A Quasi-Noncommutative Deformation of Classical Fluid Dynamics

This work proposes a deformation of the nonlinear convective term in classical fluid dynamicsinspired by the Moyal product, interpreted as a geometric correction rather than a quantum effect. Thedeformation introduces a controlled nonlocal coupling between velocity gradients through an antisymmetrictensor 𝜃𝑖𝑗, interpreted as an effective geometry induced by the flow itself. Three physically motivated modelsfor 𝜃𝑖𝑗 are analyzed: vorticity-driven, constant background anisotropy and strain-rate coupling. Their effects areevaluated on a canonical vortex model, showing that the deformation enhances sensitivity to shear, curvature,and inter-scale interactions beyond standard Navier–Stokes dynamics.