Mesoscale ocean eddies play a major role for both the intermixing of water and the transport of biological mass. This makes the identification and tracking of their shape, location and deformation over time highly important for a number of applications. While eddies maintain a roughly circular shape in the free ocean, the narrow basins of the Red Sea and Gulf of Aden lead to the formation of irregular eddy shapes that existing methods struggle to identify. We propose the following model: Inside an eddy, particles rotate around a common core and thereby remain at a constant distance under a certain parametrization. The transition to the more unpredictable flow on the outside can thus be identified as the eddy boundary. We apply this algorithm on a realistic simulation of the Red Sea circulation, where we are able to identify the shape of irregular eddies robustly and more coherently than previous methods. We visualize the eddies as tubes in space-time to enable the analysis of their movement and deformation over several weeks.