We study the relaxational dynamics of the deterministic Burgers equation, with random initial conditions, in an arbitrary spatial dimension d. In this paper we concentrate mainly on initial distributions relevant to interface growth rather than Burgers turbulence (although we shall present results for this system in d=1). By using an analytic approach, we are able to calculate both the short- and long-time forms for the kinetic energy of the fluid (or equivalently the roughness of the interface.) We find exponents describing the early-time behavior of the system.
|Number of pages||5|
|Journal||Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics|
|Publication status||Published - Aug 1993|