ИСТИНА

The lecture examines an example of non-standard hydrodynamics. In existing Today, the methods of calculating turbulence assume the fulfillment of the purely mathematical Godunov-Lax condition on the existence of a complete basis of eigenvectors on a critical manifold of multiple roots (symmetrization of the system). Under this assumption, for the Riemann problem on the decay of a discontinuity, the Maida theorem implies the existence for any two points of the phase space of a unique chain of stable shock waves, rarefaction waves, and contact discontinuities. At the same time it is well known from the experiment (Landau, Prigogine, Richardson ....) about the occurrence of a two-speed regime in the initial stage of turbulence (that is, the bifurcation of a stable shock wave), which contradicts Maida's theorem. With the possible mechanism of the occurrence of a two-speed regime (called the Prigogine Riemann-Hugoniot catastrophe), which leads to a violation of the Godunov-Lax condition, the example studied in the lecture is related. To modify the system of shallow water equations (a system for a two-component mixture), the existence of nonclassical (two-dimensional) Waves in the Riemann problem.