Self-similar Solutions of Barenblatt’s Model for Turbulence*
نویسنده
چکیده
In this paper, we consider Barenblatt’s k– model for turbulence. For the case of equal diffusion coefficients α and β, Barenblatt found explicit compactly supported self-similar solutions. From these, we obtain compactly supported solutions for α 6= β by transforming the equations into a four-dimensional quadratic system and verifying a transversality condition for a saddle-point connection. This involves the Poincaré transformation as well as classical properties of the hypergeometric equation and its solutions.
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