Do transience gravity waves in a shear flow break?

PULIDO M.; RODAS C.

QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY

Wiley - Royal Meteorological Society

Lugar: Reading UK; Año: 2008 vol. 134 p. 1083 - 1094

0035-9009

The propagation of transience gravity waves in a shear flow towards their critical levels is examined using ray tracing approximation and a higher degree approximation (quasi-optic approximation). Because of its transience forcing, the amplitude of transience waves decays to zero in the neighbourhood of the critical region so that it is not clear whether transience gravity waves will reach the convective instability threshold  or not. The analysis shows that the horizontal perturbation decays asymptotically as the inverse of the square root of time, while the vertical wavenumber depends linearly with time thus transience gravity waves attain the convective instability for long times. The theoretical results are confronted with numerical simulations. The ray path approximation is not able to reproduce the maximum amplitude, quasi-optic approximation gives a reasonable agreement at short and long times. There are three breaking regimes for transience gravity waves; for wave packets with a narrow frequency spectrum (quasi-steady waves) and large enough initial wave amplitude, the wave breaking is similar to the abrupt monochromatic wave overturning. On the other hand highly transience wave packets will dissipate  near the critical region for very long times with small wave amplitudes and high vertical wavenumber. The third regime is a transition between the two extremes, in this case both wave amplitude and vertical wavenumber are important to produce the convective threshold. The dependencies of the convective instability height (a quantity that may be useful for gravity wave parameterisations) with the Richardson number, and the frequency spectral width are obtained.