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Mathematical and numerical treatment of instabilities of non-axisymmetric confined vortices under the Dirichlet boundary conditions

Authors
Journal
Applied Mathematical Modelling
0307-904X
Publisher
Elsevier
Publication Date
Volume
37
Issue
6
Identifiers
DOI: 10.1016/j.apm.2012.09.019
Keywords
  • Convective Instability
  • Confined Vortex
  • Boundary Adapted Collocation
Disciplines
  • Computer Science
  • Mathematics

Abstract

Abstract This paper is concerned with an efficient analytical and numerical method for computing instability bounds of non-axisymmetric confined vortices. We propose a new approach based on a recently mathematical method of meshless collocation, when the shifted orthogonal Chebyshev base is adapted to satisfy the boundary conditions. Appropriately modified Tollmien–Schlichting modes used for the linear stability analysis offer the main advantage of dealing with a steady perturbation model of a confined vortex that leads to a variety of information describing the behavior of the full three-dimensional unsteady flow.

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