Expanding self-similar discontinuities and shock waves in dispersive hydrodynamics
Abstract
Nonlinear flows in nondissipative dispersive hydrodynamics are investigated theoretically. It is shown that, in order to describe flows of this type, a special 'self-similar' discontinuity must be introduced which is a nondissipative shock wave and can replace the strong discontinuity used in conventional hydrodynamics. The self-similar discontinuity expands linearly with time. It is shown that the self-similar discontinuity can be introduced into the solutions to the Euler equations. The conditions obtained for the boundary of the self-similar discontinuity permit the closure of the Euler equations. A classification of arbitrary initial discontinuities in the hydrodynamics of a strongly nonisothermal plasma is presented based on the closed solution to the Euler equations.
- Publication:
-
Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki
- Pub Date:
- October 1984
- Bibcode:
- 1984ZhETF..87.1277G
- Keywords:
-
- Magnetoplasmadynamics;
- Nonlinear Systems;
- Shock Wave Propagation;
- Wave Dispersion;
- Asymptotic Methods;
- Flow Equations;
- Nonisothermal Processes;
- One Dimensional Flow;
- Plasma Waves;
- Shock Discontinuity;
- Fluid Mechanics and Heat Transfer