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DynamisLab/docs/JFM_WYQ/FIGURE_PLANS/SECTION_02_EQUATION_SPEC.md
Frank14f 1a8b994a03 refactor(workflow): update JFM research workflow and remove obsolete figures
Revise the JFM research workflow documentation to clarify project structure, decision-making processes, and tool routing. Remove outdated figures and images that are no longer relevant to the current manuscript. Ensure that the workflow aligns with the latest research objectives and safety protocols.
2026-08-11 21:25:33 +08:00

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Section 2 equation specification

Required equations

  1. Re_D=Uref D/nu; bulk/mean Uref for parabolic inflow, uniform speed for uniform inflow, and Umax ~= 1.5 Uref. Parabolic inherited labels remain unconverted until source metadata bind U0.
  2. (Uw,Vw)=(-omega r_y, omega r_x), positive omega counter-clockwise; s_i=omega_i R/Uref. Historical source-native alpha_i=omega_i/U0; general s_i=alpha_i R(U0/Uref), reducing to alpha_i R only when U0=Uref is established.
  3. Online objective: compact force plus sparse-sensor discrepancy; exact weights optional and run-bound.
  4. Mean field L2: area/coordinate-weighted, Uref-normalized vector error over declared ROI with roles/comparator explicit.
  5. Phase L2: same spatial contract by periodic slot; slots are not repeated-cycle samples.
  6. DTW recurrence/path or rigorous prose; state distance/similarity, normalization, channels, aggregation, window and constraints.
  7. Comparator-relative reduction optional only under one exact role/ROI/mask/weight/window contract.

Readiness contract

Authority is frozen Section 2 plus the sensor/field report. Equations 12 are configuration definitions; 37 require result-local chain/config/case/seed/role/comparator bindings. ROI/mask/weight/window are N/A: physical/method definition for 13 and mandatory for 47. Action sign/order and metric orientation accompany reuse. Implementation constants and rows are dependency-gated; no equation implies an artifact. Caption ceiling is definitions only. Fallback retains Reynolds, action, mean L2 and rigorous prose DTW; recurrence/detail may move to supplement.

Plan specified; evidence read; metric definition-ready; render N/A: typeset equations, not artifact panels; disposition retain-with-gates.