## Abstract

Stochastic counterparts of hydrodynamic equations are studied by means of non-perturbative functional methods of quantum field theory. In particular, we discuss the fully developed turbulence, including the leading corrections on possible compressibility of fluids; transport through porous media, explaining the Kolmogorov and Richardson empirical laws; formulate the theory of waterspouts, tsunami waves, and synaptic eddies and calculate the energy spectra for them. We also study the branching representations for the Navier-Stocks equation providing a ground for the optimization of existing numerical simulation algorithms for the large-scale simulations in hydrodynamics. The proposed approach is closely related to the Nelson stochastic mechanics, the probabilistic interpretation of dynamical equations, and the critical phenomena theory. Although the application of non-perturbative methods of the quantum-field theory in stochastic nonlinear dynamics has a long history (commenced in 1976), it still remains surprisingly enigmatic for the broad auditorium. The aim of this chapter is to change the situation and to demonstrate that these methods can be successfully applied in studies of complex nonlinear dynamical systems and hydrodynamics, in particular. In this review, we provide a state-of-the-art sum of results and theories dealing with non-perturbative methods of quantum field theory in studies of hydrodynamics. Our report is of interest to the broad auditorium of natural scientists, physicists and applied mathematicians, with a background in nonlinear dynamical systems, having an interest in both methodological developments and interdisciplinary applications related to hydrodynamics.

Original language | English |
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Title of host publication | Turbulence |

Subtitle of host publication | Theory, Types and Simulation |

Publisher | Nova Science Publishers, Inc. |

Pages | 407-478 |

Number of pages | 72 |

ISBN (Print) | 9781617617355 |

State | Published - 2011 |

## Keywords

- Fully developed turbulence
- Synaptic eddies
- Tsunami waves
- Waterspouts