By using the velocity potential obtained by the method of multiscale asymptotic expansions to within the quantities of the third order of smallness, we study the dependences of the components of the velocity of motion of a homogeneous liquid under the floating ice cover on the thickness of the cover and its modulus of elasticity in the process of propagation of periodic waves of finite amplitude. It is shown that the presence of broken ice leads to a decrease in the moduli of components of the velocity of liquid particles and the phase delay of generated oscillations. The effect of the elasticity of ice becomes more pronounced as the wavelength of the initial harmonic decreases and manifests itself in the increase in the maximum values of the components of velocity and in the phase shift of oscillations in the direction of propagation of waves.
Similar content being viewed by others
References
A. E. Bukatov and V. V. Zharkov, “Influence of broken ice on the velocity of wave currents in the presence of progressive waves propagating over a bottom terrace,” Morsk. Gidrofiz. Zh., No. 5, 3–14 (2001).
G. G. Stokes, “On the theory of oscillatory waves,” Math. Phys. Pap. Cambridge Univ., 1, 197–229 (1847).
S. V. Nesterov, “Excitation of waves of finite amplitude by a running system of pressures,” Izv. Akad. Nauk SSSR. Fiz. Atmosf. Okean., 4, No. 10, 1123–1125 (1968).
J. N. Newman, Marine Hydrodynamics, MIT Press, Cambridge (1977).
M. S. Longuet-Higgins, “Lagrangian moments and mass transport in Stokes waves,” J. Fluid Mech., 179, 547–555 (1987).
L. N. Sretenskii, Theory of Wave Motions in Liquids [in Russian], Nauka, Moscow (1977).
Yu. Z. Aleshkov, Currents and Waves in the Ocean [in Russian], St.-Petersburg Univ., St.-Petersburg (1996).
M. S. Longuet-Higgins, “Lagrangian moments and mass transport in Stokes waves. Part 2. Water of finite depth,” J. Fluid Mech., 186, 321–336 (1988).
A. E. Bukatov and A. A. Bukatov, “Propagation of the surface waves of finite amplitude in a basin with floating broken ice,” Int. J. Offshore Polar Eng., 9, No. 3, 161–166 (1999).
Ant. A. Bukatov and O. M. Bukatova, “Velocities of motion of liquid in a running periodic wave of finite amplitude,” in: Systems of Monitoring of the Environment [in Russian], Marine Hydrophysical Institute, Ukrainian National Academy of Sciences, Sevastopol (2008), pp. 269–271.
A. E. Bukatov and A. A. Bukatov, “Waves of finite amplitude in a homogeneous fluid with floating elastic plate,” Prikl. Mekh. Tekh. Fiz., 50, No. 5, 67–74 (2009).
A. H. Nayfeh, Perturbation Methods, Wiley, New York (1973).
Author information
Authors and Affiliations
Additional information
Translated from Morskoi Gidrofizicheskii Zhurnal, No. 1, pp. 15–24, January–February, 2011.
Rights and permissions
About this article
Cite this article
Bukatov, A.A., Bukatov, A.A. Velocities of motion of liquid particles under the floating ice cover in the case of propagation of periodic waves of finite amplitude. Phys Oceanogr 21, 13–22 (2011). https://doi.org/10.1007/s11110-011-9100-z
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11110-011-9100-z