Jaykov Foukzon^*

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Department of Mathematic, Israel Institute of Technology, Haifa, Israel.
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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.

Keywords: 3D Turbulence, Chaos, Quantum Chaos, Additive Thermal Noise, Nikolaevskii System

Cite this paper: Foukzon, J. (2015) New Scenario for Transition to Slow 3-D Turbulence. Journal of Applied Mathematics and Physics, 3, 371-389. doi: 10.4236/jamp.2015.33048.

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