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This chapter reviews some mathematical methods which are useful to solve simple but instructive problems of superfluid hydrodynamics which are concerned with sound waves and vortices. Besides the GPE, which is the major model used to study quantum fluids, these methods include the Vortex Point Model (VPM) for 2D flows, the Vortex Filament Model for 3D flows, their finite-temperature generalization (the Schwarz equation), and, finally, the Hall-Vinen-Bekharevic-Khalatnikov (HVBK) equations, which generalise Landau’s two-fluid equations presented in Chap.  6 to the presence of vortex lines in the system. A basic understanding of these methods will be required to make sense of the rich variety of vortex phenomena which will be presented in Chap.  9 .

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Hydrodynamic Methods

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  • 发表日期：

    2026年

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  • Carlo F. Barenghi,
  • Thomas Bland,
  • Nick G. Parker

摘要

This chapter reviews some mathematical methods which are useful to solve simple but instructive problems of superfluid hydrodynamics which are concerned with sound waves and vortices. Besides the GPE, which is the major model used to study quantum fluids, these methods include the Vortex Point Model (VPM) for 2D flows, the Vortex Filament Model for 3D flows, their finite-temperature generalization (the Schwarz equation), and, finally, the Hall-Vinen-Bekharevic-Khalatnikov (HVBK) equations, which generalise Landau’s two-fluid equations presented in Chap.  6 to the presence of vortex lines in the system. A basic understanding of these methods will be required to make sense of the rich variety of vortex phenomena which will be presented in Chap.  9 .