INERTIAL RANGE STATISTICS OF BURGERS TURBULENCE

Velocity structure function of Burgers turbulence in the inertial range is studied by mapping closure. It is shown that in the inertial range 〈|u(x+l,t)-u(x,t)|q〈=n(t)〉|Δu(t)| q〉|l| and the spectrum E(k,t) = (1/2π)n(t)〈|Δu(t) |2〉k-2 for initially support broad spectrum, where n(t) is the average of the number density of shocks and 〈|Δu(t)| q〉 is qth moment of shock strength. Agreement with DNS is found to be good for initially Gaussian fields. Statistics at large time is also studied by the mapping closure using time dependent reference field. It is found that the length scale of the field and the decay law of the total kinetic energy are self-similar in time and various quantities are given as functions of the exponent n of the initial energy spectrum E(k,0) ∝ kn at low wave-number range. Extension to more general initial conditions with non-Gaussian statistics is also discussed. © 1994 American Institute of Physics.