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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Nonlinear Ice sheet/liquid interaction due to an o
bstruction - Yuriy Semenov (Academy of Sciences\,
Ukraine)
DTSTART;TZID=Europe/London:20220929T140000
DTEND;TZID=Europe/London:20220929T143000
UID:TALK178415AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/178415
DESCRIPTION:The two-dimensional nonlinear problem of steady fl
ow with obstruction beneath an ice sheet is consid
ered. The mathematical model of the flow is based
on the velocity potential theory with fully nonlin
ear boundary conditions on the ice/liquid interfac
e and on the nonlinear Cosserat plate model for an
ice sheet\, which are coupled throughout a numeri
cal procedure which provide the same pressure dist
ribution on the interface from the liquid and the
elastic ice sheet sides. The integral hodograph me
thod is employed to derive analytical expressions
of the complex potential and the complex velocity
of the flow both as functions of a parameter varia
ble. The problem is reduced to a system of integra
l equations which are solved using the method of s
uccessive approximation and the collocation method
. Case studies are conducted for a body submerged
beneath the interface in the infinitely deep liqui
d and for the obstruction located on the bottom of
the finite depth channel. For each case\, both su
bcritical and supercritical flow regimes are studi
ed. Results for interface shape\, bending moment\,
and pressure distribution are presented for the w
ide ranges of Froude numbers and depths of submerg
ence. In the case of infinite depth fluid\, the di
spersion equation predicts two waves of different
lengths which may exist on the interface. The firs
t longest wave is that caused by gravity located d
ownstream of the body\, and the second shorter wav
e is that caused by the ice sheet and is located u
pstream of the body. They exhibit a strongly nonli
near interaction above the submerged body near the
critical Froude number such that occurs some rang
e of submergences in which the solution does not c
onverge. It is different in the case of the finite
depth channel. The two waves may exist in the ran
ge of depth-based Froude Fcr
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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