PT - JOURNAL ARTICLE
AU -
TI - The development of wavepackets in unstable flows
DP - 1981 Jan 07
TA - Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
PG - 457--476
VI - 373
IP - 1755
4099 - http://rspa.royalsocietypublishing.org/content/373/1755/457.short
4100 - http://rspa.royalsocietypublishing.org/content/373/1755/457.full
SO - Proc R Soc Lond A Math Phys Sci1981 Jan 07; 373
AB - By using a model form of the complex dispersion relation for unstable flows, the linear evolution of a localized three-dimensional wavepacket is determined. The disturbance is expressed as a double Fourier integral which is evaluated asymptotically by the saddle-point method. On making certain approximations, simple closed-form solutions are obtained, some of which resemble the curved wavepackets observed by Gaster & Grant (1975) and some the ‘ elliptic ’ packet found by Benjamin (1961). The range of validity of theories which lead to an elliptic packet is clarified. An alternative derivation of some of the results is given by using a multiple-scales technique. The relative merits of the two methods are thereby illuminated.