← NS-INRS / DCRP97 / X72R80 · Dual-Lock PSD Cone and the Pancake Gap
Following DCRP96's dual-lock deviatoric covariance cone, this round finds that the originally planned next step — imposing the increment-covariance condition Qn=0 directly from the normal vector of the DCRP40 vorticity covariance — had silently conflated two distinct objects, the velocity-increment covariance Q and the filtered-vorticity covariance B_ω, and so first performs a 'scope repair,' measuring the misalignment between the two via the increment normal share θ_Q instead. Anchored at the DCRP40 canonical pancake affine jet A*, it proves that the positive-SGS-work lock forces the sum of θ_Q and the strain's deviation from A* to have a positive lower bound: under an exact planar lock the pancake-equality state is excluded because it would give negative work, but under a general rank-two anisotropic strain the dual-lock cone is not empty, so pure algebra cannot complete the proof. The conclusion notes that the dual-lock survivor maintains a consistent transversal distance from the old D40–60 pancake/X72 equality manifold, leaving the next round to reattach this transversal gap to X72, non-affine vorticity stretching, or material-turnover coordinates.
Relationship to the rest of the series, stated as closely as possible in the document's own words, not my interpretation.
Loading…