Analytical solutions for the interfacial viscous capillary-gravity waves due to an oscillating Stokeslet

Lu, Danni

doi:10.1007/s42241-019-0087-0

Cited by 2 publications

(1 citation statement)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Although capillary gravity surface waves have been studied for a long time, they are still a fascinating and interesting subject [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. The dispersion of linear and nonlinear waves, wave damping in deep water owing to viscosity, and weakly nonlinear waves in shallow water are classic problems that have long been studied [16].…”

Section: Introductionmentioning

confidence: 99%

Bifurcation Analysis and Propagation Conditions of Free-Surface Waves in Incompressible Viscous Fluids of Finite Depth

Ghahraman

Bene

2023

Fluids

View full text Add to dashboard Cite

Viscous linear surface waves are studied at arbitrary wavelength, layer thickness, viscosity, and surface tension. We find that in shallow enough fluids no surface waves can propagate. This layer thickness is determined for some fluids, water, glycerin, and mercury. Even in any thicker fluid layers, propagation of very short and very long waves is forbidden. When wave propagation is possible, only a single propagating mode exists for a given horizontal wave number. In contrast, there are two types of non-propagating modes. One kind of them exists at all wavelength and material parameters, and there are infinitely many such modes for a given wave number, distinguished by their decay rates. The other kind of non-propagating mode that is less attenuated may appear in zero, one, or two specimens. We notice the presence of two length scales as material parameters, one related to viscosity and the other to surface tension. We consider possible modes for a given material on the parameter plane layer thickness versus wave number and discuss bifurcations among different mode types. Motion of surface particles and time evolution of surface elevation is also studied at various parameters in glycerin, and a great variety of behaviour is found, including counterclockwise surface particle motion and negative group velocity in wave propagation.

show abstract

Section: Introductionmentioning

confidence: 99%

Bifurcation Analysis and Propagation Conditions of Free-Surface Waves in Incompressible Viscous Fluids of Finite Depth

Ghahraman

Bene

2023

Fluids

View full text Add to dashboard Cite

show abstract

On the initial values of kinematic and dynamic free-surface boundary conditions for water wave problems

2020

J Hydrodyn

View full text Add to dashboard Cite

Analytical solutions for the interfacial viscous capillary-gravity waves due to an oscillating Stokeslet

Cited by 2 publications

References 11 publications

Bifurcation Analysis and Propagation Conditions of Free-Surface Waves in Incompressible Viscous Fluids of Finite Depth

Bifurcation Analysis and Propagation Conditions of Free-Surface Waves in Incompressible Viscous Fluids of Finite Depth

On the initial values of kinematic and dynamic free-surface boundary conditions for water wave problems

Contact Info

Product

Resources

About