Evolutionary clustering of Lagrangian trajectories in turbulent Rayleigh-Bénard convection flows

The paper builds weighted trajectory networks, applies NCut with SEBA, and introduces two evolutionary clustering frameworks (sliding-window and PCM) to track coherent sets in RBC. It verifies that the Lagrangian time-average of the local Nusselt along uniformly seeded tracers matches the Eulerian Nusselt, and shows that coherent sets (identified by large Smax or small normalized node degree d = du/dw) contribute less to heat transport, with ≈30% (2D) and ≈13% (3D) reductions. These steps, numbers, and spectral signatures of mergers/splits (via gaps in the spectrum of D_t^{-1/2} W_t D_t^{-1/2} or Ŵ_t) align with the candidate solution’s outline and details. Where the model adds informal justification (incompressibility/ergodicity and a two-compartment toy model), the paper reports empirical verification rather than a formal proof; otherwise, the methods and conclusions are in tight agreement. Key evidence appears in the method definitions, equality check for 〈Nu_local〉_{T,L} ≈ Nu_E, 2D and 3D statistics, and the evolutionary clustering constructions and spectral footprints of merges/splits.