Controlled Acoustic Collapse in a Compressible Medium: Non-Linear Modulation of Navier-Stokes Equations via an Irrational Spectral Coupling

This paper proposes a fundamentally new approach to controlling non-linear effects in continuous media, based on transforming the mathematical singularity of the Navier-Stokes equations (finite gradient blow-up) from a destructive factor into a tool for focused energy accumulation. To suppress harmonic stagnation and overcome symmetric scattering, an irrational scaling factor of 1.475, derived from the analytical properties of the Riemann zeta function, is introduced. A model of a one-dimensional acoustic waveguide with two opposing emitters implementing quasi-periodic parametric pumping of the medium is considered.