Scale-conditioned structure-based closure for homogeneous turbulence: Ray-Column Interacting Particle Representation Model
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.