MODEL TEST · STRUCTURED DYNAMICS CHALLENGER

Phase + Residual POD

Separate the repeatable Cl-aligned coherent cycle from cycle-specific residual dynamics, then model the deterministic part of the residual with its own multi-frequency coefficient representation.

PRODUCTIVE · DEPLOYEDCoherent + spectral-residual live reconstruction available

OVERVIEW

Make the dynamics structure explicit before reconstructing the field

Phase clock

Cl-derived physical phase

Equivalent positive-going crossings define cycle boundaries instead of assuming every 64 raw samples are exactly one period.

Coherent field

Aligned phase POD

Each physical cycle is mapped to a common 64-point phase grid before the coherent mean is formed.

Residual field

Original snapshots retained

Residuals are evaluated at every original snapshot so amplitude modulation and secondary/broadband content are not phase-averaged away.

Residual time model

32 spectral frequencies

A deterministic multi-frequency model reconstructs the spectrally concentrated part of each residual POD coefficient trajectory.

RESULT SNAPSHOT

Phase correction matters; the residual remains genuinely rich

0.486 → 0.972U50 Cl cycle correlationnominal → aligned

19coherent u modes99.5% energy

145residual u modes99.5% energy

42.8%u residual energy captured32-frequency deterministic fit

Phase period and alignment diagnostics — Physical phase-clock diagnostics show why nominal 64-sample cycle indexing can accumulate substantial drift.

Residual POD coefficient spectral overview — The residual contains structured multi-frequency content together with unresolved broadband/irregular variation.

Takeaway

The coherent component becomes much cleaner after physical phase alignment, but the residual is not just a small correction. The current live model intentionally reconstructs only its deterministic spectral component.

LIVE DEMONSTRATOR

Coherent + spectral-residual reconstruction

Switch between coherent-only and coherent + residual modes while exploring the same five flow quantities and synchronized Cd/Cl.

Structured deployment

Evidence boundaryUnresolved broadband residual variance is intentionally not synthesized. Continuous-speed interpolation is a fitted deployment model, not held-out validation.

SUMMARY

A useful challenger, but added complexity must earn its place

Strength

Separates coherent phase physics from secondary dynamics and gives a natural path toward spectral or stochastic residual models.

Limitation

The deterministic spectral fit captures only part of the residual coefficient energy, especially for w and volume Cp.

Role

Compare directly with Raw POD on prediction, stability and interpretability rather than preferring it merely because the decomposition is more sophisticated.

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