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