Material surfaces in stochastic flows: Integrals of motion and intermittency.

We consider the line, surface, and volume elements of fluid in stationary isotropic incompressible stochastic flow in d-dimensional space and investigate the long-time evolution of their statistic properties. We report the discovery of a family of d!-1 stochastical integrals of motion that are universal in the sense that their explicit form does not depend on the statistics of velocity. Only one of them has been discussed previously.

Long-term properties of finite-correlation-time isotropic stochastic systems.

We consider finite-dimensional systems of linear stochastic differential equations ∂_{t}x_{k}(t)=A_{kp}(t)x_{p}(t), A(t) being a stationary continuous statistically isotropic stochastic process with values in real d×d matrices. We suppose that the laws of A(t) satisfy the large-deviation principle. For these systems, we find exact expressions for the Lyapunov and generalized Lyapunov exponents and show that they are determined in a precise way only by the rate function of the diagonal elements of A.

Stationary scaling in small-scale turbulent dynamo problem.

We consider forced small-scale magnetic field advected by an isotropic turbulent flow. The random driving force is assumed to be distributed in a finite region with a scale smaller than the viscous scale of the flow. The two-point correlator is shown to have a stationary limit for any reasonable velocity statistics. Its spatial dependence is found to be a power law. The scaling exponent is found to be close to 3.

Turbulent transport in reaction-diffusion systems.

The impact of turbulent advection in reaction-diffusion systems is investigated for the viscous range of scales. We show that the population size can increase exponentially even in systems with density saturation, at the expense of exponential propagation of the reaction front. Exact expressions for scaling exponents of the density and population size are calculated in different intermediate asymptotics of the process. The system appears to demonstrate high intermittency.

Passive scalar transport by a non-Gaussian turbulent flow in the Batchelor regime.

We analyze passive scalar advection by a turbulent flow in the Batchelor regime. No restrictions on the velocity statistics of the flow are assumed. The properties of the scalar are derived from the statistical properties of velocity; analytic expressions for the moments of scalar density are obtained. We show that the scalar statistics can differ significantly from that obtained in the frames of the Kraichnan model.

Correlation of radio and gamma emissions in lightning initiation.

The results of simultaneous radio and gamma emission measurements during thunderstorms are presented. A gamma detector situated at the height 3840 m and two radio detectors of Tien-Shan Mountain Scientific Station (altitude 3340 m) registered intensive gamma flashes and radio pulses during the time of lightning initiation. The radio-gamma correlation grows abruptly at the initial moment (a few hundred microseconds), and the correlation coefficient reaches 0.9-0.95. The gamma-energy spectrum measured during lightning initiation is close to the characteristic spectrum of runaway breakdown. Radio pulses observed at the same time have highest amplitudes. Combined observation of gamma and radio emissions confirm the conception of lightning initiation due to multiple simultaneous electric discharges at hydrometeors stimulated and synchronized by low-energy electrons generated in the runaway breakdown process.

Multifractal structure of fully developed turbulence.

The appearance of vortex filaments, the power-law dependence of velocity and vorticity correlations and their multiscaling behavior are derived from the Navier-Stokes equation. This is possible due to interpretation of the Navier-Stokes equation as an equation with multiplicative noise and remarkable properties of random matrix products.

Observation of the avalanche of runaway electrons in air in a strong electric field.

The generation of an avalanche of runaway electrons is demonstrated for the first time in a laboratory experiment. Two flows of runaway electrons are formed sequentially in an extended air discharge gap at the stage of delay of a pulsed breakdown. The first, picosecond, runaway electron flow is emitted in the cathode region where the field is enhanced. Being accelerated in the gap, this beam generates electrons due to impact ionization. These secondary electrons form a delayed avalanche of runaway electrons if the field is strong enough. The properties of the avalanche correspond to the existing notions about the runaway breakdown in air. The measured current of the avalanche exceeds up to an order the current of the initiating electron beam.

Vortex filament model and multifractal conjecture.

We develop a theory of turbulence based on the inviscid Navier-Stokes equation. We get a simple but exact stochastic solution (vortex filament model) which allows us to obtain a power law for velocity structure functions in the inertial range. Combining the model with the multifractal conjecture, we calculate the scaling exponents without using the extended self-similarity approach. The results obtained are shown to be in very good agreement with numerical simulations and experimental data. The role of more general stochastic solutions of the Navier-Stokes equation is discussed.

Strong flux of low-energy neutrons produced by thunderstorms.

We report here for the first time about the registration of an extraordinary high flux of low-energy neutrons generated during thunderstorms. The measured neutron count rate enhancements are directly connected with thunderstorm discharges. The low-energy neutron flux value obtained in our work is a challenge for the photonuclear channel of neutron generation in thunderstorm: the estimated value of the needed high-energy γ-ray flux is about 3 orders of magnitude higher than that one observed.

Lagrangian and Eulerian velocity structure functions in hydrodynamic turbulence.

The Lagrangian and Eulerian transverse velocity structure functions of fully developed fluid turbulence are found based on the inviscid Navier-Stokes equation. The structure functions are shown to obey the scaling relations S(n)(L)(tau) proportional to tau(xi(n)) and S(n)(E)(l) proportional to l(zeta(n)) inside the inertial range. The scaling exponents zeta(n) and xi(n) are calculated analytically without using dimensional considerations. This result is a significant step toward understanding the nature of hydrodynamic turbulence. The obtained values are in agreement with recent numerical and experimental data.

Structure functions of fully developed hydrodynamic turbulence: an analytical approach.

We develop a theory of turbulence based on the inviscid Navier-Stokes equation, without using dimensional or phenomenological considerations. The theory allows us to obtain the scaling law and to calculate the scaling exponents of the Lagrangian and Eulerian velocity structure functions in the inertial range. The obtained results are shown to be in very good agreement with numerical simulations and experimental data. The introduction of stochasticity into the equations is discussed in detail. The main equation of the theory obtained directly from the Navier-Stokes equation is analyzed by means of continual integration.

Lagrangian statistical theory of fully developed hydrodynamical turbulence.

The Lagrangian velocity structure functions in the inertial range of fully developed fluid turbulence are for the first time derived based on the Navier-Stokes equation. For time tau much smaller than the correlation time, the structure functions are shown to obey the scaling relations K_{n}(tau) proportional, varianttau;{zeta_{n}}. The scaling exponents zeta_{n} are calculated analytically without any fitting parameters. The obtained values are in amazing agreement with the experimental results of the Bodenschatz group. A new relation connecting the Lagrangian structure functions of different orders analogously to the extended self-similarity ansatz is found.