arXiv subjects

Alex Fedoseyev

Publications and source records attributed to Alex Fedoseyev.

5 recordsLinked to original sources

arXiv2026

Analytical Kink-Type Solutions and Streak Formation in Turbulent Channel Flow

An analytical framework for turbulent channel flow is developed based on the Alexeev hydrodynamic equations, focusing on the coupled behavior of streamwise and transverse velocity components. The mean streamwise velocity is represented as a superposition of a laminar (parabolic) component and a nonlinear turbulent contribution, yielding velocity profiles that agree with experimental data from channel and pipe flows over a wide range of Reynolds numbers, $3\times10^3 \le Re \le 3.5\times10^7$, with deviations of approximately $1\%$ at moderate Reynolds numbers and up to $3\%$ at the highest Reynolds numbers. The transverse velocity component is analyzed using a simplified form of the governing equations, leading to analytical expressions that capture its dominant spatial structure. The coupling between transverse velocity and streamwise momentum is then examined, revealing that the streamwise turbulent component admits a family of kink-type solutions. These solutions exhibit localized monotonic transitions separating regions of nearly uniform velocity and are interpreted as analytical representations of streamwise streaks. The model predicts characteristic streak properties, including spacing, thickness, intensity, and streamwise extent, which are shown to be consistent in order of magnitude with experimental observations of near-wall streaks. The results provide a unified analytical description of mean velocity profiles, secondary flows, and streak formation in wall-bounded turbulence, and suggest a mechanism linking transverse velocity fluctuations to the emergence of coherent streamwise structures.

physics.flu-dyn↗

arXiv2025

Analytical Solutions for Turbulent Channel Flow Using Alexeev and Navier-Stokes Hydrodynamic Equations: Comparison with Experiments

Understanding turbulent boundary layer flows is important for many application areas. Enhanced theoretical models may provide deeper insights into the fundamental mechanisms of turbulence that elude current models; therefore, the search for improved kinetic equations and their respective hydrodynamic equations continues. In this work, we consider the Generalized Boltzmann Equation (GBE), proposed by Alexeev (1994). The GBE accounts for finite particle size and the variation of the distribution function over timescales of the order of the collision time. The Alexeev hydrodynamic equations are derived from the GBE. In this work, the Alexeev hydrodynamic equations (AHE) and Navier-Stokes (NS) equations are solved analytically for turbulent channel flow under the assumption that stationary solutions yield the mean flow velocity. The analytical solutions of the AHE are validated by numerical solutions and compared with the NS solutions and experimental data for turbulent channel flow from multiple sources, spanning Reynolds numbers from 3,000 to 35,000,000. Solutions of the AHE demonstrate significantly better agreement with experimental data than those obtained from the NS equations. The analytical solution revealed a new similarity parameter: the boundary layer thickness scale, which coincides with the Kolmogorov microscale observed in experiments. The mechanisms for turbulence generation and control are discussed.

physics.flu-dyn↗

arXiv2025

Improved Analytical Solution for Turbulent Flow in Channel and Circular Pipe

The approximate analytical solution for turbulent flow in a channel was proposed in Fedoseyev (2023). It described the mean turbulent flow velocity as a superposition of parabolic (laminar) and superexponential (turbulent) solutions. The Alexeev Hydrodynamic Equations (AHE), proposed by Alexeev (1994), were used as the governing equations to describe turbulent flow. Compared to the Navier-Stokes equations, the AHE include additional terms representing temporal and spatial fluctuations. These additional terms include a timescale multiplier $\tau$, and the AHE reduce to the Navier-Stokes equations in the limit as $\tau \to 0$ In this study, we propose an improved analytical solution formula that provides better agreement with experimental data at high Reynolds numbers. The maximum discrepancy between the analytical solution and experimental data has been reduced from 5% to 2% for Reynolds numbers of order 100,000, and from 10% to 4% for Reynolds numbers up to 35,000,000, based on comparisons with experimental results ranging from the legacy work of Nikuradse (Prandtl group, 1932) to studies by Wei (1989), Zagarola (1996), van Doorne (2007), and the recent work of Pasch (2023).

physics.flu-dyn↗

arXiv2024

Minimization Principle for Analytical Solution of Turbulent Flow in Channel

The analytical solution for turbulent flow in channel presented in Fedoseyev (2023), described the mean turbulent flow velocity as a superposition of the laminar (parabolic) and turbulent (superexponential) solutions. In this study, the coefficients of superposition are proposed to obtain through the minimization principle, the principle of minimum viscous dissipation. The obtained analytical solutions agree well with the experimental data for turbulent flow.

physics.flu-dyn↗

arXiv2023

Analytical Solution for Turbulent Flow in Channel

In this work the exact and approximate analytical solution of the GHE for turbulent flow in channel are presented. It was discovered first by numerical simulations, Fedoseyev and Alexeev (2010), and now the explicit formula are obtained. 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 is proposed 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 Van Doorne (2007) confirmed this suggestion. The Navier-Stokes equations do not have the 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 close agreement with experiments for turbulent flows.

physics.flu-dyn↗