Clustering of the resonant triads induced by vertical-shear instability in astrophysical discs

Clustering of resonant triads that are induced by vertical-shear instability (VSI), driven by the combined effect of the vertical speed shear and small temperature gradients, is studied for vertically isothermal thin unmagnetized Keplerian discs. The authors' recent study of isolated VSI resonant triads is extended to illustrate their clustering. The coupling conditions for two VSI resonant triads with one common mode are derived and generalized to higher dimension clustering. The clustering of two, three, and four triads connected via one common mode is numerically simulated. The numerical simulations demonstrate the chaotization of non-linear oscillations about the prototypes of the linearly stable modes with a growing cluster's dimension that is accompanied by a decrease of the characteristic time of chaotization and an increase of the characteristic frequency of perturbations. The chaos associated with the VSI resonant clustering is believed to precede transition to sustainable turbulence in astrophysical discs.