Articles | Volume 20, issue 4
Nonlin. Processes Geophys., 20, 571–580, 2013
Nonlin. Processes Geophys., 20, 571–580, 2013

Research article 07 Aug 2013

Research article | 07 Aug 2013

Fourier spectrum and shape evolution of an internal Riemann wave of moderate amplitude

E. Kartashova1, E. Pelinovsky1,2,3,4, and T. Talipova2,3 E. Kartashova et al.
  • 1Institute for Analysis, Johannes Kepler University, Linz, Austria
  • 2Department of Nonlinear Geophysical Processes, Institute of Applied Physics, Nizhny Novgorod, Russia
  • 3Department of Applied Mathematics, Nizhny Novgorod State Technical University, Nizhny Novgorod, Russia
  • 4Department of Information Systems, National Research University – Higher School of Economics, Nizhny Novgorod, Russia

Abstract. The nonlinear deformation of long internal waves in the ocean is studied using the dispersionless Gardner equation. The process of nonlinear wave deformation is determined by the signs of the coefficients of the quadratic and cubic nonlinear terms; the breaking time depends only on their absolute values. The explicit formula for the Fourier spectrum of the deformed Riemann wave is derived and used to investigate the evolution of the spectrum of the initially pure sine wave. It is shown that the spectrum has exponential form for small times and a power asymptotic before breaking. The power asymptotic is universal for arbitrarily chosen coefficients of the nonlinear terms and has a slope close to –8/3.