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- W2024296073 abstract "An exact equation is obtained which relates the products of two-point differences of a scalar quantity and those differences with the difference of velocity and other quantities. The averages of such products are structure functions. Equations that follow from the scalar equation but with no other approximations are called “exact” here. Exact equations for structure functions are obtained. Ensemble, temporal, and spatial averages are all considered because each one produces different statistical equations from the others and because they differ in application to theoretical purposes, experiment, and numerical simulation of turbulence. The midpoint and the difference of the two points at which the hydrodynamic quantities are obtained are X and r, respectively. Use of X and r as independent variables combined with Reynolds decomposition reveals quantifiable effects of inhomogeneity and large-scale structures. Exact equations obtained by averaging over a sphere in r space have a particularly simple form. The case of a numerical simulation that has periodic boundary conditions leads to particularly simple equations. For the case of grid-generated wind-tunnel turbulence, approximate equations are derived relating structure functions of fluctuations. Applications of the equations to experiments and direct numerical simulation are discussed." @default.
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- W2024296073 date "2002-04-05" @default.
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- W2024296073 title "Structure-function equations for scalars" @default.
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