On the coupled time-harmonic motion of water and a body freely floating in it

Kuznetsov, Nikolay; Motygin, Oleg V.

doi:10.1017/jfm.2011.161

Cited by 15 publications

(23 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This paper continues the rigorous study (initiated in [3]) of a freely floating rigid bodies trapping time-harmonic waves in an inviscid, incompressible, heavy fluid, say water (see also [6,7,8] and [4]). We consider the infinitely deep water in irrotational motion bounded from above by a free surface unbounded in all horizontal directions, but unlike the cited papers dealing with the open surface, we assume here that it is totally covered with the brash ice.…”

Section: Introductionmentioning

confidence: 58%

On freely floating bodies trapping time-harmonic waves in water covered by brash ice

Kuznetsov¹,

Motygin²

2015

Preprint

Self Cite

View full text Add to dashboard Cite

A mechanical system consisting of water covered by brash ice and a body freely floating near equilibrium is considered. The water occupies a half-space into which an infinitely long surface-piercing cylinder is immersed, thus allowing us to study two-dimensional modes of the coupled motion which is assumed to be of small amplitude. The corresponding linear setting for time-harmonic oscillations reduces to a spectral problem whose parameter is the frequency. A constant that characterises the brash ice divides the set of frequencies into two subsets and the results obtained for each of these subsets are essentially different.For frequencies belonging to a finite interval adjacent to zero, the total energy of motion is finite and the equipartition of energy holds for the whole system. For every frequency from this interval, a family of motionless bodies trapping waves is constructed by virtue of the semi-inverse procedure. For sufficiently large frequencies outside of this interval, all solutions of finite energy are trivial.

show abstract

Section: Introductionmentioning

confidence: 58%

On freely floating bodies trapping time-harmonic waves in water covered by brash ice

Kuznetsov¹,

Motygin²

2015

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…In the same way as in Kuznetsov & Motygin (2011, 2012, this yields the following assertion about the kinetic and potential energy of the water motion. that is, ϕ ∈ H 1 (W).…”

Section: Equipartition Of Energymentioning

confidence: 71%

“…This paper continues the rigorous study (initiated in Kuznetsov 2011) of the coupled time-harmonic motion of a freely floating rigid body and an inviscid, incompressible, heavy fluid, say water; see also Kuznetsov & Motygin (2011, 2012, 2015 and Kuznetsov (2015). We consider infinitely deep water in irrotational motion, bounded from above by a free surface unbounded in all horizontal directions, but unlike the cited papers dealing with the open surface, we assume here that it is totally covered with brash ice.…”

Section: Introductionmentioning

confidence: 93%

On the coupled time-harmonic motion of a freely floating body and water covered by brash ice

Kuznetsov

Motygin

2016

J. Fluid Mech.

Self Cite

View full text Add to dashboard Cite

A mechanical system consisting of water covered by brash ice and a body freely floating near equilibrium is considered. The water occupies a half-space into which an infinitely long surface-piercing cylinder is immersed, thus allowing us to study two-dimensional modes of the coupled motion, which is assumed to be of small amplitude. The corresponding linear setting for time-harmonic oscillations reduces to a spectral problem whose parameter is the frequency. A constant that characterises the brash ice divides the set of frequencies into two subsets and the results obtained for each of these subsets are essentially different. For frequencies belonging to a finite interval adjacent to zero, the total energy of motion is finite and the equipartition of energy holds for the whole system. For every frequency from this interval, a family of motionless bodies trapping waves is constructed by virtue of the semi-inverse procedure. For sufficiently large frequencies outside of this interval, all solutions of finite energy are trivial.

show abstract

“…As in Theorem 4.3, the velocity potential ϕ m satisfies relations (7) and (8), whereas the boundary condition (9) holds on every S k in view of the way how these surfaces are constructed using the displacement vectors (31). It remains to verify 6N equations (10) of which 5N take the same form as equalities (27) with the exception of the first one. The latter is as follows:…”

Section: Modified Stream Functions and Heaving Trapping Structuresmentioning

confidence: 99%

Freely floating structures trapping time-harmonic water waves

Kuznetsov

Motygin

2015

The Quarterly Journal of Mechanics and Applied Mathematics

View full text Add to dashboard Cite

We study the coupled small-amplitude motion of the mechanical system consisting of infinitely deep water and a structure immersed in it. The former is bounded above by a free surface, whereas the latter is formed by an arbitrary finite number of surface-piercing bodies floating freely. The mathematical model of time-harmonic motion is a spectral problem in which the frequency of oscillations serves as the spectral parameter. It is proved that there exist axisymmetric structures consisting of N ≥ 2 bodies; every structure has the following properties: (i) a time-harmonic wave mode is trapped by it; (ii) some of its bodies (may be none) are motionless, whereas the rest of the bodies (may be none) are heaving at the same frequency as water. The construction of these structures is based on a generalization of the semi-inverse procedure applied earlier for obtaining trapping bodies that are motionless although float freely.

show abstract

On the coupled time-harmonic motion of water and a body freely floating in it

Cited by 15 publications

References 16 publications

On freely floating bodies trapping time-harmonic waves in water covered by brash ice

On freely floating bodies trapping time-harmonic waves in water covered by brash ice

On the coupled time-harmonic motion of a freely floating body and water covered by brash ice

Freely floating structures trapping time-harmonic water waves

Contact Info

Product

Resources

About