Flow Coupling Alters Topological Phase Transition in Nematic Liquid Crystals

We investigate how coupling to fluid flow influences defect-mediated transitions in two-dimensional passive nematic fluids using fluctuating nematohydrodynamic simulations. The system is driven by tuning the fluctuation strength, with increasing (decreasing) fluctuations defining the forward (backward) protocol. In the absence of flow coupling, the transition follows the Berezinskii--Kosterlitz--Thouless (BKT) scenario, governed by reversible binding and unbinding of $\pm 1/2$ defect pairs. When hydrodynamics is included, the outcome is controlled by the flow--alignment parameter. For non-aligning nematics ($λ=0$), the transition remains consistent with BKT. By contrast, for strain-rate--aligning nematics ($λ\neq 0$), bend--splay walls emerge, lowering the defect nucleation threshold and preventing sustained recombination: once created, defects remain unbound across the full range of fluctuation strengths in both forward and backward protocols. These results identify flow alignment as a fundamental control parameter for topological phase behavior and suggest that the canonical BKT transition emerges only in the absence of flow alignment.