# Overstability of acoustic waves in strongly magnetized anisotropic magnetohydrodynamic shear flows

## Abstract

We present a linear stability analysis of the perturbation modes in anisotropic magnetohydrodynamic (MHD) flows with velocity shear and strong magnetic field. Collisionless or weakly collisional plasma is described within the 16-momentum MHD fluid closure model that takes into account not only the effect of pressure anisotropy but also the effect of anisotropic heat fluxes. In this model, the low frequency acoustic wave is revealed into a standard acoustic mode and higher frequency fast thermo-acoustic and lower frequency slow thermo-acoustic waves. It is shown that thermo-acoustic waves become unstable and grow exponentially when the heat flux parameter exceeds some critical value. It seems that velocity shear makes thermo-acoustic waves overstable even at subcritical heat flux parameters. Thus, when the effect of heat fluxes is not profound acoustic waves will grow due to the velocity shear, while at supercritical heat fluxes the flow reveals compressible thermal instability. Anisotropic thermal instability should be also important in astrophysical environments, where it will limit the maximal value of magnetic field that a low density ionized anisotropic flow can sustain.

- Authors:

- Abastumani Astrophysical Observatory, Ilia State University, Tbilisi, Georgia (United States)
- (United States)
- Institut für Theoretische Physik IV: Weltraum- und Astrophysik, Ruhr-Universitat Bochum, 44780 Bochum (Germany)
- (Belgium)
- Faculty of Exact and Natural Sciences, Javakhishvili Tbilisi State University, 3 Chavchavadze Ave., Tbilisi 0179, Georgia (United States)
- Centre for Mathematical Plasma Astrophysics, Department of Mathematics, KU Leuven, Celestijnenlaan 200B, 3001 Leuven (Belgium)
- (LMCC), KU Leuven, Celestijnenlaan 200B, 3001 Leuven (Belgium)

- Publication Date:

- OSTI Identifier:
- 22303787

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Plasmas; Journal Volume: 21; Journal Issue: 8; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ANISOTROPY; ASTROPHYSICS; COLLISIONAL PLASMA; HEAT FLUX; MAGNETIC FIELDS; MAGNETOHYDRODYNAMICS; SHEAR; SOUND WAVES

### Citation Formats

```
Uchava, E. S., Nodia Institute of Geophysics, Javakhishvili Tbilisi State University, Tbilisi, Georgia, Faculty of Exact and Natural Sciences, Javakhishvili Tbilisi State University, 3 Chavchavadze Ave., Tbilisi 0179, Georgia, Shergelashvili, B. M., Abastumani Astrophysical Observatory, Ilia State University, Tbilisi, Georgia, CODeS, KU Leuven Campus Kortrijk, E. Sabbelaan 53, 8500 Kortrijk, Tevzadze, A. G., Poedts, S., and Leuven Mathematical Modeling and Computational Science Center.
```*Overstability of acoustic waves in strongly magnetized anisotropic magnetohydrodynamic shear flows*. United States: N. p., 2014.
Web. doi:10.1063/1.4892402.

```
Uchava, E. S., Nodia Institute of Geophysics, Javakhishvili Tbilisi State University, Tbilisi, Georgia, Faculty of Exact and Natural Sciences, Javakhishvili Tbilisi State University, 3 Chavchavadze Ave., Tbilisi 0179, Georgia, Shergelashvili, B. M., Abastumani Astrophysical Observatory, Ilia State University, Tbilisi, Georgia, CODeS, KU Leuven Campus Kortrijk, E. Sabbelaan 53, 8500 Kortrijk, Tevzadze, A. G., Poedts, S., & Leuven Mathematical Modeling and Computational Science Center.
```*Overstability of acoustic waves in strongly magnetized anisotropic magnetohydrodynamic shear flows*. United States. doi:10.1063/1.4892402.

```
Uchava, E. S., Nodia Institute of Geophysics, Javakhishvili Tbilisi State University, Tbilisi, Georgia, Faculty of Exact and Natural Sciences, Javakhishvili Tbilisi State University, 3 Chavchavadze Ave., Tbilisi 0179, Georgia, Shergelashvili, B. M., Abastumani Astrophysical Observatory, Ilia State University, Tbilisi, Georgia, CODeS, KU Leuven Campus Kortrijk, E. Sabbelaan 53, 8500 Kortrijk, Tevzadze, A. G., Poedts, S., and Leuven Mathematical Modeling and Computational Science Center. Fri .
"Overstability of acoustic waves in strongly magnetized anisotropic magnetohydrodynamic shear flows". United States.
doi:10.1063/1.4892402.
```

```
@article{osti_22303787,
```

title = {Overstability of acoustic waves in strongly magnetized anisotropic magnetohydrodynamic shear flows},

author = {Uchava, E. S. and Nodia Institute of Geophysics, Javakhishvili Tbilisi State University, Tbilisi, Georgia and Faculty of Exact and Natural Sciences, Javakhishvili Tbilisi State University, 3 Chavchavadze Ave., Tbilisi 0179, Georgia and Shergelashvili, B. M. and Abastumani Astrophysical Observatory, Ilia State University, Tbilisi, Georgia and CODeS, KU Leuven Campus Kortrijk, E. Sabbelaan 53, 8500 Kortrijk and Tevzadze, A. G. and Poedts, S. and Leuven Mathematical Modeling and Computational Science Center},

abstractNote = {We present a linear stability analysis of the perturbation modes in anisotropic magnetohydrodynamic (MHD) flows with velocity shear and strong magnetic field. Collisionless or weakly collisional plasma is described within the 16-momentum MHD fluid closure model that takes into account not only the effect of pressure anisotropy but also the effect of anisotropic heat fluxes. In this model, the low frequency acoustic wave is revealed into a standard acoustic mode and higher frequency fast thermo-acoustic and lower frequency slow thermo-acoustic waves. It is shown that thermo-acoustic waves become unstable and grow exponentially when the heat flux parameter exceeds some critical value. It seems that velocity shear makes thermo-acoustic waves overstable even at subcritical heat flux parameters. Thus, when the effect of heat fluxes is not profound acoustic waves will grow due to the velocity shear, while at supercritical heat fluxes the flow reveals compressible thermal instability. Anisotropic thermal instability should be also important in astrophysical environments, where it will limit the maximal value of magnetic field that a low density ionized anisotropic flow can sustain.},

doi = {10.1063/1.4892402},

journal = {Physics of Plasmas},

number = 8,

volume = 21,

place = {United States},

year = {Fri Aug 15 00:00:00 EDT 2014},

month = {Fri Aug 15 00:00:00 EDT 2014}

}