Application of Padé Approximation to Turbulence Problem
Abstract
The energy spectrum function E(k, t) for one dimensional Burgers’ turbulence is defined as a Taylor series expansion in time variable t. Assuming a multivariate Gaussian distribution of velocity field at an initial instant, first six coefficients of this Taylor series are calculated explicitly in terms of the initial energy spectrum. To approximate to E(k, t) the Padé approximation is adopted. The numerical results show that a Padé approximant to it is much better than a partial sum of Taylor series as an approximation to E(k, t) for the wave numbers not so large compared with a representative wave number.
 Publication:

Journal of the Physical Society of Japan
 Pub Date:
 May 1983
 DOI:
 10.1143/JPSJ.52.1593
 Bibcode:
 1983JPSJ...52.1593F
 Keywords:

 Flow Theory;
 Pade Approximation;
 Turbulent Flow;
 Boundary Value Problems;
 Burger Equation;
 Energy Spectra;
 Series Expansion;
 Taylor Series;
 Fluid Mechanics and Heat Transfer