Analytical Solution for Turbulent Flow in Channel

Generalized Hydrodynamic Equations (GHE) proposed by Boris Alexeev (1994) have been successfully used for simulations of incompressible viscous flows for a wide range of problems and flow parameters, including high Reynolds number turbulent flows with thin boundary layers, providing good agreement with experiments, Fedoseyev and Alexeev (1998, 2010, 2012), Fedoseyev (2000, 2001a, 2001b). The GHE model has also been applied to the hypersonic flows which are very challenging problems as such flows can exhibit both continuum and non-continuum flow regimes. The results by Fedoseyev (2020), Fedoseyev and Griaznov (2021) and Fedoseyev, Griaznov and Ouazzani (2022) demonstarted good agreement with experiments, including the highly rarefied flows. In this work an approximate analytical solution of the GHE for turbulent flow in channel is presented. The solution is a superposition of the laminar (parabolic) and turbulent (superexponential) solutions. The analytical solution compares well with the experimental data by Van Doorne (2007) for axial velocity and data by Nikuradse (1933) for axial velocity, for flows in pipes. It helps to explain the nature of turbulence as oscillations between the laminar (parabolic) and turbulent (superexponential) solutions. Good comparison of the analytical formula, a difference of the parabolic and superexponential solutions, for turbulent velocity fluctuations with the experiment by Doorne (2007) confirmed this suggestion. The Navier-Stokes equations can not have such superexponential solution. The obtained analytical solution provides a complete structure of the turbulent boundary layer that compares well with the experiments by Wei and Willmarth (1989). It also presents an explicit verifiable proof that Alexeev's generalized hydrodynamic theory (GHE) is in closer agreement with experiments for turbulent flows than currently available theories.Comment: 16 pages, 7 figures, presented at AMITANS Conf. June 2023, Albena, Bulgaria,submitted to Physics of Fluid

Conservation laws and angular transverse shifts of the reflected and transmitted light beams

The relation between the angular transverse shifts of the beams reflected and transmitted at a plane interface of two isotropic transparent media is established. The derivation of this relation is based on the conservation law of the transverse component of the Minkowski linear momentum, which takes place in the processes of the reflection and transmission of wave packets.Comment: 11 pages, 3 figure

Polarization-dependent transformation of a paraxial beam upon reflection and refraction: a real-space approach

We analyze the paraxial beam transformation upon reflection and refraction at a plane boundary. In contrast to the usual approach dealing with the beam angular spectrum, we apply the continuity conditions to explicit spatial representations of the electric and magnetic fields on both sides of the boundary. It is shown that the polarization-dependent distortions of the beam trajectory (in particular, the "longitudinal" Goos-H\"anchen shift and the "lateral" Imbert-Fedorov shift of the beam center of gravity) are directly connected to the incident beam longitudinal component and appear due to its transformation at the boundary.Comment: 10 pages, 1 figure. Formulae (32), (33), footnote 2 and Ref. 27 are added, some sentences are correcte

Influence of Photoexcitation Depth on Luminescence Spectra of Bulk GaAs Single Crystals and Defect Structure Characterization

The results of investigation of bulk GaAs photoluminescence are presented taken from near-surface layers of different thicknesses using for excitation the light with the wavelengths which are close but some greater than the excitonic absorption resonances (so-called bulk photoexcitation). Only the excitonic and band-edge luminescence is seen under the interband excitation, while under the bulk excitation, the spectra are much more informative. The interband excited spectra of all the samples investigated in the present work are practically identical, whereas the bulk excited PL spectra are different for different samples and excitation depths and provide the information on the deep-level point defect composition of the bulk materials.Comment: Aalborg Summer School on Nonlinear Optics, Aalborg, Denmark, 7-12 August 199

Goos-H\"{a}nchen and Imbert-Fedorov shifts of polarized vortex beams

We study, analytically and numerically, reflection and transmission of an arbitrarily polarized vortex beam on an interface separating two dielectric media and derive general expressions for linear and angular Goos-Hanchen and Imbert-Fedorov shifts. We predict a novel vortex-induced Goos-Hanchen shift, and also reveal direct connection between the spin-induced angular shifts and the vortex-induced linear shifts.Comment: 4 pages, 2 figures, to appear in Optics Letter

Unsteady Fluid Motion Between Two Infinite Walls Under Variable Body Force

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/77247/1/AIAA-2002-3079-152.pd

One-dimensional unsteady fluid motion between two infinite walls

We considered an incompressible fluid motion driven by space-dependent body force. For a one-dimensional case, the problem was solved analytically, with the arbitrary choice of body force coordinate dependence. It was shown that unsteady fluid flow can be represented as a series of separate modes, each with its own characteristic response time. © 2002 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70559/2/PHFLE6-14-7-2572-1.pd

Dynamics and statics of nonaxisymmetric liquid bridges

We finished the construction of the experimental apparatus and the design and testing of some of the visualization and data acquisition techniques. Experimental work focused on three areas: force measurements, loss of stability to nonaxisymmetric bridges, and vibration behavior. The experimental work is summarized in section 2. Selected results from our force measurement experiments are outlined in section 3. In addition we worked on the theory of the dynamic stability of axisymmetric bridges and undertook numerical simulation of the effects of inclined gravity vectors on the minimum volume stability limit for static bridges. The results and status of our theoretical work and numerical simulation are described in section 4. Papers published and in preparation, conference presentations, etc., are described in section 5. Work planned for the third year is discussed in section 6. References cited in the report are listed in section 7

Astrophysical Rates for Explosive Nucleosynthesis: Stellar and Laboratory Rates for Exotic Nuclei

A selected overview of stellar effects and reaction mechanisms with relevance to the prediction of astrophysical reaction rates far off stability is provided.Comment: 4 pages, 2 figures (contining 2 subfigures each); Proceedings of 10th Intl. Conference on Nucleus-Nucleus Collisions, Beijing, China, August 2009; to appear in Nuclear Physics