Spectral Tail of a Gravity Wave Train Propagating in a Shearing Background

Abstract

The causes of the appearance of a tail in the power spectrum of a gravity wave train in a shearing background terminating under the Hodges condition are studied. The power spectrum of this train for a wavenumber greater than the cutoff value has amplitudes and slopes similar to the observed in actual wind profiles. It is shown that the Fourier transform for large wavenumbers can be expressed as an inverse power series of the wavenumber, where the first two terms are dominant (k?1 and k?2) with a power spectrum slope from ?2 to ?4 in the tail. The main features that produce the tail are the discontinuities in the profile. An observed profile is analyzed showing that the power spectral amplitudes do not necessarily come from the waves contained in the profile; they can arise from irregularities, nonperiodic jumps that could be interpreted as discontinuities.