Statistical Bias, Parallel Scaling, and Geometric Depletion of the Projected Pressure Hessian in Extreme Isotropic Turbulence

We provide a high-fidelity numerical characterisation of pressure–strain statistics and topological alignment within the extreme intermittency tail of isotropic turbulence at Reλ ≈ 433. Velocity gradient data were extracted from the JHTDB isotropic1024coarse dataset (1024³ DNS) via high-order Lagrange interpolation (sinterp = 40). Probes were filtered to retain only events where |ω| > 150 s⁻¹, corresponding to approximately 12 times the root-mean-square (rms) vorticity of the domain. A targeted ‘Vortex Cloud’ sampling strategy isolated N = 274 spatially distinct extreme cores, of which 98.54% satisfy the Q-criterion (Q > 0), confirming coherent vortex-tube topology. The projected pressure Hessian gap G = −(H₁₁ − H₂₂), evaluated in the local strain eigenframe, exhibits a measurable negative bias (Mean: −1,940.37 s⁻³; Median: −2,098.84 s⁻³), reflecting a structural preference for stabilisation in high-enstrophy regions. Bulk log–log regression identifies a parallel scaling regime where |G| ∝ |ω|²·²³ and |Σ| ∝ |ω|²·²³, suggesting a stable structural relationship in the extreme tail. Despite this parallel intensification, pointwise evaluation demonstrates that the stabilisation ratio remains small (Median R₂ ≈ 0.0205; Bootstrap 95% CI: ±4.2%, M = 1,000). Furthermore, a strain eigenframe audit reveals a dominant alignment of the vorticity vector with the intermediate strain eigenvector (⟨|cosθ₂|⟩ = 0.825 ± 0.217), confirming persistent geometric depletion. These results demonstrate that local regulation at the geometric centres of extreme events is not achieved by pressure–strain interactions alone, but is structurally buffered by topological misalignment, necessitating the non-local stabilisation mechanisms investigated in Papers 3 and 4 of this series.