Ray-Column IPRM: Restoring Radial Spectral Scale to Structure-Based Turbulence Modeling

TL;DR

This paper introduces a scale-conditioned Ray-Column extension to the IPRM turbulence model, restoring radial spectral scale information for improved turbulence structure representation.

Contribution

The novel Ray-Column extension decomposes spectral vectors into orientation and radial wavenumber, enabling scale-conditioned structural states and closure evaluation in turbulence modeling.

Findings

The model captures turbulence dynamics across different flow configurations.

Retaining radial spectral scale improves the accuracy of low-pass observable reconstructions.

The approach demonstrates benefits in rotating-shear turbulence comparisons with LES data.

Abstract

The particle representation model (PRM) and interacting particle representation model (IPRM) describe homogeneous turbulence through orientation-conditioned structural states. In their original form, the conditional state is organized by the unit spectral direction, while the radial spectral coordinate is integrated out. We introduce a scale-conditioned Ray-Column extension in which the spectral vector is decomposed into orientation and radial wavenumber, and the conditional structure state is projected onto finite radial bands. The formulation starts from the continuum spectral tensor and is then reduced to the ray-packet ensemble sums used in the implementation. The bands are projections of an orientation-wavenumber tensor density and retain scale-conditioned structural populations for closure evaluation. The rapid dynamics remain ray-packet resolved, while the nonlinear slow and terminal closure coefficients are evaluated from band-aggregate structure tensors formed by integrating over orientation and wavenumber within each band. The present reference closure omits conservative cascade modeling among bands. A reference closure is built from PRM rapid kinematics, band-local effective-gradient response, slow rotational randomization, and an active large-scale enstrophy (LSE) terminal-drain map. In the active-LSE closure, the misalignment-sensing factor Psi_fd regularizes the LSE structure-to-dissipation map; the Ray-Column formulation evaluates this map on band-aggregate structural populations. The model is assessed in irrotational strain, homogeneous shear, elliptic-streamline, and rotating-shear configurations. The rotating-shear comparison with filtered LES data illustrates the payoff of retaining band information: filtered or low-pass observables can be formed before scale information is lost in the one-point reconstruction.