INTERFACE GROWTH AND BURGERS TURBULENCE - THE PROBLEM OF RANDOM INITIAL CONDITIONS

We study the relaxational dynamics of the deterministic Burgers equati on, with random initial conditions, in an arbitrary spatial dimension d. In this paper we concentrate mainly on initial distributions releva nt to interface growth rather than Burgers turbulence (although we sha ll present results for this system in d = 1). By using an analytic app roach, we are able to calculate both the short- and long-time forms fo r the kinetic energy of the fluid (or equivalently the roughness of th e interface.) We find exponents describing the early-time behavior of the system.