Validate the self-similar error-front law in finite-band SQG turbulence

Establish whether the self-similar upscale error-front law derived for an inertial interval remains valid for finite-band surface-quasigeostrophic turbulence by resolving the finite-band residual budget, including edge corrections, conservative-transfer leakage, dissipation, forcing mismatch, and closure memory.

Background

The paper derives a scalar error-growth law from a self-similar relative-error spectrum and an independently prescribed error-front speed. That derivation is valid on an effectively unbounded inertial interval, whereas the analyzed SQG simulations use a finite k=10–20 band that is too narrow to establish the asymptotic front law.

A finite-band validation would require accounting for profile-edge terms and the additional projected-budget residuals, then comparing the independently determined front prediction with paired truth–perturbation histories. The current SQG analysis does not supply these evaluations, so the finite-band test remains unresolved.

References

The present SQG bands lack the residual accounting required to equate these objects. Equation~eq:front therefore carries the status of an inertial similarity theorem, while its finite-band SQG test remains open.

— When Does Forecast-Error Energy Grow Logistically in Geophysical Turbulence?  (2608.26492 - Peña, 27 Aug 2026) in Similarity-front theorem, paragraph following Eq. (finite)