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53) is the first important parameter. 5. Kolmogorov assumed that the velocity fluctuations are both isotropic and homogeneous in the inertial range. His assumption makes sense because the fluctuations are well removed from the mechanism which generated the turbulence. 56) to describe the structure function. These eddies are also far from the dissipation mechanism which removes energy since the inertial range is characterized solely by interactions among the turbulent eddies. Only redistribution of energy among eddy sizes should be important.

The random medium can often be considered to be homogeneous over the small sensor separations usually employed in terrestrial measurements. This means that statistical averages of ∆ε do not depend on position. In other words, one should measure the same covariance if the two sensors are translated together to any other position in the region. 30) In a sense, homogeneity of the random medium is the spatial analogy of the stationarity of δε(t). We will discover a connection of these characteristics in Chapter 6 when we introduce Taylor’s hypothesis to describe temporal changes of the irregularities.

63 for humidity. These relationships mean that the random velocity and the passivescalar fluctuations are attenuated by viscosity before diffusion starts to destroy the eddies. For scalar advection Batchelor showed that the inertial-range spectrum 11 changes from κ− 3 to κ−3 in the range where ν becomes important but diffusion has not yet exerted control [18]. This milder decline implies a rise in the dissipation factor F(κη) and is confirmed by careful measurements. The rise in F(κη) is cut down by diffusion soon after it begins because ν and D are nearly the same in air.

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A Computer Simulation Of An Induction Heating System - Magnetics, Ieee Transactions On

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