MODEL TEST · SPECTRAL PROPER ORTHOGONAL DECOMPOSITION

SPOD

SPOD asks a different question from global POD: which spatial structures dominate at each frequency? It is useful when coherent oscillatory physics should be separated by frequency rather than mixed into one variance-ranked basis.

PROMISING ANALYSISSpectral structure is clear; compact deployment/LOSO is not yet finished

WHAT WE TESTED

Frequency-conditioned modes across all seven U-sweep speeds

Input

Same canonical CFD fields

u, w, volume Cp, ω, surface Cp and surface Cf are analyzed at each of the seven speed anchors.

Frequency scale

Consistent coherent fundamental

The dominant normalized fundamental lies around f* ≈ 0.0232–0.0242 across the seven speeds.

Mode ranking

Eigenvalue at each frequency

SPOD ranks coherent spatial structures by spectral energy separately at each frequency instead of globally over all snapshots.

Deployment idea

Phase-locked harmonic reconstruction

The proposed generator combines mean + selected SPOD modes at f0, 2f0, 3f0… using the physical phase clock.

RESULT

The fundamental is strongly low-rank

99.78–99.98%rank-1 fraction · uat the fundamental

99.78–99.98%rank-1 fraction · wat the fundamental

98.41–99.90%rank-1 fraction · Cpvolume pressure

94.61–99.59%rank-1 fraction · ωmore spectral complexity

SPOD spectrum overview across fields and speeds — SPOD spectrum overview. The dominant frequency family is consistent across speed, while harmonic content differs by field.

Fundamental SPOD velocity mode across seven speeds — Leading joint u–w SPOD rank-1 structure at the coherent fundamental. The seven speed anchors are arranged compactly as four + three panels for direct visual comparison.

SUMMARY

Useful spectral evidence; not yet a finished surrogate

What worked

The fundamental coherent structure is exceptionally rank-1 dominated for velocity and pressure, which makes SPOD an attractive compact representation of the periodic physics.

What remains

The proposed mean + selected harmonic SPOD reconstruction still needs quantitative CFD reconstruction error, arbitrary-speed alignment/interpolation and seven-fold LOSO validation before it should be presented as a deployable competitor to Raw POD.

Current decision

Keep SPOD as a promising representation/reconstruction path and a strong dynamics diagnostic, but do not imply that a validated real-time SPOD surrogate already exists.