NDLI: On the forward motion of an interface-crossing body in a two-layer fluid: the role of asymptotics in the problem’s statement

Content Provider	Springer Nature Link
Author	Motygin, Oleg Kuznetsov, Nikolay
Copyright Year	2010
Abstract	A two-dimensional body moves forward with a constant velocity in an inviscid, incompressible fluid under gravity. The fluid consists of two layers having different densities, and the body is totally submerged so that it intersects the interface between the fluids. The resulting fluid motion is assumed to be steady-state in a coordinate system attached to the body. A well-posed statement of the problem for the velocity potentials is proposed in the framework of linearized water-wave theory. This statement consists of the so-called Neumann–Kelvin problem augmented by supplementary conditions, formulated in terms of the interface’s elevation at the points, where the body intersects the interface. The analysis which leads to these two conditions involves the derivation of asymptotics near the intersection points and Green’s representation for solutions to the Neumann–Kelvin problem. The uniqueness theorem for the suggested statement is proved under the assumption that the kinetic energy is finite. The asymptotics of a solution at infinity is found and an explicit formula for the resistance to forward motion is derived. The relationship of the formulae with the supplementary conditions is discussed.
Starting Page	113
Ending Page	134
Page Count	22
File Format	PDF
ISSN	00220833
Journal	Journal of Engineering Mathematics
Volume Number	69
Issue Number	2-3
e-ISSN	15732703
Language	English
Publisher	Springer Netherlands
Publisher Date	2010-05-25
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Asymptotic formulae Forward motion Interface-crossing body Resistance Two-layer fluid Well-posed problem Numeric Computing Mathematical Modeling and Industrial Mathematics Analysis Applications of Mathematics Mechanics
Content Type	Text
Resource Type	Article
Subject	Mathematics Engineering

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