TY - JOUR
T1 - The development of wavepackets in unstable flows
JF - Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
JO - Proc R Soc Lond A Math Phys Sci
SP - 457
LP - 476
M3 - 10.1098/rspa.1981.0004
VL - 373
IS - 1755
AU -
Y1 - 1981/01/07
UR - http://rspa.royalsocietypublishing.org/content/373/1755/457.abstract
N2 - 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.
ER -