EFFECT OF FINITE COMPUTATIONAL DOMAIN ON TURBULENCE SCALING LAW IN BOTH PHYSICAL AND SPECTRAL SPACES

The well-known translation between the power law of the energy spectru m and that of the correlation function or the second order structure f unction has been widely used in analyzing random data. Here, we show t hat the translation is valid only in proper scaling regimes. The regim es of valid translation are different for the correlation function and the structure function. Indeed, they do not overlap. Furthermore, in practice, the power laws exist only for a finite range of scales. We s how that this finite range makes the translation inexact even in the p roper scaling regime. The error depends on the scaling exponent. The c urrent findings are applicable to data analysis in fluid turbulence an d other stochastic systems. [S1063-651X(98)13911-9].