In the present study, we construct a nonlinear whistler wave model to explain the magnetic field spectra observed for lion roars in the Earth’s magnetosheath region. We use two-fluid theory and semi-analytical approach to derive the dynamical equation of whistler wave propagating along the ambient magnetic field. We examine the magnetic field localization of parallel propagating whistler wave in the intermediate beta plasma applicable to the Earth’s magnetosheath. In addition, we investigate spectral features of the magnetic field fluctuations and the spectral slope value. The magnetic field spectrum obtained by semi-analytical approach shows a spectral break point and becomes steeper at higher wave numbers. The observations of IMP6 plasma waves and magnetometer experiment reveal the existence of short period magnetic field fluctuations in the magnetosheath. The observation shows the broadband spectrum with a spectral slope of −4.5 superimposed with a narrow band peak. The broadband fluctuations appear due to the energy cascades attributed by low-frequency magnetohydrodynamic modes, whereas, a narrow band peak is observed due to the short period lion roars bursts. The energy spectrum predicted by the present theoretical model shows a similar broadband spectrum in the wave number domain with a spectral slope of −3.2, however, it does not show any narrow band peak. Further, we present a comparison between theoretical energy spectrum and the observed spectral slope in the frequency domain. The present semi-analytical model provides exposure to the whistler wave turbulence in the Earth’s magnetosheath. © 2017, Springer Science+Business Media B.V.