Figure 2

Separation precision, d/σ, as a function of time t at three different eigenvalues: λ = 0 (solid line), small λ with t_λ = |λ|⁻¹ ≫ t_s (dashed line), and large λ with t_λ = |λ|⁻¹ ≪ t_s (dotted line).

Here, t_s indicates the separation time scale at which d/σ ≈ 1. For a vanishing eigenvalue λ (i.e., a singular velocity gradient tensor), d/σ monotonically increases with t, while for a non-zero eigenvalue, d/σ is saturated to a constant value after the saturation time scale, t_λ.