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In this paper, we propose a novel reduced order model (ROM) lengthscale thatis constructed by using energy distribution arguments. The new energy-based ROMlengthscale is fundamentally different from the current ROM lengthscales, whichare built by using dimensional arguments. To assess the novel, energy-based ROMlengthscale, we compare it with a standard, dimensionality-based ROMlengthscale in two fundamentally different types of models: (i) themixing-length ROM (ML-ROM), which is a ROM closure model; and (ii) theevolve-filter-relax ROM (EFR-ROM), which is a regularized ROM. We test the fourcombinations (i.e., ML-ROM and EFR-ROM equipped with the energy-based anddimensionality-based lengthscales) in the numerical simulation of the turbulentchannel flow at $Re_{\tau} = 395$. The numerical investigation yields thefollowing conclusions: (i) The new energy-based ROM lengthscale issignificantly (almost two orders of magnitude) larger than the standarddimensionality-based ROM lengthscale. As a result, the energy-based lengthscaleyields more stable ML-ROMs and EFR-ROMs than the dimensionality-basedlengthscale. (ii) The energy-based lengthscale displays the correct asymptoticbehavior with respect to the ROM dimension, whereas the dimensionality-basedlengthscale does not. (iii) The energy-based lengthscale yields ML-ROMs and(when significant filtering is effected) EFR-ROMs whose parameters are lesssensitive (i.e., more robust) than the parameters of the ML-ROMs and EFR-ROMsbased on the dimensionality-based lengthscale. The novel energy-basedlengthscale could enable the development of better scale-aware ROM strategiesfor flow-specific applications and is expected to have long term applicationsin nuclear reactor thermal-hydraulics.

An Energy-Based Lengthscale for Reduced Order Models of Turbulent Flows