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

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 \ell(t). In this state the turbulent energy decays as \includegraphics{dummy.eps}. The correlation function is expressed as R(r, t)/R(0, t)≃1-0.73 r/\ell(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\{k\ell(t)\}^-2, A being constant, at large wave numbers.