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SUMMARY:Nonlinear Ice sheet/liquid interaction due to an obstruction - Yur
 iy Semenov (Academy of Sciences\, Ukraine)
DTSTART:20220929T130000Z
DTEND:20220929T133000Z
UID:TALK178415@talks.cam.ac.uk
DESCRIPTION:The two-dimensional nonlinear problem of steady flow with obst
 ruction beneath an ice sheet is considered. The mathematical model of the 
 flow is based on the velocity potential theory with fully nonlinear bounda
 ry conditions on the ice/liquid interface and on the nonlinear Cosserat pl
 ate model for an ice sheet\, which are coupled throughout a numerical proc
 edure which provide the same pressure distribution on the interface from t
 he liquid and the elastic ice sheet sides. The integral hodograph method i
 s employed to derive analytical expressions of the complex potential and t
 he complex velocity of the flow both as functions of a parameter variable.
  The problem is reduced to a system of integral equations which are solved
  using the method of successive approximation and the collocation method. 
 Case studies are conducted for a body submerged beneath the interface in t
 he infinitely deep liquid and for the obstruction located on the bottom of
  the finite depth channel. For each case\, both subcritical and supercriti
 cal flow regimes are studied. Results for interface shape\, bending moment
 \, and pressure distribution are presented for the wide ranges of Froude n
 umbers and depths of submergence. In the case of infinite depth fluid\, th
 e dispersion equation predicts two waves of different lengths which may ex
 ist on the interface. The first longest wave is that caused by gravity loc
 ated downstream of the body\, and the second shorter wave is that caused b
 y the ice sheet and is located upstream of the body. They exhibit a strong
 ly nonlinear interaction above the submerged body near the critical Froude
  number such that occurs some range of submergences in which the solution 
 does not converge. It is different in the case of the finite depth channel
 . The two waves may exist in the range of depth-based Froude Fcr
LOCATION:Seminar Room 1\, Newton Institute
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