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 characteristic scales. This formulation yields a compact, grid-independent encoding while enabling analytical evaluation of derived quantities such as vorticity and enstrophy. The approach is assessed on three-dimensional Taylor–Green vortex fields spanning different stages of flow evolution, from smooth laminar configurations to fully developed turbulence. We quantify the compression–accuracy trade-off using both primary flow variables and derivative-sensitive diagnostics. The baseline isotropic formulation achieves high velocity reconstruction accuracy at compression ratios exceeding 1 0 3 – 1 0 4 , but exhibits substantial degradation in enstrophy due to the loss of small-scale turbulent structures. To address this limitation, we investigate several structure-aware extensions, including adaptive kernel placement, multi-resolution kernel distributions, and anisotropic Gaussian kernels. Among these, the anisotropic formulation provides the most consistent improvement, enabling better alignment with elongated vortical structures and improved recovery of intermediate- and high-wavenumber content. Adaptive and multi-resolution strategies yield only modest gains under comparable conditions. We also examine an alternative compact-support Beta basis, which can improve enstrophy recovery in some cases but introduces localized reconstruction artifacts and reduced smoothness. Overall, the results show that the principal limitation of baseline Gaussian representations lies in their geometric expressiveness rather than in parameter count alone. The proposed framework provides a compact, interpretable, and continuous representation of turbulent flows, and establishes a foundation for structure-aware and physics-informed approaches to compact, continuous representations of turbulent flows.
Vittal-Shenoy et al. (Fri,) studied this question.