Special class of solutions of the kinetic equation of a bubbly fluid

A new class of solutions is constructed for the kinetic model of bubble motion in a perfect fluid proposed by Russo and Smereka. These solutions are characterized by a linear relationship between the Riemann integral invariants. Using the expressions following from this relationship, the construction of solutions in the special class is reduced to the integration of a hyperbolic system of two differential equations with two independent variables. Exact solutions in the class of simple waves are obtained, and their physical interpretation is given.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 2, pp. 33–43, March–April, 2005.