Lagrangian Phase-Lag and Geometric Precedence in Turbulent Vortex Stretching

This study investigates the causal timeline of vortex stretching in high-Reynolds-number turbulence ($Re_\lambda \approx 433$) using Lagrangian tracking in $1024^3$ direct numerical simulations. While classical theories often assume an instantaneous alignment between strain and vorticity, the present analysis identifies a systematic Lagrangian phase lag governing the onset of intense dissipation. By conditionally averaging the dynamics of fluid parcels, a distinct phase-space hysteresis is revealed. Trajectories are captured by the saddle-point topology of the pressure field ($\lambda_{min}^p < 0$) prior to experiencing peak enstrophy amplification. This temporal ordering ($\tau > 0$) demonstrates that the pressure topology acts as a deterministic geometric precursor, organizing the flow structure before the bursting event occurs. The robustness of this mechanism is verified in magnetohydrodynamic (MHD) turbulence, where the Lorentz force is found to suppress the hysteresis loop, forcing a transition from causal precedence to simultaneous locking.