Dynamical instability of a homoentropic rotating torus and an upper limit on the growth rate

Details Dynamical instability of a homoentropic rotating torus and an upper limit on the growth rate Dynamical instability of a homoentropic rotating torus and an upper limit on the growth rate

Dec 1986

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986mnras.223..859h&link_type=abstract

Monthly Notices of the Royal Astronomical Society (ISSN 0035-8711), vol. 223, Dec. 15, 1986, p. 859-865.

Astronomy and Astrophysics

Astrophysics

17

Angular Momentum, Astrophysics, Dynamic Stability, Entropy, Rotating Bodies, Toruses, Eigenvalues, Gravitational Effects, Kelvin-Helmholtz Instability, Perturbation Theory, Rotating Plasmas

Scientific paper

The dynamical stability of a rotating homoentropic torus is investigated in the present paper. A necessary condition for instability is obtained for arbitrary angular momentum distributions. As a result, a rigidly rotating torus is proved to be stable. In other words, when the angular velocity is not constant, dynamically unstable modes can exist. Also, an upper limit on the growth rate is derived from the necessary condition for instability. The growth rate should be less than the maximum of (r/2) d(Omega)/dr, where Omega and r are the angular velocity and the radial distance, respectively. In this sense, this instability is identified with the shear (Kelvin-Helmholtz) instability. Also, the eigenfunctions of the unstable modes are restricted by the necessary condition for instability. In general, the perturbation can grow only when the azimuthal wavelength is shorter than or comparable with the vertical height of the torus. In other words, when the azimuthal wavelength is short enough, the perturbation can be unstable in all types of torus except the rigidly rotating one.

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