Abstract
Analytical expressions for the decay rates of surface (on the free boundary) and internal (on the interface) waves in a two-layer fluid are derived in the small kinematic viscosity asymptotics. The internal wave decay rates are found to be approximately two orders smaller than those of the surface waves, which is attributable to the difference in their frequencies, all other factors being the same. The decay rates depend on the kinematic viscosities of both media but, when the viscosity of one of the media is small, they are chiefly determined by the viscosity of the other medium, which allows one to use the model of the contact between viscous and inviscid media. The frequencies of the capillary surface and internal waves in the capillary counterpart of the “dead water” effect considerably differ in value which has an effect on the large difference in the decay rates.
Similar content being viewed by others
References
L.N. Sretenskii, Theory of Wave Motions of Fluids [in Russian], Nauka, Moscow (1977).
I.M. Mindlin, Integro-Differential Equations in Dynamics of Heavy Layered Fluids [in Russian], Nauka, Moscow (1996).
A.I. Grigor’ev, M.S. Fedorov, and S.O. Shiryaeva, “Wave Motion in a Gravity Field on the Free Surfaced and Stratification Interface of a Fluid with Stratified Inhomogeneity. Nonlinear Analysis,” Fluid Dynamics 45(5), 793 (2010).
A.I. Grigor’ev, S.O. Shiryaeva, and M.S. Fedorov, “Capillary Counterpart of the ‘Dead Water’ Effect in a Stratified Fluid with a Charged Interface,” Zh. Tekhn. Fiz. 80(7), 8 (2010).
A.I. Grigor’ev, M.S. Fedorov, and S.O. Shiryaeva, “Nonlinear Analysis of the Distinctive Features of the Interaction between Capillary Finite-Amplitude Waves in a Layered Nonhomogeneous Fluid,” Zh. Tekhn. Fiz. 82(6), 9 (2012).
L.S. Rozumenko and V.I. Tkachenko, “Instability of the Interface between Viscous Flows,” Vestn. Kharkov Un-ta. Ser. Fizika No. 710 (3), 73 (2005).
S.O. Shiryaeva, O.A. Grigor’ev, and A.I. Grigor’ev, “Dynamic Surface Tension Effect and Capillary Wave Motion on a Charged Fluid Surface,” Zh. Tekhn. Fiz. 66(10), 31 (1996).
M.J. Mercier, R. Vasseur, and T. Dauxois, “Resurrecting Dead-Water Phenomenon,” Nonlin. Proc. Geophys. 18, 193 (2011).
S.O. Shiryaeva, and A.I. Grigor’ev, Scalarization of Vectrorial Boundary Value Problems in Fluid Dynamics [in Russian], Yaroslavl, Yaroslavl Univ. Press (2010).
A.I. Grigor’ev, D.M. Pozharitskii, and S.O. Shiryaeva, “Structure of the Velocity Field Connected with the Wave Motion on a Uniformly Charged Interface between Two Viscous Immiscible Fluids,” Zh. Tekhn. Fiz. 79(9), 36 (2009).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © A.I. Grigor’ev, M.S. Fedorov, S.O. Shiryaeva, 2014, published in Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, 2014, Vol. 49, No. 6, pp. 37–44.
Rights and permissions
About this article
Cite this article
Grigor’ev, A.I., Fedorov, M.S. & Shiryaeva, S.O. Viscosity effect on the surface and internal waves in a two-layer fluid with a free surface. Fluid Dyn 49, 733–739 (2014). https://doi.org/10.1134/S0015462814060040
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0015462814060040