New scenario for transition to slow 3D turbulence

TL;DR

This paper presents an analytical study of a nonlinear stochastic PDE related to seismic waves, proposing a new quantum chaos mechanism for turbulence transition driven by thermal noise destabilization.

Contribution

It introduces a novel quantum chaos mechanism in nonlinear dynamical systems with infinite degrees of freedom, linking it to turbulence transition.

Findings

Thermal noise destabilizes the ground state of the system.

Transition from uniform to turbulent state caused by noise.

Proposes quantum chaos as a physical turbulence mechanism.

Abstract

Analytical non-perturbative study of the three-dimensional nonlinear stochastic partial differential equation with additive thermal noise, analogous to that proposed by V.N. Nikolaevskii [1]-[5]to describe longitudinal seismic waves, is presented. The equation has a threshold of short-wave instability and symmetry, providing long wave dynamics. New mechanism of quantum chaos generating in nonlinear dynamical systems with infinite number of degrees of freedom is proposed. The hypothesis is said, that physical turbulence could be identified with quantum chaos of considered type. It is shown that the additive thermal noise destabilizes dramatically the ground state of the Nikolaevskii system thus causing it to make a direct transition from a spatially uniform to a turbulent state.