A NOTE ON THE EIGENVALUE PROBLEM IN FORCED CAPILLARY-GRAVITY WAVES INSIDE A CIRCULAR BASIN UNDER HOCKING’S EDGE CONDITION
The purpose of this paper is to further explore the eigenvalues occurring in the linear problem of forced capillary-gravity waves generated inside of a cylinder in consideration of the surface tension and the edge condition proposed by Hocking [1]. A numerical method to evaluate them is constructed as well.
capillary-gravity waves, Hocking’s edge condition.
Received: August 2, 2021; Accepted: September 8, 2021; Published: September 29, 2021
How to cite this article: Nai-Sher Yeh, A Note on the Eigenvalue Problem in Forced Capillary-Gravity Waves Inside a Circular Basin Under Hocking’s Edge Condition, Advances and Applications in Fluid Mechanics 27(1) (2021), 1-35. DOI: 10.17654/FM027010001
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References:
[1] L. M. Hocking, The damping of capillary-gravity waves at a rigid boundary, J. Fluid Mech. 179 (1987), 253-266.[2] T. H. Havelock, Forced surface waves on water, Philos. Mag. 8 (1929), 569-576.[3] D. V. Evans, The influence of surface tension on the reflection of water waves by a plane vertical barrier, Proc. Cambridge Philos. Soc. 64 (1968), 795-810.[4] D. V. Evans, The effect of surface tension on the waves produced by a heaving circular cylinder, Proc. Cambridge Philos. Soc. 64 (1968), 833-847.[5] J. W. Miles, Capillary-viscous forcing of surface waves, J. Fluid Mech. 219 (1990), 635-646.[6] C.-L. Ting and M. Perlin, Boundary conditions in the vicinity of the contact line at a vertically oscillating upright plate: an experimental investigation, J. Fluid Mech. 295 (1995), 263-300.[7] N.-S. Yeh, Hocking’s edge condition reconsidered: solution of the problem of capillary-gravity waves in a special setting, Advances and Applications in Fluid Mechanics 17(2) (2015), 241-264.[8] M.-C. Shen, S.-M. Sun and D.-Y. Hsieh, Forced capillary-gravity waves in a circular basin, Wave Motion 18 (1993), 401-412.[9] M.-C. Shen and N.-S. Yeh, Exact solution for forced capillary-gravity waves in a circular basin under Hocking’s edge condition, Wave Motion 26 (1997), 117-126.[10] M.-C. Shen and N.-S. Yeh, On a special case of forced capillary-gravity waves in a circular basin under Hocking’s edge condition, Wave Motion 30 (1999), 91-96.[11] J. Miles, The capillary boundary layer for standing waves, J. Fluid Mech. 222 (1991), 197-205.[12] J. Miles, On forced capillary-gravity waves in a circular cylinder, Wave Motion 23 (1996), 387-391.[13] S. G. Mikhlin, Variational Methods in Mathematical Physics, Pergamon Press, 1964.[14] I. C. Gohberg and M. G. Kreĭn, Introduction to the theory of linear nonselfadjoint operators, American Mathematical Society, Providence, 1969.