TY - JOUR
T1 - Evolution of packets of surface gravity waves over smooth topography
AU - Benilov, E. S.
AU - Flanagan, J. D.
AU - Howlin, C. P.
PY - 2005/6/25
Y1 - 2005/6/25
N2 - Weakly nonlinear packets of surface gravity waves over topography are governed by a nonlinear Schrödinger equation with variable coefficients. Using this equation and assuming that the horizontal scale of topography is much larger than the width of the packet, we show that, counter-intuitively, the amplitude of a shoaling packet decays, while its width grows. Such behaviour is a result of the fact that the coefficient of the nonlinear term in the topography-modified Schrödinger equation decreases with depth. Furthermore, there exists a critical depth, hcr, where this coefficient changes sign - if the packet reaches hcr, it disperses.
AB - Weakly nonlinear packets of surface gravity waves over topography are governed by a nonlinear Schrödinger equation with variable coefficients. Using this equation and assuming that the horizontal scale of topography is much larger than the width of the packet, we show that, counter-intuitively, the amplitude of a shoaling packet decays, while its width grows. Such behaviour is a result of the fact that the coefficient of the nonlinear term in the topography-modified Schrödinger equation decreases with depth. Furthermore, there exists a critical depth, hcr, where this coefficient changes sign - if the packet reaches hcr, it disperses.
UR - http://www.scopus.com/inward/record.url?scp=22144457925&partnerID=8YFLogxK
U2 - 10.1017/S0022112005004246
DO - 10.1017/S0022112005004246
M3 - Article
AN - SCOPUS:22144457925
SN - 0022-1120
VL - 533
SP - 171
EP - 181
JO - Journal of Fluid Mechanics
JF - Journal of Fluid Mechanics
ER -