UC San Diego

Boundary layers arise wherever a fluid moves relative to a solid surface. They govern key performance limits in aerospace and marine vehicles, energy systems and thermal management of high-performance electronics. Whether they remain laminar or become turbulent affects drag, heat transfer, mixing, noise and engineering performance. Yet laminar--turbulent transition remains a central unresolved problem in fluid dynamics.This dissertation examines that transition through a unifying dynamical-systems framework: turbulence emerges through progressive symmetry breaking in space and time. To this end, we derive symmetry-decomposed Navier--Stokes equations and a corresponding stability framework for temporal and spatial symmetry breaking about a symmetry-preserving reference state. High-fidelity simulations reveal that canonical transition first proceeds through precisely such a state: fully nonlinear and rich in turbulence-like vortical structure, yet time-periodic and reflection-symmetric. Unsupervised, energy-optimal modal decomposition then identifies dominant space-time structures through which this ordered state loses time-periodicity and spatial symmetry, while energy-transfer analysis reveals how they channel energy from the ordered state into broadband turbulence. Using system identification and data-driven stability analysis, we identify their earliest dynamical behavior as unstable Floquet modes of the nonlinear periodic state.Later, at finite amplitude, symmetry breaking stresses feed back nonlinearly on the deterministic state that produced them. At peak skin friction, they oppose wall shear and supply a crucial momentum-inhibiting feedback to close the deterministic momentum balance. Symmetry breaking therefore not only initiates departure from deterministic behavior; it also provides the nonlinear saturation required to complete transition toward turbulence. Together, these results show that in deterministic transition, symmetry breaking is not random disorder appearing late in transition. It is the mechanism by which organized states lose stability, acquire new degrees of freedom and unlock broadband turbulent dynamics.More broadly, the symmetry-decomposed governing and stability equations developed here provide a general mathematical framework for characterizing how organized nonlinear states lose symmetry and progress toward chaos. Combined with data-driven operator learning, this framework enables interpretable scientific machine learning directly from high-dimensional data without intrusive access to the underlying solver. The resulting approach is transferable to fluid flows and other complex dynamical systems.