Large-Scale Dynamics in Burgers Equation

(Received 14 May 1996, received in final form 14 August 1996, accepted 27 August 1996)

Abstract
The problem of turbulent transport in Burgers equation is discussed. Both the vertex and the eddy-viscosity appearing in the renormalized equation governing the dynamics of the large scales are determined analytically for time-independent flow. It is shown that the effect of such static small-scale flow is to deplete transport and that the resulting large-scale renormalization can be absorbed into a simple rescaling of the time variable. The analytical predictions are compared with the results of direct numerical simulations, using a dimension-doubling method optimized for situations with widely separated scales.