There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

The structure

Cascades and transitions in turbulent flows

The mechanics of blood flow in arteries plays a key role in the health of individuals. In this framework, the role played by the presence of helical flow in the human aorta is still not clear in its relation to physiology and pathology. We report here a method for quantifying helical flow in vivo employing time-resolved cine phase contrast magnetic resonance imaging to obtain the complete spatio-temporal description of the three-dimensional pulsatile blood flow patterns in aorta. The method is applied to data of one healthy volunteer. Particle traces were calculated from velocity data: to them we applied a Lagrangian-based method for helical flow quantification, the Helical Flow Index, which has been developed and evaluated in silico in order to reveal global organization of blood flow. Our results: (i) put in evidence that the systolic hemodynamics in aorta is characterized by an evolving helical flow (we quantified a 24% difference in terms of the content of helicity in the streaming blood, between mid and early systole); (ii) indicate that in the first part of the systole helicity is ascrivable mainly to the asymmetry of blood flow in the left ventricle, joined with the laterality of the aorta. In conclusion, this study shows that the quantification of helical blood flow in vivo is feasible, and it might allow detection of anomalies in the expected physiological development of helical flow in aorta and accordingly, could be used in a diagnostic/prognostic index for clinical practice.

In Vivo Quantification of Helical Blood Flow in Human Aorta by Time-Resolved Three-Dimensional Cine Phase Contrast Magnetic Resonance Imaging

Quantifying air–sea exchanges of enthalpy and momentum is important for understanding and skillfully predicting tropical cyclone intensity, but the magnitude of the corresponding wind speed–dependent bulk exchange coefficients is largely unknown at major hurricane wind speeds greater than 50 m s−1. Since direct turbulent flux measurements in these conditions are extremely difficult, the momentum and enthalpy fluxes were deduced via absolute angular momentum and total energy budgets. An error analysis of the methodology was performed to quantify and mitigate potentially significant uncertainties resulting from unresolved budget terms and observational errors. An analysis of six missions from the 2003 Coupled Boundary Layers Air–Sea Transfer (CBLAST) field program in major hurricanes Fabian and Isabel was conducted using a new variational technique. The analysis indicates a near-surface mean drag coefficient CD of 2.4 × 10−3 with a 46% standard deviation and a mean enthalpy coefficient CK of 1.0 × 1...

Air–Sea Enthalpy and Momentum Exchange at Major Hurricane Wind Speeds Observed during CBLAST

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.

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

Lidar study of aerosol turbulence characteristics in the troposphere: Kolmogorov and non-Kolmogorov turbulence

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 today’s 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.

Behavior of structure function of refraction coefficients in different turbulent fields.

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.

Ephim Golbraikh

Papers

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

Lidar study of aerosol turbulence characteristics in the troposphere: Kolmogorov and non-Kolmogorov turbulence

Behavior of structure function of refraction coefficients in different turbulent fields.

Hindered Energy Cascade in Highly Helical Isotropic Turbulence.

Some limitations on optical communication reliability through Kolmogorov and non-Kolmogorov turbulence