[Amath-seminars] Next Boeing Colloquium Speaker: Professor Diane Henderson from Pennsylvania State University (on Thursday, April 4)

[Anastassiya Semenova via Amath-seminars]

Dear All,

Our next Boeing Colloquium will feature *Professor Diane Henderson* from
Pennsylvania State University. The talk will take place in *Smith Hall,
Room 205, from 4:00pm to 5:00pm on Thursday, April 4th*. Please let me know
if you have any questions.

Here is the title and abstract for the talk:

*Title:* Understanding nonlinear surface water waves on deep water
*Abstract:* Oceanographers in the 60s conducted an ambitious experiment (1)
in which they tracked waves that were generated by large storms near New
Zealand across the Pacific Ocean until they hit the beaches at Alaska.
Paradoxically, at about the same time, mathematicians in the Soviet Union,
the U.S., and England (2) independently developed mathematical models that
predicted such waves to be unstable, meaning that they could not survive to
be tracked all the way across the Pacific. In the 70s experimentalists (3)
conducted laboratory experiments on these types of waves. They generated
waves with a given frequency that propagated down a wavetank, but at the
end of the wavetank, the waves had a slightly lower frequency. The
mathematical model did not explain this observation. In this talk, we
consider these observations and our experiments on modulated wavetrains
within the framework of the mathematical models: the scalar and vector
nonlinear Schroedinger equations with and without dissipation and/or higher
order terms. We examine the data within the context of conserved quantities
of these equations to determine when the models are likely to be valid or
not. We present recent results from our quest, motivated by recent
stability analyses of Stokes waves (4), to observe subharmonic
instabilities of waves in deep, finite and shallow water.

*References:* (1) Snodgrass, F. E., G. W. Groves, K. F. Hasselmann, G. R.
Miller, W. H. Munk, and W. H. Powers (1966), Propagation of ocean swell
across the Pacific, Philos. Trans. R. Soc. London A, 259, 431–497.
(2a) Benney, D. J. & Newell, A. C. 1967 The propagation of nonlinear wave
envelopes. Stud. Appl.Maths 46, 133–139.
(2b) Lighthill, M. J. 1965 Contribution to the theory of waves in nonlinear
dispersive systems. J. Inst. Math. Applics. 1, 269–306.
(2c) Benjamin, T. B. & Feir, J. E. 1967 The disintegration of wavetrains in
deep water. Part 1. J. Fluid Mech. 27, 417–430.
(2d) Ostrovsky, L. A. 1967 Propagation of wave packets and space-time
self-focussing in a nonlinear medium. Sov. Phys. J. Exp. Theor. Phys. 24,
797–800.
(2e) Whitham, G. B. 1967 Nonlinear dispersion of water waves. J. Fluid
Mech. 27, 399–412.
(2f) Zakharov, V. E. 1967 Instability of self-focusing of light. Sov. Phys.
J. Exp. Theor. Phys. 24, 455–459.
(2g) Zakharov, V. E. 1968 Stability of periodic waves of finite amplitude
on the surface of a deep fluid. J. Appl. Mech. Tech. Phys. 2, 190–194.
(3a) Lake, B. M. & Yuen, H. C. 1977 A note on some water-wave experiments
and the comparison ofdata with theory. J. Fluid Mech. 83, 75–81.
(3b) Lake, B. M., Yuen, H. C., Rungaldier, H. & Ferguson, W. E. 1977
Nonlinear deep-water waves:theory and experiment. Part 2. Evolution of a
continuous wave train. J. Fluid Mech. 83, 49–74.
(4) B. Deconinck, S. A. Dyachenko, P. M. Lushnikov, A. Semenova, The
instability of near-extreme Stokes waves, Proceedings of the National
Academy of Sciences,

Best Regards,

Anastassiya Semenova

Department of Applied Mathematics

University of Washington
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