Contributed Papers

Acta Mechanica

, Volume 93, Issue 1, pp 1-11

First online:

Exact nonlinear travelling hydromagnetic wave solutions

  • M. VenkatachalappaAffiliated withUGC-DSA Centre in Fluid Mechanics, Department of Mathematics, Central College, Bangalore University
  • , N. RudraiahAffiliated withVice-Chancellor, Gulbarga University
  • , P. L. SachdevAffiliated withDepartment of Mathematics, Indian Institute of Science

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Exact travelling wave solutions for hydromagnetic waves in an exponentially stratified incompressible medium are obtained. With the help of two integrals it becomes possible to reduce the system of seven nonlinear PDE's to a second order nonlinear ODE which describes an one dimensional harmonic oscillator with a nonlinear friction term. This equation is studied in detail in the phase plane. The travelling waves are periodic only when they propagate either horizontally or vertically. The reduced second order nonlinear differential equation describing the travelling waves in inhomogeneous conducting media has rather ubiquitous nature in that it also appears in other geophysical systems such as internal waves, Rossby waves and topographic Rossby waves in the ocean.