{
  "abstract": "Since the pioneering work of Taylor and Goldstein in 1931 laid the foundation for the study of parallel stratified shear flows, non-parallel configurations have received comparatively little attention. We study the stability of the 3D Boussinesq system near the plane Couette flow $V^*=(y,0,0)$ under the vertically stratified background $η^*=αz$. The shear and stratification directions are perpendicular. This geometry produces two structural effects that are absent in the parallel configuration: an additional nonlocal coupling in the non-zero-mode system, which obstructs a directly useful symmetrization, and a wave-shear coupled lift-up mechanism for the zero modes. The $L^p$ transient growth due to the lift-up effect can be suppressed either by sufficiently strong stratification (for $p>2$) or under suitable assumptions on the initial data (for $p\\geq 2$). To study the nonzero-mode system, we introduce a reformulation based on the linearized potential vorticity (PV), a fundamental quantity in geophysical fluid dynamics, to recover a better energy structure. We establish the inviscid damping of $u_{1,\\neq}$ and $u_{2,\\neq}$. We further apply the linearized PV formulation to study the linear stability of the tilted Couette flow. Finally, we use this formulation to prove the nonlinear stability for perturbations on $\\mathbb{T}\\times\\mathbb{R}\\times\\mathbb{T}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.33960",
  "author_total": 1,
  "authors": [
    {
      "name": "Yiting Yao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4br7dtpzmyc3q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.33960",
  "fulltext_url": null,
  "id": "4br7dtpzmyc3q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.33960",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2604|Navier-Stokes equation solutions"
    ]
  ],
  "openalex": "W7214724024",
  "pdf_url": "https://arxiv.org/pdf/2609.33960",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4br7dtpzmyc3q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:31:00Z",
      "native_id": "2609.33960",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.33960"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Stability of 3D Stratified Plane Couette Flow: A New Lift-up Mechanism and Potential Vorticity",
  "title_text": "Stability of 3D Stratified Plane Couette Flow: A New Lift-up Mechanism and Potential Vorticity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:47Z",
  "url": "https://research.draconitic.com/paper/4br7dtpzmyc3q",
  "venue": "arXiv",
  "versions": []
}