##
**The stability of long, steady, two-dimensional salt fingers.**
*(English)*
Zbl 0588.76069

From author’s summary: In this paper we study the stability of long steady, two-dimensional salt fingers. It is already known that salt fingers carrying a large enough density flux are unstable to long- wavelength internal-wave perturbations (collective instability). We extend the earlier work [the author, ibid. 110, 195-207 (1981; Zbl 0484.76057)] to include perturbations of all wavelengths. By applying the methods of Floquet theory to the periodic salt fingers, the growth rates of perturbations are found. For both heat-salt and salt-sugar systems the collective instability, which can be recognized by its frequency of oscillation, does not have the largest growth rate. There is a new, non- oscillatory instability, which, according to linear theory, grows faster than the collective instability. We study the instabilities that arise by using a combination of analytical and numerical methods.

Reviewer: M.Boudourides

### MSC:

76E15 | Absolute and convective instability and stability in hydrodynamic stability |

76R10 | Free convection |

### Keywords:

heat-salt systems; stability; long steady, two-dimensional salt fingers; long-wavelength internal-wave perturbations; collective instability; methods of Floquet theory; periodic salt fingers; growth rates of perturbations; salt-sugar systems; frequency of oscillation; non- oscillatory instability; combination of analytical and numerical methods### Citations:

Zbl 0484.76057
Full Text:
DOI

### References:

[1] | DOI: 10.1017/S0022112080000511 |

[2] | Drazin, Proc. R. Soc. Lond. A 356 pp 411– (1977) |

[3] | Chen, J. Fluid Mech. 138 pp 405– (1984) |

[4] | Beaumont, J. Fluid Mech. 108 pp 461– (1981) |

[5] | Williams, Science 185 pp 941– (1974) |

[6] | DOI: 10.1016/0146-6313(56)90095-8 |

[7] | Stern, Deep-Sea Res. 16 pp 497– (1969) |

[8] | DOI: 10.1017/S0022112069001066 · Zbl 0164.28802 |

[9] | Stern, Tellus 12 pp 172– (1960) |

[10] | Schmitt, J. Mar. Res. 37 pp 419– (1979) |

[11] | Schmitt, J. Mar. Res. 40 pp 659– (1982) |

[12] | Linden, Deep-Sea Res. 20 pp 325– (1973) |

[13] | DOI: 10.1017/S0022112072000916 |

[14] | Huppert, J. Fluid Mech. 106 pp 299– (1981) |

[15] | Holyer, J. Fluid Mech. 110 pp 195– (1981) |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.