evolution. Analyzing their development and transport behavior requires a stable extraction of both their shape and properties of water masses within. We present a framework for extracting the time series of full 3D eddy geometries based on an winding angle criterion. Our analysis tools enables users to explore the results in-depth by linking extracted volumes to extensive statistics collected across several ensemble members. The methods are showcased on an ensemble simulation of the Red Sea. We show that our extraction produces stable and coherent geometries even for highly irregular eddies in the Red Sea. These capabilities are utilized to evaluate the stability of our method with respect to variations of user-defined parameters. Feedback gathered from domain experts was very positive and indicates that our methods will be considered for newly simulated, even larger data sets.