Spatial-Carrier-Modulated Turbulence Constructive Solution for NS Equation

We present the Spatial-Carrier-Modulated Turbulence Constructive Solution (SCM-Turb), which views a turbulent field as a three-dimensional random carrier folded in space and locally modulated by inertia. An incompressible random background flow U(x,t) serves as the carrier; the nonlinear term |(U•∇)U| acts as the gating signal that triggers sparse fractal bursts (fractional Brownian noise, H<0.5) via a Sigmoid switch. A Reynolds-number-saturated gain (≤30%) controls the global modulation depth. The resulting synthetic fields reproduce the k^(-5/3) energy spectrum, coherent vortices, intermittency, and heavy-tailed gradient distributions at a computational cost orders of magnitude lower than DNS. SCM-Turb offers a ready-to-use turbulent prior for data-hungry applications and engineering closure development.