DENSITY FIELDS IN BURGERS AND KDV-BURGERS TURBULENCE

A model analytical description of the density field advected in a velo city field governed Gy the multidimensional Burgers equation is sugges ted. This model field satisfies the mass conservation law and, in the zero viscosity limit, coincides with the generalized solution of the c ontinuity equation. A numerical and analytical study of the evolution of such a model density field is much more convenient than the standar d method of simulation of transport of passive tracer particles in the fluid. In the 1-dimensional case, a more general Korteweg-deVries (Kd V)-Burgers equation is suggested as a model which permits an analytica l treatment of the density held in a strongly nonlinear model of compr essible gas which takes into account dissipative and dispersive effect s as well as pressure forces, the former not being accounted for in th e standard Burgers framework. The dynamical and statistical properties of the density field are studied. In particular, utilizing the above model in the 2-dimensional case and the (most interesting for us) situ ation of small viscosity, we can follow the creation and evolution of the cellular structures in the density field and the subsequent creati on of the ''quasi-particle'' clusters of matter of enormous density. I n addition, it is shown that in the zero viscosity limit, the density field spectrum has a power tail proportional to k(-n), with different exponents in different regimes.