Ephim Golbraikh

Propagation of electromagnetic waves in Kolmogorov and non-Kolmogorov atmospheric turbulence: three-layer altitude model

Turbulence properties of communication links (optical and microwave) in terms of log-amplitude variance are studied on the basis of a three-layer model of refractive index fluctuation spectrum in the free atmosphere. We suggest a model of turbulence spectra (Kolmogorov and non-Kolmogorov) changing with altitude on the basis of obtained experimental and theoretical data for turbulence profile in the troposphere and lower stratosphere.

Behavior of structure function of refraction coefficients in different turbulent fields

Deviations of experimental data on the effect of atmospheric turbulence on electromagnetic wave propagation from a standard Kolmogorov (or Obukhov-Kolmogorov) model are examined from the standpoint of the behavior of atmospheric passive scalar spectrum. It is pointed out that these deviations are not random and can be explained on the basis of todays ideas of passive scalar behavior in the atmosphere. This approach allows us to view electromagnetic radiation transfer in random media in a new way and to make the necessary steps for developing a generalized model of this phenomenon.

Different spectra formation in the presence of helical transfer

The Letter presents arguments which state that not only the energy flux but also the one of helicity should be involved in the structure function in both inertial and dissipation intervals.

Helical turbulence: Turbulent viscosity and instability of the second moments

The evolution of weak large-scale disturbances in the helical turbulence is considered. High-order statistical moments are taken into account in the frames of two-scale analog of Orszag diffusion approximation. The appearance of the instability of second moments is demonstrated for k<α/ν (k is wave vector, α and ν are proportional to the mean helicity and mean energy viscosity, respectively). Turbulent viscosity diminishing in comparison with the non-helical case is also demonstrated. These phenomenona qualitatively agree with previous results of other authors on the slow-down of energy transfer along the spectrum, from large to small scales at non-zero helicity.

Generalized atmospheric turbulence: implications regarding imaging and communications

At present, system design usually assumes the Kolmogorov model of refractive index fluctuation spectra in the atmosphere. However, experimental data indicates that in the atmospheric boundary layer and at higher altitudes the turbulence can be different from Kolmogorovs type. In optical communications, analytical models of mean irradiance and scintillation index have been developed for a traditional Kolmogorov spectrum and must be revised for non-Kolmogorov turbulence. The image quality (resolution, MTF, etc.) is essentially dependent on the properties of turbulent media. Turbulence MTF must be generalized to include non-Kolmogorov statistics. The change in fluctuation correlations of the refractive index can lead to a considerable change in both the MTF form and the resolution value. In this work, on the basis of experimental observations and modeling, generalized atmospheric turbulence statistics including both Kolmogorov and non-Kolmogorov path components are discussed, and their influence on imaging and communications through the atmosphere estimated for different scenarios of vertical and slant-path propagation. The atmospheric model of an arbitrary (non-Kolmogorov) spectrum is applied to estimate the statistical quantities associated with optical communication links (e.g., scintillation and fading statistics) and imaging systems. Implications can be significant for optical communication, imaging through the atmosphere, and remote sensing.

The role of helicity in turbulent MHD flows

We have studied the behavior of a helical homogeneous small-scale MHD turbulent flow under the influence of a weak inhomogeneous large-scale disturbance. We have shown that turbulent energy redistribution in the presence of nonzero helicity occurs mainly over large scales. Helicity increases correlation time, leading to the weakening of a direct cascade and to the formation of steep spectra over small scales, with simultaneous turbulent energy growth over large scales. Furthermore, an expression for the effective viscosity of the mean flow is derived. It is shown that the magnetic field, in addition to the helicity, reduces the effective viscosity of the medium. This may be important in the study of MHD flow around obstacles in the presence of an external magnetic field.

Hindered Energy Cascade in Highly Helical Isotropic Turbulence.

The conventional approach to the turbulent energy cascade, based on Richardson-Kolmogorov phenomenology, ignores the topology of emerging vortices, which is related to the helicity of the turbulent flow. It is generally believed that helicity can play a significant role in turbulent systems, e.g., supporting the generation of large-scale magnetic fields, but its impact on the energy cascade to small scales has never been observed. We suggest, for the first time, a generalized phenomenology for isotropic turbulence with an arbitrary spectral distribution of the helicity. We discuss various scenarios of direct turbulent cascades with new helicity effect, which can be interpreted as a hindering of the spectral energy transfer. Therefore, the energy is accumulated and redistributed so that the efficiency of nonlinear interactions will be sufficient to provide a constant energy flux. We confirm our phenomenology by high Reynolds number numerical simulations based on a shell model of helical turbulence. The energy in our model is injected at a certain large scale only, whereas the source of helicity is distributed over all scales. In particular, we found that the helical bottleneck effect can appear in the inertial interval of the energy spectrum.

An asymptotic model for the Kelvin–Helmholtz and Miles mechanisms of water wave generation by wind

The generalized Kelvin–Helmholtz (KH) and Miles mechanisms of the water wave generation by wind are investigated for two-layer piecewise linear model of the wind profile. It is shown by asymptotic expansions in small air-to-water density ratio that two mechanisms of the instability operate in quite different scales. Miles’ short waves are generated by weak winds, in particular, Miles’ regime is responsible for initiation of the instability at the minimum wind speed, while the generalized KH regime dominates at strong winds and raises moderately short waves.

Helicity spectra and dissipation

We study the helicity dissipation and spectrum on the basis of an asymptotic model introducing a dependence of the angle between turbulent vorticity and velocity components on the governing parameters into it. This leads to helicity spectra similar to those observed experimentally and obtained by DNS model computations by various authors.

On the universality of large-scale turbulence

Large-scale three-dimensional turbulence is a challenge to researchers, being one of the most complicated aspects of turbulence studies. The universal large scales behavior connected with the inverse energy cascade in two-dimensional turbulence has been known for about 35 years and studied experimentally and numerically. We have revealed the universality of three-dimensional large-scale turbulence properties experimentally and described it theoretically. A rigorous solution of this problem in the presence of an energy source gives scaling exponents −4/3 for velocity correlations and 1/3 for energy spectra of the large-scale turbulence. Such spectra are also observed in atmospheric air flows under different conditions—stable, convective, in cirrus clouds. The revealed physical phenomenon is important for the development of turbulence theory complementing the results obtained for its smaller scales.