Vertical shear-induced resonant triads in Keplerian discs

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Abstract

The vertical-shear instability (VSI) is studied through weakly non-linear analysis of unmagnetized vertically isothermal thin Keplerian discs under small radial temperature gradients. Vertically global and radially local axisymmetric compressible perturbations are considered. The VSI excites three classes of quasi-resonant triads of non-linearly interacting modes characterized by distinct temporal evolution. Most of the triads belong to the two-mode regime of non-linear interaction. Such triads are comprised of one unstable non-linear mode that grows quasi-exponentially, and two other modes that practically decoupled from the former. The latter two modes perform non-linear oscillations around their either linear prototypes (class I) or respective initial values (class II). The rest of the resonant triads belong to class III where all three modes exhibit non-linear oscillations. The proposed model describes an intermediate non-linear stage of the VSI prior to its saturation.

Original languageEnglish
Pages (from-to)4207-4219
Number of pages13
JournalMonthly Notices of the Royal Astronomical Society
Volume488
Issue number3
DOIs
StatePublished - 21 Sep 2019

Keywords

  • Accretion, accretion discs
  • Hydrodynamics
  • Instabilities
  • Planetary systems
  • Protoplanetary discs

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