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• W2001262550 abstract "A model analytical description of the density field advected in a velocity field governed by the multidimensional Burgers equation is suggested. This model field satisfies the mass conservation law and, in the zero viscosity limit, coincides with the generalized solution of the continuity equation. A numerical and analytical study of the evolution of such a model density field is much more convenient than the standard method of simulation of transport of passive tracer particles in the fluid. In the 1-dimensional case, a more general Korteweg–de Vries (KdV)–Burgers equation is suggested as a model which permits an analytical treatment of the density field in a strongly nonlinear model of compressible gas which takes into account dissipative and dispersive effects as well as pressure forces, the former not being accounted for in the 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) situation of small viscosity, we can follow the creation and evolution of the cellular structures in the density field and the subsequent creation of the “quasi-particle” clusters of matter of enormous density. In addition, it is shown that in the zero viscosity limit, the density field spectrum has a power tail $alpha k^{ - n} $, with different exponents in different regimes." @default.
• W2001262550 created "2016-06-24" @default.
• W2001262550 creator A5019474939 @default.
• W2001262550 creator A5062011807 @default.
• W2001262550 date "1996-08-01" @default.
• W2001262550 modified "2023-09-26" @default.
• W2001262550 title "Density Fields in Burgers and KdV–Burgers Turbulence" @default.
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• W2001262550 doi "https://doi.org/10.1137/s0036139994266475" @default.
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