Abstract

A More Precise Equation for Sound Beams in Dissipative Fluids. Effect Shock-Shocks

I.Molotkov (Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation, IZMIRAN, Moscow Region, Troitsk, Russia); B.O.Enflo (Department of Mechanics, Royal Institute of Technology, Stockholm, Sweden)

e-mail: molotkov@izmiran.rssi.ru

The well known scalar nonlinear acoustic wave (SNAW) equation is based on the fundamental hydrodynamic equations for viscous and heat conducting fluids. It is possible from the SNAW equation to derive in leading order the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation for description of bounded sound beams in dissipative fluids. One can obtain from the SNAW equation an equation more precise than the KZK equation. Namely, for the two-dimensional beams it is possible to derive a KZK equation with five additional correct terms. One of the mentioned terms has a particular interest. It describes an important effect of the transversal self-action of the beam. An explicit solution of the KZK equation with this term is obtained. That solution depends on the evolution coordinate and two parameters-the width of the beam and a phase variable. Critical values of the parameters are found, at which the formation of a secondary transversal shock wave starts (shock-shocks effect ). In the evolution process the initial pulse with maximal intensity in the beam center is transformed into a pulse with maximal amplitude on its boundaries. The authors are indebted to Prof. O.V.Rudenko for very fruitful discussions.

Section : 1