A Numerical Study of the Burgers Turbulence at Extremely Large Reynolds Numbers

Abstract

The Burgers turbulence at extremely large Reynolds numbers expressed as a train of random triangular shocks is investigated by calculating its temporal development numerically. As a result it is found that the train of random triangular shocks settles down to a similarity state determined by the mean interval between two consecutive shock fronts l(t). In this state the turbulent energy decays as (Remark: Graphics omitted.). The correlation function is expressed as R(r, t)⁄R(0, t)\simeq1−0.73r⁄l(t) for small r and vanishes for large r, remaining positive. The energy spectrum E(k, t) is approximately conserved in time at small wave numbers and constant with respect to k, and E(k, t)=A{kl(t)}⁻², A being constant, at large wave numbers.