A Lagrangian description of transport associated with a front-eddy interaction: Application to data from the North-Western Mediterranean Sea

► Dynamical systems tools are employed to study Lagrangian transport in a realistic, oceanic flow consisting of a time-dependent jet and a system of eddies. ► The concepts a Lagrangian eddy and a Lagrangian front, and their finite-time stable and unstable invariant manifolds, are used to understand intricate transport pathways in the system. ► The importance of transitions between distinct Lagrangian configurations (e.g. birth or death of a Lagrangian eddy) is identified and discussed. ► The notion of a Lagrangian interaction between coherent Lagrangian structures is introduced and utilised in the analysis. ► A formal justification of two-dimensional analysis of Lagrangian transport in stratified 3D flows is given.