This note is concerned with the problem of forced motion due to a vertical circular cylindrical wave-maker immersed in a liquid with an inertial surface composed of uniformly distributed floating particles. The techniques of Laplace transform in time and Weber transform in the radial co-ordinate are used to obtain the velocity potential and hence the inertial surface depression. For the special case of a time-harmonic wave-maker, the potential function is analysed for its steady-state development. It is shown that if the inertial surface is "too heavy", the disturbance due to the wave-maker remains confined within a short distance only. © 1989.

KRISHNA KUNDU

Applied Mathematics

B N MANDAL

University of Calcutta (informally known as Calcutta University or CU) is a collegiate public state university located in Kolkata, West Bengal, India.&nbsp;Within India it is recognized as a &quot;Five-Star University&quot; and accredited &quot;A&quot; Grade by National Assessment and Accreditation Council.

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The University of Calcutta has secured the Fifth position among the Universities of India in the prestigious &quot;Indian University Ranking 2019&quot; list, released by the NIRF of the Ministry of Human Resource Development, Government of India.

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It was established on 24 January 1857, and was one of the first institutions in Asia to be established as a multidisciplinary and Western-style university. Its alumni and faculty include several heads of state, heads of government, social reformers, prominent artists, only academy award winner and Dirac medal winner in India, many Fellows of the Royal Society and five Nobel laureates as of 2019 which is highest in South Asia.

University Of Calcutta

A note on the cylindrical wave-maker problem in a liquid with an inertial surface

International Journal of Engineering Science

The problem of generation of waves in a liquid of uniform finite depth with an inertial surface composed of a thin but uniform distribution of disconnected floating particles, due to forced axisymmetric motion prescribed on the surface of an immersed vertical cylindrical wave-maker of circular cross section under the influence of surface tension at the inertial surface, is discussed. The techniques of Laplace transform in time and the modified Weber transform involving Bessel functions in the radial coordinate have been employed to obtain the velocity potential. The steady-state development to the potential function as well as the inertial surface depression due to time-harmonic forced oscillations of the wave-maker are deduced. It is found that the presence of surface tension at the inertial surface ensures the propagation of time-harmonic progressive waves of any angular frequency.

Fulltext

Journal of the Australian Mathematical Society Series B-Applied Mathematics

A CYLINDRICAL WAVE-MAKER PROBLEM IN A LIQUID OF FINITE DEPTH WITH AN INERTIAL SURFACE IN THE PRESENCE OF SURFACE-TENSION

In the present note the classical vertical cylindrical wave-maker problem in water of finite depth under the influence of surface tension is reinvestigated by employing a suitable Weber transform in the radial coordinate. © 1991 Taylor and Francis Group, LLC.

International Journal of Mathematical Education in Science and Technology

The cylindrical wave-maker problem in water of uniform finite depth in the presence of surface tension

The velocity potential due to a submerged circular ring source of time-dependent strength outside an immersed vertical co-axial circular cylinder is obtained for a liquid of finite depth bounded by an inertial surface composed of uniformly distributed noninteracting floating particles. The modified Weber transform formula as used in [1] in the radial coordinate has been employed to obtain the transformed velocity potential after using Laplace transform in time. For time-harmonic source strength, the steady-state development shows that the progressive waves generated by the ring source in the presence of the cylinder cannot propagate if the inertial surface is too heavy. © 1991.

Ring source potential outside a vertical co-axial circular cylinder in a liquid of finite depth with an inertial surface

The velocity potential due to the presence of a horizontal circular ring of wave sources of time-dependent strength in a fluid of finite constant depth with an inertial surface composed of uniformly distributed floating particles is obtained when the effect of surface tension at the inertial surface is included. © 1987.

Journal	Data powered by TypesetInternational Journal of Engineering Science
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ISSN	0020-7225
Open Access	No