Physical processes underlying the development of shear turbulence

A physical model of the development of turbulence in free shear flows is proposed. The model is based on the results of numerical simulations of turbulent flow development. The main ideas of the proposed theory of turbulence are stated as follows: the onset of turbulence begins with the formation of large vortices; spectral energy transfer involves both direct and inverse cascades; and the inertial range of the energy spectrum develops as a result of concurrent direct and inverse cascades. The dominant physical factors that determine the spectrum include Joukowski forces.     

Computing the sound power in non-uniform flow

An expression for the sound power in an annular duct with swirling mean flow is derived in the high-frequency limit relevant to fan aeroacoustics. The sound power is expressed in terms of the duct normal modes which are computed for several mean flows. It is shown that the mean flow non-uniformity modifies both the pressure-dominated modes and the expression for the sound power. The pressure-dominated modes are not orthogonal and thus one must account for interference between the different radial modes. The interference effects are small for the case of a potential mean flow. For a vortical mean flow interference terms may become significant.     

First-principles calculations of the hyperfine fields on ligands in fluorides

In solid-state physics, a crystal lattice is frequently approximated by an array of interacting ions. In this case, the wave functions of individual ions are assumed to be a fairly good zeroth approximation in calculating the matrix elements of the interaction Hamiltonian of electrons and nuclei of the lattice from first principles. Use of the second-quantization method is proposed for such calculations in the basis of these functions. As an example, the electron transition amplitude from a ligand to the central ion is estimated. The results agree well with the experimental data.     

Inhomogeneous states of a thin-film incommensurate ferroelectric

Nonuniform distributions of the order parameter in a film of an incommensurate ferroelectric whose free energy expansion does not contain Lifshitz invariants are considered. An equation describing the order parameter distribution over the film thickness is derived in the approximation of slowly varying amplitudes. The effect of film thickness and surface properties on the temperature of transition to the incommensurate phase is analyzed.     

Features of light attenuation in crystals under violation of the Bouguer law

A computer simulation and measurements of the light transmittance of germanium and paratellurite crystals of different thickness were used to show that, at scattering probabilities of photons comparable to their absorption probabilities, the standard methods for calculating light extinction coefficients on the basis of the Bouguer law lead to rough errors in estimation of the optical quality of a material.     

Fundamentals of physics of fluid flow reconsidered

Recently, two significant defects of the state-of-the-art of theoretical fluid mechanics have been evidenced, namely the ambiguity of the Navier Stokes equations with respect to the viscous stress tensor, and the inconsistency of the Reynolds stress approach with the symmetry of the inertial tensor. Therefore, by means of two classical topics of fluid mechanics, namely the universal velocity profile and the laminar boundary layer, the physics of fluid flow are scrutinized. The validity of the so obtained results is tested at the example of an exact solution of the Navier Stokes equations, namely the diffusion of the circulation of an eddy.