### 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

Original language | English |
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Title of host publication | Critical hydrodynamics: From turbulence to tsunami waves, to synaptic eddies |

Pages | 407-478 |

State | Published - Dec 1 2011 |

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## Cite this

Volchenkov, D. (2011). Critical hydrodynamics: From turbulence to tsunami waves, to synaptic eddies. In

*Critical hydrodynamics: From turbulence to tsunami waves, to synaptic eddies*(pp. 407-478)