Metrodynamic Modulation of Turbulence: A Temporal-Field Approach to Vorticity Control in Fluids and Plasmas

We investigate the effect of introducing a metronomic field, a smooth oscillatory scalar that modifies physical time through the reparametrisation. This transformation leaves all dynamical equations formally unchanged in the effective time variable, yet systematically alters how trajectories are traversed in physical time.

Using a comprehensive numerical program, we test this temporal mechanism across a remarkably broad class of dynamical systems: chaotic ODEs (Lorenz–63, Lorenz–96, Rössler, Hénon), nonlinear attractors, Keplerian Hamiltonian orbits, 1D/2D/3D Navier–Stokes flows (incompressible and compressible), reduced-MHD models (RMHD), full 3D linear MHD (with and without hyperviscosity), passive and active scalars, and forced turbulence.

Across all systems, the metronomic field induces:

• a consistent smoothing of gradients,
• a slight but systematic reduction of enstrophy,
• regularised scalar fields,
• delayed energy decay in physical time (but not in effective time ),
• differences in chaotic divergence rates without altering the underlying geometric trajectory.

Crucially, the metronomic modification does not alter the equations of motion, the dynamical geometry, or phase-space trajectories. It acts solely as a temporal gauge affecting the parametrisation of the flow, not its structure.

These results show that provides a universal time-warping mechanism capable of regularising gradients and modifying apparent dissipation in physical time, while preserving the intrinsic dynamics. The approach is independent of the specific structure of Navier–Stokes or MHD and appears to hold across all tested PDEs, chaotic systems, and Hamiltonian flows.

This dataset includes all numerical figures used in the manuscript, covering turbulence diagnostics, chaotic flows, RMHD dynamics, active scalar evolution, MHD energy decay, Kepler orbits, and more.