Application of Kraichnan’s decimated-amplitude scheme to the Betchov model of turbulence

Abstract
The decimated-amplitude scheme (DAS) devised by Kraichnan is applied to a random-coupling model of turbulence originally introduced by Betchov to test the direct-interaction approximation (DIA). Using a system of 32 variables, forced stochastically under appropriate statistical constraints, it is shown that the DAS can accurately represent the autocorrelation function of a full Betchov system of 96 variables. A comparison is also made between the DAS and the DIA.