Energy-Neutral Exact-Local Cascade Control in a Three-Dimensional Spectral Flow Solver

Abstract

This study introduces the EIDOS Energy-Neutral Exact-Local Cascade (EN-ELC), a numerical spectral-feedback operator designed to alter resolved interscale energy transfer without directly adding net instantaneous kinetic-energy power to the fluid as a whole. The method is implemented in a three-dimensional incompressible Fourier pseudo-spectral solver using double precision, true three-halves padding for nonlinear de-aliasing, a rotational nonlinear formulation, Helmholtz–Hodge projection, classical fourth-order Runge–Kutta integration, and adaptive stability control. The EN-ELC construction begins with an exact-local shell feedback that couples each spectral shell only to its adjacent higher shell. The component of that feedback responsible for instantaneous global power is then removed while the remaining spectral structure is retained. Pilot paired simulations were performed with identical initial conditions for baseline Navier–Stokes and EN-ELC cases. At an equal physical time of 0.008, grids of 12, 16, and 20 points per direction produced maximum absolute EN-ELC power values of approximately 1.7×10⁻19, 2.4×10⁻20, and 6.8×10⁻20, respectively, while the corresponding relative spectral-flux differences were approximately 3.82×10⁻6, 1.11×10⁻5, and 9.34×10⁻6. These results demonstrate the intended numerical energy-neutralization to near floating-point scale and show a small but measurable resolved spectral-flux perturbation in the tested pilot regime. The resolution trend is non-monotonic and the present calculations do not establish a non-zero continuum limit, a universal turbulence law, or a physical closure model. EN-ELC is therefore presented as a computational proof of concept and a testable framework for energy-neutral manipulation of resolved spectral transfer.