Query: logarithmic layer

title: An isolated logarithmic layer
abstract: To isolate the multiscale dynamics of the logarithmic layer of wall bounded turbulent flows, a novel numerical experiment is conducted in which the mean tangential Reynolds stress is eliminated except in a subregion corresponding to the typical location of the logarithmic layer in channels. Various statistical comparisons against channel flow databases show that, despite some differences, this modified flow system reproduces the kinematics and dynamics of natural logarithmic layers well, even in the absence of a buffer and an outer zone. This supports the previous idea that the logarithmic layer has its own autonomous dynamics. In particular, the results suggest that the mean velocity gradient and the wall parallel scale of the largest eddies are determined by the height of the tallest momentum transferring motions, which implies that the very large scale motions of wall bounded flows are not an intrinsic part of the logarithmic layer dynamics. Using a similar set up, an isolated layer with a constant total stress, which represents the logarithmic layer without a driving force, is simulated and examined.

title: Nonlinear mechanism of the self sustaining process in the buffer and logarithmic layer of wall bounded flows
abstract: The nonlinear mechanism in the self sustaining process (SSP) of wall bounded turbulence is investigated. Resolvent analysis is used to identify the principal forcing mode that produces the maximum amplification of the velocities in numerical simulations of the minimal channel for the buffer layer and a modified logarithmic (log) layer. The wavenumbers targeted in this study are those of the fundamental mode, which is infinitely long in the streamwise direction and once periodic in the spanwise direction. The identified mode is then projected out from the nonlinear term of the Navier Stokes equations at each time step from the simulation of the corresponding minimal channel. The results show that the removal of the principal forcing mode of the fundamental wavenumber can inhibit turbulence in both the buffer and log layer, with the effect being greater in the buffer layer. Removing other modes instead of the principal mode of the fundamental wavenumber only marginally affects the flow. Closer inspection of the dyadic interactions in the nonlinear term shows that contributions to the principal forcing mode come from a limited set of wavenumber interactions. Using conditional averaging, the flow structures that are responsible for generating the nonlinear interaction to self sustain turbulence are identified as spanwise rolls interacting with oblique streaks. This method, based on the equations of motion, validates the similarities in the SSP of the buffer and log layer, and characterises the underlying quadratic interactions in the SSP of the minimal channel.

title: An approach to determine coefficients of logarithmic velocity vertical profile in the bottom boundary layer
abstract: Velocity vertical profiles in the bottom boundary layer are important to understand the oceanic circulation. The logarithmic vertical profile, u=Alnz+B, is the universal profile for the horizontal velocity in the boundary layer, in which two coefficients (A and B) need to be determined. The two coefficients are the functions of the friction velocity (u* and the roughness length (z0) and they are calculated using u* and z0. However, the measurement of u* and z0 is a challenge. In the present study, an approach is developed to estimate the two coefficients (A and B) by using a series of flume laboratory experiments with flat boundary and regularly distributed cylinders as the rough boundaries. An acoustic doppler velocimeter (ADV) is used to measure the velocity vertical profiles of the steady flow. Using the measured velocity data, the regressed logarithmic profiles are obtained. Based on the series of the A and B values, the mathematical formula for A and B are statistically established as the function of the cylinder height, inflow velocity, and the water depth, which avoids the measurement of the friction velocity and the roughness length.

title: Intermediate scaling and logarithmic invariance in turbulent pipe flow
abstract: A three layer asymptotic structure for turbulent pipe flow is proposed revealing, in terms of intermediate variables, the existence of a Reynolds number invariant logarithmic region for the streamwise mean velocity and variance. The formulation proposes a local velocity scale (which is not the friction velocity) for the intermediate layer and results in two overlap layers. We find that the near wall overlap layer is governed by a power law for the pipe for all Reynolds numbers, whereas the log law emerges in the second overlap layer (the inertial sublayer) for sufficiently high Reynolds numbers $Re_{\tau This provides a theoretical basis for explaining the presence of a power law for the mean velocity at low $Re_{\tau and the coexistence of power and log laws at higher $Re_{\tau The classical von Karman \kappa$ and Townsend Perry $A_1$ constants are determined from the intermediate scaled log law constants; \kappa$ shows a weak trend at sufficiently high $Re_{\tau but falls within the commonly accepted uncertainty band, whereas $A_1$ exhibits a systematic Reynolds number dependence until the largest available $Re_{\tau The key insight emerging from the analysis is that the scale separation between two adjacent layers in the pipe is proportional to \sqrt {Re_{\tau (rather than $Re_{\tau and therefore the approach to an asymptotically invariant state can be expected to be slow.

title: Analytical model for the two dimensional advection diffusion equation with the logarithmic wind profile in unstable conditions
abstract: The modeling of atmospheric dispersion is the mathematical simulation of how pollutants are dispersed in the atmosphere. Based on the advection diffusion equations describing the dispersion of pollutants, dispersal models are widely used to give a spatial variability of pollutants emitted mainly by agricultural activities and industrial facilities. In this context, an analytical model is presented to study the dispersion of pollutants in the atmospheric boundary layer. The solution procedure is based on dividing the planetary boundary layer into sub domains, where in each sub domain the eddy diffusivity and the wind speed take average values. The eddy diffusivity is expressed under unstable conditions and the wind speed is represented in its logarithmic form. The findings of the current study show that the developed model is successfully validated using data sets obtained from the Copenhagen diffusion experiments in unstable conditions, after this the model is numerically applied in order to observe, in a better way, the spread of the pollutant in the atmosphere.

title: The mysteries of the best approximation and Chebyshev expansion for the function with logarithmic regularities
abstract: The best polynomial approximation and Chebyshev approximation are both important in numerical analysis. In tradition, the best approximation is regarded as more better than the Chebyshev approximation, because it is usually considered in the uniform norm. However, it not always superior to the latter noticed by Trefethen [10, 11] for the algebraic singularity function. Recently Wang [13] have proved it in theory. In this paper, we find that for the functions with logarithmic regularities, the pointwise errors of Chebyshev approximation are smaller than the errors of the best approximations except only in the very narrow boundaries. The pointwise error for Chebyshev series, truncated at the degree n is O(n k) (k min{2g+1, 2d+1} but is worse by one power of n in narrow boundary layer near the endpoints.

title: Thermal Trigger for Solar Flares I: Fragmentation of the Preflare Current Layer
abstract: We consider the effects of the heat balance on the structural stability of a preflare current layer. The problem of small perturbations is solved in the piecewise homogeneous magnetohydrodynamic (MHD) approximation taking into account viscosity, electrical and thermal conductivity, and radiative cooling. Solution to the problem allows for the formation of an instability of thermal nature. There is no external magnetic field inside the current layer in the equilibrium state, but it can penetrate inside when the current layer is disturbed. The formation of a magnetic field perturbation inside the layer creates a dedicated frequency in a broadband disturbance subject to thermal instability. In the linear phase, the growth time of the instability is proportional to the characteristic time of radiative cooling of the plasma and depends on the logarithmic derivatives of the radiative cooling function with respect to the plasma parameters. The instability results in transverse fragmentation of the current layer with a spatial period of 1 10 Mm along the layer in a wide range of coronal plasma parameters. The role of that instability in the triggering of the primary energy release in solar flares is discussed.

title: Thin layer drying models and characteristics of scent leaves (Ocimum gratissimum) and lemon basil leaves (Ocimum africanum)
abstract: The effect of air temperature on the drying kinetics and characteristics of scent and lemon basil leaves were investigated using a vacuum oven dryer at 30 degC, 40 degC, 50 degC, 60 degC and 70 degC. Suitable drying models were obtained to describe the drying process. Falling rate drying phenomenon was observed for both leaves. Six thin layer drying models namely: Lewis model, Page model, Modified Page model, Logarithmic model, Two term model and Midilli model were fitted to the moisture ratio data for both scent and lemon basil leaves. Highest coefficient of determination (R2) and least sum of square error (SSE) and root mean square error (RMSE) values were determined for the Logarithmic model for scent leaf as 0.9998, 0.0002, 0.0081, and 0.9961, 0.0034 and 0.0222 for lemon basil leaf. The Two term model showed the same values for scent leaf as the Logarithmic model and 0.9967, 0.0024 and 0.0185 for lemon basil leaf. They were the best fit models for all the drying temperatures. The results showed that scent and lemon basil leaves can best be dried at 70 degC and 60 degC, respectively. The specific energy consumption and the effective moisture diffusivities (Deff) of scent and lemon basil leaves were determined at different drying air temperatures. Deffranged from 4.76x10 13to 1.47x10 12m2/s and 4.80x10 13 to 2.06x10 12 m2/s for scent and lemon basil leaves respectively, as temperature increased. Using the Arrhenius equation, the activation energy (Ea) and pre exponential factor (Do) were determined as 25.01 kJ/mol and 8.19x10 9 m2/s for scent leaf and 32.35 kJ/mol and 1.49x10 7 for lemon basil leaves. Therefore, the Logarithmic and Two term models are recommended as the best models for the drying kinetics of scent and lemon basil leaves from the experiment.

title: Direct numerical simulations of supersonic turbulent boundary layer with streamwise striped wall blowing
abstract: Direct numerical simulations of a spatially developing Ma 2.25 supersonic turbulent boundary layer with streamwise striped wall blowing (SSB) are performed for the purpose of turbulence drag reduction. The SSB is designed to blow through long and straight slots in the flow direction. The slots are equally distributed in spanwise direction, with different stripe spacing and width. Blowing amplitudes of 0.1% and 0.2% are investigated. For comparison, uniform blowing (UB) of 0.1% is also simulated. It is found that in spite of weak control amplitudes, 7.4% and 14.5% drag reduction can be achieved in the case of 6SSB 0.1% and 6SSB 0.2% respectively. Similar to UB, the boundary layer displacement thickness is thickened by SSB, with a thicker viscous sub layer and a logarithmic zone which moving away from the wall. Turbulence intensities and turbulent coherent structures are enhanced, although the streamwise scales of the latter are attenuated. Turbulent kinetic energy analysis presents that both the production and dissipation are increased in the near wall. Compressible Renard Deck decomposition of C f shows that it is the spatially growth term that mainly responsible for the turbulence drag reduction.

title: Correlation and optimization of the optoelectrical properties of DC magnetron sputtered Cu2ZnSnS4 absorber layer as a function of the material composition
abstract: very promising to fabricate CZTS based thin film photovoltaic (PV) solar cells with regards to existent environmental and industrial issues. However, their state of the art efficiency remains limited to about 10% to date. In this work, we aim at optimizing the optical and electrical properties of the CZTS absorber by an extensive screening of their correlation with the material composition. This is widely varied by different deposition (i.e. thickness of precursors) and process (i.e. RTP) conditions. We assess the impact of absorber composition on the energy bandgap, absorption coefficient, p type carrier concentration and mobility. The most important results lie in the extensive analysis of the inverse power law trend for carrier concentration versus mobility and logarithmic trend versus bandgap. Our conclusions point the optimal composition ratios towards Cu poor and less than actual target Zn rich range. As a result, a potential roadmap is drawn up based on presented experimental results and SCAPS simulations in order to reach more than 10% cell efficiency with the target technology.