Acta Mechanica

, Volume 93, Issue 1, pp 1–11

Exact nonlinear travelling hydromagnetic wave solutions

Authors

  • M. Venkatachalappa
    • UGC-DSA Centre in Fluid Mechanics, Department of Mathematics, Central CollegeBangalore University
  • N. Rudraiah
    • Vice-ChancellorGulbarga University
  • P. L. Sachdev
    • Department of MathematicsIndian Institute of Science
Contributed Papers

DOI: 10.1007/BF01182569

Cite this article as:
Venkatachalappa, M., Rudraiah, N. & Sachdev, P.L. Acta Mechanica (1992) 93: 1. doi:10.1007/BF01182569

Summary

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.

Copyright information

© Springer-Verlag 1992