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We study the transition to turbulence from the perspective of the velocitygradient tensor dynamics. Our work is motivated by the observation of nonlinearstructures emerging during transition, as revealed by vortex identifiers suchas the Q-criterion. To that end, we have derived transport equations based onseveral invariants of the velocity gradient tensor to obtain integral budgetsspanning the different stages of transition from laminar to turbulent flow. Wehave also discussed which quantity would be the most appropriate in our study,while keeping in mind the potential for future modeling applications.

On the evolution of the velocity gradient tensor in transitional boundary layers