The relationship between a WienerHermite expansion and an energy cascade
Abstract
A theory of Burgers turbulence involving a truncated WienerHermite expansion of the velocity field is described. Numerical analysis shows that the theory predicts an insufficient rate of energy decay for Reynolds numbers larger than two. It is shown that an energy cascade in wave number space corresponds to a cascade of energy up through successive terms of the WienerHermite expansion. Results indicate that Gaussianity has no bearing on the rate of convergence of an expansion whose white noise function is associated with the initial state.
 Publication:

In Von Karman Inst. for Fluid Dyn. Statistical Theory of Turbulence 45 p (SEE N7928458 1934
 Pub Date:
 1970
 Bibcode:
 1970stt..vkifQ....C
 Keywords:

 Hermitian Polynomial;
 Turbulent Flow;
 Velocity Distribution;
 White Noise;
 Wiener Hopf Equations;
 Approximation;
 Burger Equation;
 Differential Equations;
 Energy Dissipation;
 Energy Spectra;
 Energy Transfer;
 Kernel Functions;
 Numerical Analysis;
 Random Noise;
 Shock Waves;
 Fluid Mechanics and Heat Transfer