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Turbulence
Published in Amithirigala Widhanelage Jayawardena, Fluid Mechanics, Hydraulics, Hydrology and Water Resources for Civil Engineers, 2021
Amithirigala Widhanelage Jayawardena
The first scientist to embark on turbulent flow studies through experiments on pipe flow was Osborne Reynolds (1883). In his pipe flow experiments, he observed the flow pattern to change from regular motion to irregular or turbulent flow when the Reynolds number exceeded a certain critical value. Reynolds number (Re=VDρμ=VDν) increases with increasing size of the object characterized by D, increasing velocity of flow past the object characterized by V, increasing density of the fluid ρ and decreasing viscosity of the fluid, μ. Reynolds also introduced the concept of turbulent stress which together with Reynolds number now forms the basis of modern day understanding of turbulence. He also introduced the concept of describing the instantaneous values of state variables as a sum of a mean and a fluctuating component, which is known and widely used as Reynolds’ decomposition. Boussinesq (1877) hypothesized that turbulent stresses are linearly proportional to the large scale mean strain rates. Prandtl (1925) introduced the mixing length theory and the logarithmic velocity profile near a solid wall, Taylor (1921, 2000) introduced the idea of presenting turbulence in statistical terms such as correlations, Fourier transforms and power spectra, as well as the concept of mixing length, and subsequently (1935–1936) the statistical theory of turbulence. Richardson (1922) introduced the concept of energy cascade, which was followed by Kolmogorov (1941), who postulated that the statistics of small scales are isotropic and uniquely determined by the length scale, l, the kinematic viscosity, ν, and an average rate of kinetic energy dissipation per unit mass, ε. Kolmogorov subsequently presented a statistical approach of describing turbulence. Lorenz (1963) proposed a link between chaos and turbulence.
Hydraulic Flows: Overview
Published in Marian (Editor-in-Chief) Muste, Dennis A. Lyn, David M. Admiraal, Robert Ettema, Vladimir Nikora, Marcelo H. Garcia, Experimental Hydraulics: Methods, Instrumentation, Data Processing and Management, 2017
Marian (Editor-in-Chief) Muste, Dennis A. Lyn, David M. Admiraal, Robert Ettema, Vladimir Nikora, Marcelo H. Garcia
It is useful to briefly outline Kolmogorov’s theory as it combines testable statistical hypotheses with an insightful account of key physical mechanisms involved in turbulence dynamics. According to Kolmogorov (1941), a high-Reynolds number flow represents a combination of multi-scale eddies superimposed with the mean flow (in the Reynolds sense). The largest eddies are formed as a result of hydrodynamic instability of the mean flow and thus they receive energy directly from the mean flow. These eddies are scaled with the flow dimensions and thus can be represented with the external scale L. The largest eddies, in turn, are also unstable and form smaller eddies of size r and characteristic velocity u′r. This process of creation of smaller and smaller eddies continues until the eddy Reynolds number u′rr/ν becomes so small that further generation of finer eddies is blocked by viscosity. These smallest eddies, represented by the dissipative scale η, serve as the mechanism for the energy transfer from turbulent fluctuations into heat. Thus, Kolmogorov’s concept assumes that the energy supply to turbulence occurs through largest eddies of scale L, then the energy ‘cascades’ from larger to smaller eddies without dissipation or production until the eddy size becomes small enough for viscosity to overcome the inertia. This energy cascade concept provides a clear picture of energy fate in turbulence dynamics.
Employing power spectral density method for investigating atmospheric stability impacts on power generation of a wind farm
Published in Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 2021
Mahan Saberivahidaval, Abbas Ranjbar, Majid Azadi, Majid Jamil
Considering Kolmogorov theory, turbulence flow is made of various motions inside the main motion. These motions with distinct dimensions, frequencies and speeds are called eddies (Stull 2014). In a turbulent flow, energy is transferred from large eddies to smaller ones, through a process called turbulent energy cascade (Stull 2014). To investigate atmospheric turbulence characteristics, calculating a mathematical parameter called power spectral density or briefly PSD is a useful tool (Canadillas, Bégué, and Neumann 2010).