On the edge of subcritical baroclinic instability in a local model of accretion disc
Abstract
Anticyclonic vortices are promising sites for planetesimal formation in the dead zones of protoplanetary discs. The subcritical baroclinic instability (SBI) can amplify and sustain such vortices, but requires a seed perturbation of sufficient amplitude, a threshold that has so far only been probed empirically. We characterise the boundary separating the laminar Keplerian basin of attraction from the self-sustained vortical one by applying an edge-tracking (bisection) algorithm to the two-dimensional Boussinesq shearing sheet, over an extensive grid of Reynolds, Péclet, and Richardson numbers. At all explored parameters, the computed edge state is a streamwise-elongated anticyclone satisfying the Kida vorticity/aspect-ratio relation, associated with a thermal dipole tilted away from the background entropy gradient by a diffusion-controlled angle. We construct a predictive model of the edge state, in which a marginal enstrophy balance combining the Kida relation with shear-enhanced thermal relaxation yields closed-form power laws for the critical vorticity and radial width of the seed as functions of the flow parameters, in quantitative agreement with the numerical scalings. The edge-state framework thus provides a possible predictive criterion applicable to candidate vortical seeds in protoplanetary discs.
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BibTeX
@misc{marcotte2026edge,
title = {{On the edge of subcritical baroclinic instability in a local model of accretion disc}},
author = {Florence Marcotte and Yannick Ponty},
howpublished = {HAL},
year = {2026},
month = sep,
url = {https://hal.science/hal-05751296v1},
note = {CC BY-NC 4.0},
}
RIS
TY - UNPB
TI - On the edge of subcritical baroclinic instability in a local model of accretion disc
AU - Florence Marcotte
AU - Yannick Ponty
PY - 2026
DA - 2026/09/15
PB - HAL
UR - https://hal.science/hal-05751296v1
AB - Anticyclonic vortices are promising sites for planetesimal formation in the dead zones of protoplanetary discs. The subcritical baroclinic instability (SBI) can amplify and sustain such vortices, but requires a seed perturbation of sufficient amplitude, a threshold that has so far only been probed empirically. We characterise the boundary separating the laminar Keplerian basin of attraction from the self-sustained vortical one by applying an edge-tracking (bisection) algorithm to the two-dimensional Boussinesq shearing sheet, over an extensive grid of Reynolds, Péclet, and Richardson numbers. At all explored parameters, the computed edge state is a streamwise-elongated anticyclone satisfying the Kida vorticity/aspect-ratio relation, associated with a thermal dipole tilted away from the background entropy gradient by a diffusion-controlled angle. We construct a predictive model of the edge state, in which a marginal enstrophy balance combining the Kida relation with shear-enhanced thermal relaxation yields closed-form power laws for the critical vorticity and radial width of the seed as functions of the flow parameters, in quantitative agreement with the numerical scalings. The edge-state framework thus provides a possible predictive criterion applicable to candidate vortical seeds in protoplanetary discs.
ER -