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Abstract <p>This paper considers a geometric approach to describing structures in barotropic flows of an incompressible fluid. This type of description has an analogy in geometric optics. The evolution of equilibrium flows is considered, in which the trajectories of Lagrangian invariants, expressed through the vorticity of the flow, change. The connection between vorticity and velocity is established through the asymptotic behavior of the solution to the Poisson equation. The limits of applicability of the approach are discussed, as is the possibility of its generalization for baroclinic flows.</p>

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Lagrangian (Phase) Structures in an Incompressible Fluid

  • 期刊论文

  • 发表日期：

    2025年8月14日

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  • I. G. Yakushkin

摘要

Abstract

This paper considers a geometric approach to describing structures in barotropic flows of an incompressible fluid. This type of description has an analogy in geometric optics. The evolution of equilibrium flows is considered, in which the trajectories of Lagrangian invariants, expressed through the vorticity of the flow, change. The connection between vorticity and velocity is established through the asymptotic behavior of the solution to the Poisson equation. The limits of applicability of the approach are discussed, as is the possibility of its generalization for baroclinic flows.