Elliptical vortex solutions, integrable Ermakov structure, and Lax pair formulation of the compressible Euler equations

Hongli An, Engui Fan, and Haixing Zhu
Phys. Rev. E 91, 013204 – Published 20 January 2015

Abstract

The 2+1-dimensional compressible Euler equations are investigated here. A power-type elliptic vortex ansatz is introduced and thereby reduction obtains to an eight-dimensional nonlinear dynamical system. The latter is shown to have an underlying integral Ermakov-Ray-Reid structure of Hamiltonian type. It is of interest to notice that such an integrable Ermakov structure exists not only in the density representations but also in the velocity components. A class of typical elliptical vortex solutions termed pulsrodons corresponding to warm-core eddy theory is isolated and its behavior is simulated. In addition, a Lax pair formulation is constructed and the connection with stationary nonlinear cubic Schrödinger equations is established.

  • Figure
  • Figure
  • Received 17 August 2014

DOI:https://doi.org/10.1103/PhysRevE.91.013204

©2015 American Physical Society

Authors & Affiliations

Hongli An*

  • College of Science, Nanjing Agricultural University, Nanjing 210095, PR China

Engui Fan

  • School of Mathematical Sciences and Key Laboratory of Mathematics for Nonlinear Science, Fudan University, Shanghai 200433, PR China

Haixing Zhu

  • College of Economics and Management, Nanjing Forestry University, Nanjing 210037, PR China

  • *kaixinguoan@163.com.cn; hongli.an@connect.polyu.hk

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 91, Iss. 1 — January 2015

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review E

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×