Fluid Dynamics

, Volume 20, Issue 5, pp 791–796 | Cite as

A cylindrical analog of trochoidal gerstner waves

  • N. A. Inogamov


This paper investigates isobaric motions for which the values of the pressure are conserved in fluid particles. In it, a new analytic exact particular solution of nonlinear multidimensional hydrodynamic equations is obtained; it describes a trochoidal wave in cylindrical geometry. It is also proved that trochoidal waves in cylindrical and plane geometry exhaust the class of nonlinear isobaric motions. Here and below by a wave in plane geometry we mean a wave in a uniform gravitational field which is characterized by the wave vector k. It is obvious that waves in both plane and cylindrical geometry are two-dimensional motions, since the fluid particles in motion are fixed in the plane and the motions in parallel planes are the same. The trochoidal wave in cylindrical geometry is of interest, since it describes a nonlinear wave on the surface of a cavity in a rotating fluid, a situation which is frequently encountered in applications.


Wave Vector Gravitational Field Nonlinear Wave Parallel Plane Hydrodynamic Equation 
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Copyright information

© Plenum Publishing Corporation 1986

Authors and Affiliations

  • N. A. Inogamov
    • 1
  1. 1.Moscow

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