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Experimental investigation on the evolution of the modulation instability with dissipation

Published online by Cambridge University Press:  03 September 2012

Y. Ma ,
G. Dong ,
M. Perlin ,
X. Ma  and
G. Wang
Y. Ma*
Affiliation:
State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian, 116024, China
G. Dong
Affiliation:
State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian, 116024, China
M. Perlin
Affiliation:
Department of Naval Architecture and Marine Engineering, University of Michigan, Ann Arbor, MI 48109, USA
X. Ma
Affiliation:
State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian, 116024, China
G. Wang
Affiliation:
School of Harbor, Coastal and Offshore Eningeering, Hohai University, Nanjing, 210098, China
*
†Email address for correspondence: yuxma@126.com
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Abstract

An experimental investigation focusing on the effect of dissipation on the evolution of the Benjamin–Feir instability is reported. A series of wave trains with added sidebands, and varying initial steepness, perturbed amplitudes and frequencies, are physically generated in a long wave flume. The experimental results directly confirm the stabilization theory of Segur et al. (J. Fluid Mech., vol. 539, 2005, pp. 229–271), i.e. dissipation can stabilize the Benjamin–Feir instability. Furthermore, the experiments reveal that the effect of dissipation on modulational instability depends strongly on the perturbation frequency. It is found that the effect of dissipation on the growth rates of the sidebands for the waves with higher perturbation frequencies is more evident than on those of waves with lower perturbation frequencies. In addition, numerical simulations based on Dysthe’s equation with a linear damping term included, which is estimated from the experimental data, can predict the experimental results well if the momentum integral of the wave trains is conserved during evolution.

JFM classification

Geophysical and Geological Flows: Ocean processes Waves/Free-surface Flows: Surface gravity waves
Type
Papers
Information
Journal of Fluid Mechanics , Volume 711 , 25 November 2012 , pp. 101 - 121
Copyright
Copyright © Cambridge University Press 2012

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