Spectral Reconstruction for Under-Resolved Turbulence Measurements Using a Variational Cutoff Dissipation Model

TL;DR

This paper introduces a spectral model based on a variational principle that accurately reconstructs turbulent kinetic energy from under-resolved measurements, outperforming classical models and requiring minimal parameters.

Contribution

A novel spectral model derived from a variational principle that provides bounded support and superior TKE recovery without adjustable parameters beyond the Kolmogorov constant.

Findings

Achieves over 98% TKE recovery from truncated spectra

Accurately captures spectral rolloff in high-Reynolds-number turbulence

Outperforms classical models like Pao and Pope in spectral reconstruction

Abstract

This technical note addresses the challenge of accurate turbulence characterization using robust, bandwidth-limited sensors which fail to resolve the high-wavenumber dissipation range. To correct the resulting underestimation of turbulent kinetic energy (TKE), a novel analytical spectral model is derived from a variational principle governing cascade resistance, yielding a Ginzburg-Landau domain wall solution. Unlike classical asymptotic decay formulations such as the Pao or Pope models, the proposed formulation features bounded spectral support with a hard energetic cutoff at the Kolmogorov wavenumber ($k_{\eta}$) and requires no adjustable parameters beyond the Kolmogorov constant ($C_K$). Validation against high-Reynolds-number experimental data confirms that the model accurately captures the spectral rolloff and achieves superior TKE recovery, restoring over 98\% of the variance from spectra truncated as early as $k\eta=0.15$, thereby offering a robust tool for industrial and aeroacoustic flow diagnostics.