# Nonlinear dynamics of magnetohydrodynamic flows of a heavy fluid in the shallow water approximation

## Abstract

The system of the magnetohydrodynamic equations for a heavy fluid has been analyzed in the shallow water approximation. All discontinuous self-similar solutions and all continuous centered self-similar solutions have been found. It has been shown that magnetogravity compression waves are broken with the formation of a magnetogravity shock wave. The initial decay discontinuity problem for the magnetohydrodynamic equations has been solved in the explicit form in the shallow water approximation. The existence of five different configurations implementing the solution of the decay of an arbitrary discontinuity has been demonstrated. The conditions necessary and sufficient for the implementation of each configuration have been found.

- Authors:

- Russian Academy of Sciences, Space Research Institute (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22028013

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Experimental and Theoretical Physics

- Additional Journal Information:
- Journal Volume: 113; Journal Issue: 3; Other Information: Copyright (c) 2011 Pleiades Publishing, Ltd.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1063-7761

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; APPROXIMATIONS; COMPRESSION; DIFFERENTIAL EQUATIONS; FLUID FLOW; FLUIDS; MAGNETOHYDRODYNAMICS; MATHEMATICAL SOLUTIONS; NONLINEAR PROBLEMS; SHOCK WAVES

### Citation Formats

```
Karelsky, K. V., Petrosyan, A. S., E-mail: apetrosy@iki.rssi.ru, and Tarasevich, S. V., E-mail: aprilfire.ru@gmail.com.
```*Nonlinear dynamics of magnetohydrodynamic flows of a heavy fluid in the shallow water approximation*. United States: N. p., 2011.
Web. doi:10.1134/S106377611107003X.

```
Karelsky, K. V., Petrosyan, A. S., E-mail: apetrosy@iki.rssi.ru, & Tarasevich, S. V., E-mail: aprilfire.ru@gmail.com.
```*Nonlinear dynamics of magnetohydrodynamic flows of a heavy fluid in the shallow water approximation*. United States. doi:10.1134/S106377611107003X.

```
Karelsky, K. V., Petrosyan, A. S., E-mail: apetrosy@iki.rssi.ru, and Tarasevich, S. V., E-mail: aprilfire.ru@gmail.com. Thu .
"Nonlinear dynamics of magnetohydrodynamic flows of a heavy fluid in the shallow water approximation". United States. doi:10.1134/S106377611107003X.
```

```
@article{osti_22028013,
```

title = {Nonlinear dynamics of magnetohydrodynamic flows of a heavy fluid in the shallow water approximation},

author = {Karelsky, K. V. and Petrosyan, A. S., E-mail: apetrosy@iki.rssi.ru and Tarasevich, S. V., E-mail: aprilfire.ru@gmail.com},

abstractNote = {The system of the magnetohydrodynamic equations for a heavy fluid has been analyzed in the shallow water approximation. All discontinuous self-similar solutions and all continuous centered self-similar solutions have been found. It has been shown that magnetogravity compression waves are broken with the formation of a magnetogravity shock wave. The initial decay discontinuity problem for the magnetohydrodynamic equations has been solved in the explicit form in the shallow water approximation. The existence of five different configurations implementing the solution of the decay of an arbitrary discontinuity has been demonstrated. The conditions necessary and sufficient for the implementation of each configuration have been found.},

doi = {10.1134/S106377611107003X},

journal = {Journal of Experimental and Theoretical Physics},

issn = {1063-7761},

number = 3,

volume = 113,

place = {United States},

year = {2011},

month = {9}

}