New analytical approach for transition to slow 3-D turbulence

[摘要] Analytical non-perturbative study of the three-dimensional nonlinear stochastic partial differential equation with additive thermal noise analogous to that proposed by Nikolaevskii V.N. 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 says 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 causing it to make a direct transition from a spatially uniform to a turbulent state.

[发布机构] Department of Mathematics, Israel Institute of Technology, Haifa, Israel^1;All-Russian Research Institute for Optical and Physical Measurements, Moscow, Russia^2;Kotel'Nikov Institute of Radioengineering and Electronics, Russian Academy of Sciences, Moscow, Russia^3

[效力级别] 数学

[关键词] Analytical approach;Direct transition;Infinite numbers;New mechanisms;Nonlinear stochastic partial differential equations;Quantum chaos;Short-wave instability;Turbulent state