Testing of logarithmic-law for the slip with friction boundary condition

Large eddy simulation (LES) seeks to predict the dynamics of the organized structures in the flow, that is, local spatial averages u ̄ $\bar{u}$ of the velocity u of the fluid. Although LES has been extensively used to model turbulent flows, very often, the model has difficulty predicting turbulence generated by interactions of a flow with a boundary. A critical problem in LES is to find appropriate boundary conditions for the flow averages, which depend on the behavior of the unknown flow near the wall. In the light of the works of Navier and Maxwell, we use boundary conditions on the wall. We compute the appropriate friction coefficient β for channel flows and investigate its asymptotic behavior as the averaging radius δ → 0 and as the Reynolds number Re → ∞. No-slip conditions are recovered in the first limit, and free-slip conditions are recovered in the second limit. This study is not intended to develop new theories of the turbulent boundary layer; we use available boundary layer theories to improve numerical boundary conditions for flow averages.

Kinetic Description of Nonequilibrium Transfer Processes

The paper uses the example of the Brownian motion to kinetically describe the process of entropy increment in a nonequilibrium medium. The study shows that depending on the degree of nonequilibrium, the convergence to an equilibrium state occurs according to different laws. In the case of a strongly nonequilibrium medium, the entropy increment is described mathematically by the weakest logarithmic law, and in the case of a close-to-equilibrium medium, the entropy seeks a maximum value according to the strongest mathematical law --- the exponential law. The obtained expressions describing the Brownian motion can be extended to all other nonequilibrium processes. Mathematical modeling made it possible to calculate the process of entropy increment for an arbitrary degree of nonequilibrium and establish the parameters at which the transition from logarithmic to exponential law of entropy increment occurs when the thermodynamic system seeks an equilibrium state

Wall Bounded Flows and a General Proof of the Validity of the Universal Logarithmic Law of the Wall

The logarithmic law of the wall is usually derived for the flat plate assuming stationary, two-dimensional fully developed flow with no external pressure gradient. The Prandtl mixing length model for the turbulence is applied, which assumes homogeneous turbulence and two empirical constants, and the logarithmic wall law is derived. It is than stated in the textbooks that it is universally valid without a proof. As a justification experimental evidence is shown. First this proof will be shown in detail. Than a more general approach based on similarity considerations is made to show the universal validity of the logarithmic law of the wall. Starting from the Navier-Stokes equation a general non dimensional form of this equation is derived showing its dependency from four non-dimensional numbers, the Strouhal, Euler, Reynolds and the Froude number. Then wall bounded laminar flows are analyzed by dimensional analysis. The laminar boundary length and time scales are derived and used to non-dimensionalize the Navier-Stokes equation. With this specific non-dimensionalization for the laminar boundary layer a more specific non dimensional Navier-Stokes equation is derived. Then the high Reynolds limit is taken with considerations of orders of magnitude and the boundary layer equations are derived. Finally, for turbulent near wall flows a dimensional analysis is made and the corresponding near wall non-dimensional velocities and coordinates y+ and u+ are derived from the Buckingham-Π theorem. Using these variables to non-dimensionalize the Navier-Stokes equations in the near wall turbulent region the third author Malcherek showed that the so derived non-dimensional Navier-Stokes equations do not depend on any non-dimensional number and has a unique solution. Hence, the logarithmic law of the wall must be universally valid, without any simplification, any turbulence model, empirical constant or further assumptions. In such a way the students do not have to believe anymore in the universality of the logarithmic law of the wall based on empirical evidence only, now this fact has been proven by the third author Malcherek and the larger context has been elaborated by all authors for an advanced teaching of wall bounded flows.

Wind Energy Assessment during High-Impact Winter Storms in Southwestern Europe

The electricity produced through renewable resources is dependent on the variability of weather conditions and, thus, on the availability of the resource, as is the case with wind energy. This study aims to assess the wind resource available and the wind energy potential (WEP) during the December months for the three years 2017, 2018, and 2019, in southwestern Europe, when several high-impact storms affected the region. Additionally, a comparison of Prandtl’s logarithmic law and Power-law equations for extrapolation of the vertical wind profile is performed for onshore conditions, to evaluate the differences in terms of energy production, with the use of different equations. To assess the effect of the strong winds associated with the storms, 10 m wind components are used, with a 6-hourly temporal resolution, for the December months over the southwestern Europe region (30° N–65° N; 40° W–25° E). Results are compared to the climatology (1981–2010) and show an increase of wind intensity of 1.86 m·s−1 in southwestern Europe during December 2019, and a decrease up to 2.72 m·s−1 in December 2018. WEP is calculated for the selected wind turbine, 4 MW E-126 EP3—ENERCON, as well as the values following the wind resource record, that is, (i) higher values in December 2019 in the offshore and onshore regions, reaching 35 MWh and 20 MWh per day, respectively, and (ii) lower values in December 2018, with 35 MWh and 15 MWh per day for offshore and onshore. Differences in WEP when using the two equations for extrapolation of wind vertical profile reached 60% (40%) in offshore (onshore) regions, except for the Alps, where differences of up to 80% were reached. An additional analysis was made to understand the influence of the coefficients of soil roughness and friction used in each equation (Prandtl’s logarithmic law and Power-law), for the different conditions of onshore and offshore. Finally, it is notable that the highest values of wind energy production occurred on the stormy days affecting southwestern Europe. Therefore, we conclude that these high-impact storms had a positive effect on the wind energy production in this region.

Development of surface roughness length and drag parameterizations over deep seas

<p>Many formulations to determine the sea surface roughness length (z<sub>0</sub>) have been proposed in the past. The well-known Charnock’s equation is applied in most of the previous research. In this study, a different point of view is adopted to develop a new formulation. The starting point is an alternative method for surface roughness length calculation, i.e., the Lettau’s method. This method has already been validated onshore in the presence of obstacles over a domain; for obstacles with a defined cross-section perpendicular to the wind direction plane. Over deep waters, it is expected to find only one type of obstacle, i.e., consecutive waves forming straight lines. Different wave systems and the presence of swell add complexity to determine the sea surface profile. Hence, the adaptation of Lettau’s method seems reasonable, but the demonstrated dependency of z<sub>0</sub> to wave age cannot be neglected.</p><p>Wind-generated waves result from a kinetic energy transfer between the atmosphere and the sea surface. However this physical process is not represented in the well-known logarithmic law. While this effect can be neglected onshore, in offshore environments it can be significant, as 20% of the time z<sub>0</sub> is found to be over the expected range. Therefore, a kinetic energy transfer correction is included into an offshore logarithmic law. With an aerodynamic z<sub>0</sub>, achieved by the adaptation of the Lettau’s equation, and the new offshore logarithmic law, an empirical method for the kinetic energy transfer correction is proposed.</p>

Nonequilibrium Fluctuations of a Brownian Particle in a Medium with Production of Entropy

The study statistically describes Brownian motion in a locally nonequilibrium medium, taking into account the production of entropy, and proposes to describe the nonequilibrium fluctuations of the velocity of a Brownian particle using a linear integro-differential equation. The characteristic functions of fluctuations of the Brownian particle velocity are obtained, which make it possible to carry out a complete statistical description of Brownian motion in a medium with the production of entropy. Findings of research show that the variance of these fluctuations increases with time according to the logarithmic law. The correlation function of fluctuations of the Brownian particle velocity is calculated and it is shown that it consists of two terms. The first term, which has a power-law dependence, describes equilibrium fluctuations, and the second, which has a logarithmic dependence, describes nonequilibrium fluctuations

Research of the properties of quarry tuff-stone for complex processing

This article focuses on the complex processing of quarry tuffs-stone to extract metals (iron, titanium, copper, silver, etc.) and obtain raw materials for construction and agriculture. The issue of tuff-stone softening was investigated and the analytical dependence of the regularity of tuff-stone softening at water saturation was established, which indicates that the saturation increases with increasing mass of the sample according to the logarithmic law, and the dehydration process occurs according to the parabolic law. Also in the course of researches the magnetic susceptibility of tuff-stone was defined, which depends on size of induction of a magnetic field. The magnetically sensitive part is up to 50% by weight of the sample, and the remaining silicate part at a magnetic field strength of 1.3 Tesla. Spectral analysis showed a high content of metals in the magnetically sensitive part of tuff-stone, which consists of iron (35-40%), titanium (2.5-4.0%) and copper in the silicate part (0.4-0.7%). It was found that the percentage of content representing commercial interest, and therefore it is appropriate complex processing.

Определение коэффициента экстинкции моноксида углерода, адсорбированного на диоксиде титана

The adsorption of carbon monoxide on the TiO2 (anatase) surface at room temperature was studied by infrared spectroscopy and volumetry. The experimental data obtained indicate weak adsorption of CO molecules on the exponentially heterogeneous surface. The adsorption heat decreases according to the logarithmic law in the coverage range of 0.002-0.03. The extinction coefficient of adsorbed CO for the heterogeneous CO/TiO2 system is calculated using the Bouguer-Lambert-Beer law with correction for the Lorenz field taken into account. The conditions for the applicability of the Bouguer-Lambert-Beer's law for the study of heterogeneous systems are discussed.

Harmonic Progression in Bioinformatics and Recurrent Series in Inherited Biostructures

The article is devoted to the study of new approaches to the development of mathematical models in genetic biomechanics, which studies the structural relationships of the genetic coding system with genetically inherited biological forms. More specifically, we are talking about models based on the recurrent harmonic progression whose connection with the information sequences of DNA molecules in the genomes of higher and lower organisms was recently revealed. In particular, the article describes previously unknown connections of the function of natural logarithms with the structures of the molecular genetic system, which allow modelling the main psychophysical logarithmic law by Weber-Fechner and also many other logarithmic structures in genetically inherited biological systems. In physics, the harmonic progression is traditionally considered, first of all, as related to standing waves in resonators. Our results are correlated with Frohlich’s vibration-resonant theory about collective quantum effects and long-range communication in biological systems.