Gaussian Field Representations for Turbulent Flow: Compression, Scale Separation, and Physical Fidelity

TL;DR

This paper introduces a Gaussian primitive-based continuous representation for turbulent flow fields that offers high compression and physical fidelity, with extensions to improve small-scale structure preservation.

Contribution

It proposes a novel Gaussian-based parametric encoding for turbulent flows, addressing limitations in geometric expressiveness and enabling structure-aware extensions.

Findings

High velocity accuracy at compression ratios over 1e3-1e4.

Baseline method degrades enstrophy due to small-scale loss.

Anisotropic Gaussians improve structure preservation.

Abstract

Representing turbulent flow fields in a compact yet physically faithful form remains a central challenge in computational fluid dynamics. We propose a continuous parametric representation based on localized Gaussian primitives, in which the velocity field is modeled as a superposition of kernels with learnable positions, amplitudes, and scales. This formulation yields a compact, grid-independent encoding while enabling evaluation of derived quantities such as vorticity and enstrophy. The approach is assessed on three-dimensional Taylor-Green vortex fields spanning stages from smooth flow to fully developed turbulence. We quantify the compression-accuracy trade-off using both primary variables and derivative-sensitive diagnostics. The baseline isotropic formulation achieves high velocity accuracy at compression ratios exceeding 1e3-1e4, but exhibits substantial enstrophy degradation due to loss of small-scale structure. To address this limitation, we investigate structure-aware extensions including adaptive placement, multi-resolution kernels, and anisotropic Gaussians. The anisotropic formulation provides the most consistent improvement, better aligning with elongated vortical structures and recovering intermediate- and high-wavenumber content, while other strategies yield modest gains. A compact-support Beta basis improves enstrophy in some cases but introduces localized artifacts. Overall, the results indicate that the main limitation of baseline Gaussian representations lies in geometric expressiveness rather than parameter count. The proposed framework provides a compact, interpretable, and continuous representation of turbulent flows, and establishes a foundation for structure-aware and physics-informed flow compression.