Energy-containing eddies

The scalar integral scale characterizes the largest structures in the scalar field, and is primarily determined by two processes (1) initial conditions - the scalar field can be initialized with a characteristic that is completely independent of the turbulence field, and (2) turbulent mixing - the energy-containing range of a turbulent flow will create scalar eddies with a characteristic length scale I.,p that is approximately equal to Lu. 

F or turbulent pipe flow, the friction velocity u = Vx ,/p used earlier in describing the universal turbulent velocity profile may be used as an estimate for V Together with the Blasius equation for the friction factor from which e may be obtained (Eq. 6-214), this provides an estimate for the energy-containing eddy size in turbulent pipe flow ... 

In order to complete the closure, the various length scales in the models above must be prescribed or related to the other independent variables through a differential equation. Daly and Harlow use a dynamical equation for S>, derived exactly from the Navier-Stokes equations and then closed by assumptions. The S) equation will be discussed presently. Daly and Harlow are now considering the use of two length-scale equations for the dissipating and energy-containing eddies. 

The wave number where viscous forces become very strong is of the same order as 1/tj. The wave number of the energy-containing eddies is of the same order as 1/4 if 4 the linear scale of the energy-containing eddies. 

Light transmittance values for times 0, t, and respectively Wave number Reaction rate constant Kolmogorofif wave number Wave number associated with the size of energy-containing eddies Constants... 

Reaction modulus, Eq. (108) Length of optical path Linear scale of energy-containing eddies Total number of drops present per unit volume of dispersion... 

A consistent theory of turbulent flow in horizontally homogeneous canopies has been developed over the last twenty five to thirty years. This theory asserts that the origin of the large energy-containing eddies that dominate canopy TKE and transport is an... 

The integral scales are those that correspond to the energy containing eddies, which also form the large (but not necessarily the largest) scales of the turbulent... 

This means that we can get an inviscid estimate for the dissipation rate from the large scale dynamics which do not involve viscosity. This implies that only a small fraction of the kinetic energy contained in the larger eddies is lost by direct viscous dissipation effects. 

This equation possesses production and dissipation terms that are similar to those in the kinetic energy transport equation, except that they are divided by the turbulence time scale of the energy containing eddies, Tf = K As for the fc-equation, the Rejmolds stresses are parameterized based on the eddy viscosity hypothesis. 

They required that the turbulence should be locally isotropic and steady, that the particle Reynolds number should be small, that the particles concentration was small, and that the particle diameter should be much smaller than the length scale of the energy containing eddies for the diffusion controlled range of the model. The model is based on the ability of the particle to respond to the motion of the surrounding fluid. It depends on particle size and density, turbulence structure of the fluid, and transversal particle concentration differences. 

To determine the energy contained in eddies of different scales, a distribution function of the kinetic energy for eddies in turbulent flows is required. A Maxwellian distribution function may be a natural and consistent choice as the eddy velocity is assumed to follow this distribution [66], but Luo and Svendsen [74] preferred an empirical energy-distribution density function for fluid particles in liquid developed by Angelidou et al [1[. The turbulent kinetic energy distribution of eddies with size A is approximated as follows ... 

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