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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Vortex waves in deep water: Lagrange approach - An
atoly Abrashkin (Higher School of Economics\, Mosc
ow)
DTSTART;TZID=Europe/London:20170810T170000
DTEND;TZID=Europe/London:20170810T180000
UID:TALK75381AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/75381
DESCRIPTION:A lecture consists of two parts. The first one dea
ls with a theory of weakly nonlinear vortex waves.
The vorticity is set in the series expansion in t
he small parameter of wave steepness. Each term of
this row is an arbitrary function of the vertical
Lagrange coordinate. We study different types of
the waves: the stationary waves on shear flow\, th
e standing vortex waves and the spatial vortex wav
es in the low vorticity fluid. The perturbation th
eory up to the third order is analyzed. The nonlin
ear Schrö\;dinger (NLS) equation describing we
akly nonlinear wave packets in an infinity-depth f
luid with non-uniform vorticity is obtained. The v
orticity is assumed to be an arbitrary function of
both Lagrangian coordinates and quadratic in the
small parameter proportional to the wave&rsquo\;s
steepness. The effects of vorticity are manifested
in a shift of the wavenumber of the carrier wave
and a changing of the coefficient in nonlinear ter
m of the NLS equation. The modulated Gouyon waves
are studied. There is a special case of the vortex
waves for which the resulting non-linearity in th
e NLS equation vanishes. The Gerstner wave belongs
among them. The second part of the lecture presen
ts the theory of strongly nonlinear waves. A vorte
x model of a rogue wave formation at the backgroun
d of uniform waves is proposed. It based on an exa
ct analytical solution of equations of 2D hydrodyn
amics of an ideal incompressible fluid. A unique f
eature of flows of this class is the dependence of
complex coordinate of liquid particle&rsquo\;s mo
tion on two functions that may be arbitrary to a l
arge extent. As a consequence the model may be use
d for the analysis of different forms of surface p
ressure as well as of liquid vorticity\, i.e. when
taking into account both these factors of air flo
w impact on the surface waves simultaneously. A pr
ocess of formation of a rogue wave in the field of
the Gerstner wave is studied. The physical parame
ters of the rogue wave and feasibility of the prop
osed scenario are disc.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:info@newton.ac.uk
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