Effects of upper disc boundary conditions on the linear Rossby wave instability

TL;DR

This study investigates how different upper boundary conditions in 3D polytropic discs influence the linear Rossby wave instability, revealing that boundary conditions opposing vertical motion slightly enhance instability growth and that RWI is fundamentally two-dimensional.

Contribution

The paper introduces a simplified numerical method to analyze RWI in 3D discs and examines the impact of various boundary conditions on the instability.

Findings

Boundary conditions opposing vertical motion increase growth rate by a few percent.

Vertical flow magnitude can be affected without changing overall flow pattern.

RWI is inherently a two-dimensional phenomenon.

Abstract

The linear Rossby wave instability (RWI) in global, 3D polytropic discs is revisited with a much simpler numerical method than that previously employed by the author. The governing partial differential equation is solved with finite differences in the radial direction and spectral collocation in the vertical direction. RWI modes are calculated subject to different upper disc boundary conditions. These include free surface, solid boundaries and variable vertical domain size. Boundary conditions that oppose vertical motion increase the instability growth rate by a few per cent. The magnitude of vertical flow throughout the fluid column can be affected but the overall flow pattern is qualitatively unchanged. Numerical results support the notion that the RWI is intrinsically two dimensional. This implies that inconsistent upper disc boundary conditions, such as vanishing enthalpy perturbation, may inhibit the RWI in 3D.