PDFS FOR VELOCITY AND VELOCITY-GRADIENTS IN BURGERS TURBULENCE

We characterize the tails of the probability distribution functions fo r the solution of Burgers' equation with Gaussian initial data and its derivatives partial derivative(k) upsilon(X,t)/partial derivative X(k ), k=0,1,2,.... The tails are ''stretched exponentials'' of the form P (theta)proportional to exp[-(Re)(-p)t(q) theta(r)], where Re is the Re ynolds number. The exponents p, q, and r depend on the initial spectru m as well as on the order of differentiation, k. These exact results a re compared with those obtained using the mapping closure technique. ( C) 1995 American Institute of Physics.