Spurious Preferential Sampling in Lagrangian Velocity-Gradient Statistics from Euler-Advected Tracers

A common workflow for Lagrangian statistics from turbulence databases — query the velocity at tracer positions, advance positions with a single forward-Euler step, repeat — silently violates incompressibility of the numerical flow map. The tracers acquire an effective inertia, drift out of vortical regions, and accumulate in strain-dominated regions, biasing enstrophy- and strain-weighted Lagrangian statistics. Using the Johns Hopkins Turbulence Database (JHTDB) and controlled 64³ DNS, we measure a bias of 0.21 (Δt/τη)0.78 for an enstrophy-weighted vorticity–strain alignment efficiency, saturating after ~50–100 advection steps. At a typical query interval (Δt ≈ 0.15 τη) the measured bias at Reλ=433 reaches +0.07 (25% relative). Because the exponent is sublinear, reducing the step is an inefficient remedy; a second-order midpoint step (one additional velocity query) removes the effect. A t=0 self-test allows retroactive checking of existing tracer data sets. Includes: preprint (PDF/TeX), all analysis and DNS scripts (Python, NumPy-only), and the raw trajectory data sets (HDF5, JHTDB layout) for all three JHTDB tracer ensembles and the paired DNS control.