Turbulent kinetic energy definition

By definition, the turbulent kinetic energy k can be found directly from the turbulent energy spectrum by integrating over wavenumber space ... 

From this definition, it can be observed that T,(k. t) is the net rate at which turbulent kinetic energy is transferred from wavenumbers less than k to wavenumbers greater than k. In fully developed turbulent flow, the net flux of turbulent kinetic energy is from large to small scales. Thus, the stationary spectral energy transfer rate Tu(k) will be positive at spectral equilibrium. Moreover, by definition of the inertial range, the net rate of transfer through wavenumbers /cei and kdi will be identical in a fully developed turbulent flow, and thus... 

As an example, for steady, incompressible, and isothermal turbulent flows using the k- model, the independent equations are (1) the continuity equation, Eq. (5.61) (2) the momentum equation, Eq. (5.65) (3) the definition of the effective viscosity, /xeff (combination of Eq. (5.64) and Eq. (5.72)) (4) the equation of turbulent kinetic energy, Eq. (5.75) and (5) the equation for the dissipation rate of turbulent kinetic energy, Eq. (5.80). Thus, for a three-dimensional model, the total number of independent equations is seven. The corresponding independent variables are (1) velocity (three components) (2) pressure (3) effective viscosity (4) turbulent kinetic energy and (5) dissipation rate of turbulent kinetic energy. Thus, the total number of independent variables is also seven, and the model becomes solvable. 

This form is appealing because the first term in F.-,/2 can be interpreted as a gradient diffusion of turbulent kinetic energy, and the second is negative-definite (suggestive of dissipation of turbulence energy). However, the rate of entropy production is proportional to... 

By definition the turbulent kinetic energy per unit mass is one half of the variance v. Therefore, if we sum over i, then (1.395) gives us the balance equation for the turbulent kinetic energy, k, per unit fluid mass, which is defined by ... 

Since m 2 is proportional to the total turbulent kinetic energy, the total energy of the turbulence is important in the early dispersion. After long times the largest eddies will contribute to Ru and Ru will not go to zero until the particle can escape the influence of the largest eddies. From its definition, K,j has the dimensions of a diffusivity, since as t —> oo... 

This function, which is simply the area under the/( ) curve up to a given value of n, shows what fraction of the turbulent kinetic energy is contained in oscillations of lower frequency. By definition, the value of F n) must approach 1 as n becomes very large. 

The Newtonian turbulent kinetic energy results of this calculation compare favorably with that of Hassid and Poreh s (15) in a circular tube. Also, Laufers (26) measured results in a large square duct agree fairly well with these predictions as shown by square data points in Fig. 8. A definite increase in k is observed for flows with drag reduction. However, measurements of turbulent kinetic energy in flows with drag reduction are... 

For short circuit of system of the equations the two-parametric model of turbulence to—e, as one of the most well-proved models for calculation of currents, such is used. At turbulence modeling, it was used toe model, for it dares two additional transport equations for the purpose of definition to turbulent kinetic energy and eturbulent energy of a dissipation. 

We have seen in Chapters 2 and 4 that turbulence dramatically strengtherrs the dissipation of kinetic energy. This property results from the definition of the instantaneous rate of kinetic energy dissipation per unit volume ... 

The definition of kinetic energy per unit volume is pv /2, whereas the kinetic energy per unit mass is just v /2. It is common to partition the kinetic energy of the flow into a portion associated with the mean velocity, v /2, and a portion associated with the turbulence, v /2. We can thus write the relations ... 

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