Extended stability timescales for the 2D3C rotating stratified Boussinesq equations
Abstract
We study the time evolution of a vertical-slice model for incompressible inhomogeneous rotating fluids perturbed around a stably stratified rest state with linear buoyancy profile. For ε-small localized initial data with vanishing potential vorticity, we prove that solutions remain of size O(ε) up to times of order ε−4/3, and up to times of order ε−2 in a regime where the Brunt--Väisälä frequency and the Coriolis parameter are comparable. The first result relies on linear dispersion with amplitude decay rate ⟨ t⟩−1/2, while the second exploits the absence of three-wave resonances via a normal form transformation. Our results remain valid for small nonzero initial potential vorticity, whose size is propagated by means of an intrinsic change of coordinates.
Related
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- Stability threshold for 3D Boussinesq equations with rotation near the Couette flow and vertical stratified temperature
- Vanishing transport noise enhances stability of stratified Couette flow in the 3D Boussinesq system
- Stability threshold of the Poiseuille flow in 2D Navier-Stokes Boussinesq equations
- Stability threshold of the Couette flow in 2D Navier-Stokes Boussinesq equations on 𝕋 × [−1, 1] and ℝ × [−1, 1]
BibTeX
@misc{zotto2026extended,
title = {{Extended stability timescales for the 2D3C rotating stratified Boussinesq equations}},
author = {Augusto Del Zotto and Luca Melzi and Haoling Xiang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37013},
eprint = {2610.37013},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37013},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Extended stability timescales for the 2D3C rotating stratified Boussinesq equations
AU - Augusto Del Zotto
AU - Luca Melzi
AU - Haoling Xiang
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37013
UR - https://arxiv.org/abs/2610.37013
AB - We study the time evolution of a vertical-slice model for incompressible inhomogeneous rotating fluids perturbed around a stably stratified rest state with linear buoyancy profile. For ε-small localized initial data with vanishing potential vorticity, we prove that solutions remain of size O(ε) up to times of order ε^−4/3, and up to times of order ε^−2 in a regime where the Brunt--Väisälä frequency and the Coriolis parameter are comparable. The first result relies on linear dispersion with amplitude decay rate ⟨ t⟩^−1/2, while the second exploits the absence of three-wave resonances via a normal form transformation. Our results remain valid for small nonzero initial potential vorticity, whose size is propagated by means of an intrinsic change of coordinates.
ER -