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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Long non-linear flexural-gravitational waves in th
e sea\, covered with Ice - Vitaliy Yakovlev (Acade
my of Sciences\, Ukraine)
DTSTART;TZID=Europe/London:20220927T100000
DTEND;TZID=Europe/London:20220927T103000
UID:TALK178376AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/178376
DESCRIPTION:Longwave nonlinear dispersion model\, that describ
es flexural-gravitational waves propagating in icy
cover on the surface of the sea\, is developed by
expanding the original three-dimensional problem
of hydroelastic oscillations of the system "elasti
c plate - a layer of an ideal incompressible fluid
of variable depth " in a small parameter. The mod
el takes into account effects of non-linear fluid
dispersion as well inertia\, elasticity and geomet
rically nonlinear plate deflection. Proceeding fro
m received equations\, there were built an hierarc
hical sequence of more simple models\, generalizin
g equations of Peregrine \, Boussinesque and Korte
weg- de Vries\, known from surface waves theories\
, for the case of flexural-gravitational waves . F
or the special case of generalized Korteweg-de-Vri
es equation analitic solutions\, describing propag
ation of solitons and cnoidal waves in the sea\, c
overed with continuous or broken ice\, were built
and analyzed. It is shown that flexural-gravitatio
nal waves possess some mirrored properties as comp
ared to long non-linear water waves. As to soliton
this means that without changing the form a depre
ssion propagates\, not a hump\, as in the clean wa
ter case\, and speed of it&rsquo\;s propagation de
creases with increasing the amplitude rather than
increases . In addition\, the characteristics of t
he flexural-gravitational waves are determined by
the wave amplitude and dispersion of plate flexura
l rigidity\, and do not depend on the water disper
sion and inertial properties of the icy cover. The
re are determined areas of task parameters changin
g\, where various types of soliton-like decisions
for given equation may exist. In a similar setting
\, the generalized Kadomtsev - Petviashvili type e
quation\, modeling the propagation of long non-lin
ear two-dimensional flexural-gravitational waves i
n the sea covered with continuous ice\, has been d
erived. Assuming periodicity for transverse coordi
nate\, the analitic solution for the equation rece
ived has been built in the form of a wave packet.
Relations among character parameters of the task \
, which provide the existence of such a solution\,
were defined.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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