Temperature and velocity fluctuations measured in Van Mijen Fjord in Svalbard and interpreted as the fluctuations induced by internal waves revealed the existence of short-period internal waves with an amplitude of approximately 1？m and a period of approximately 5–10？min that correlate with the ice cover fluctuations of the same period with an amplitude of a few millimeters. 1. Introduction We analyze the measurements of temperature, velocity, and pressure at the bottom to study the influence of internal waves on the ice cover. The “rigid lid” approximation is almost always used in the theoretical study of internal waves under the ice cover or even without it. This approximation filters off the surface mode and adequately describes the properties of both the internal waves in ice-free conditions and long internal waves under the ice cover [1, 2]. In the “rigid lid” approximation, the vertical velocity at the surface is assumed to be equal to zero; therefore, due to the kinematic condition, the internal waves cannot cause any vertical displacements of the ice cover. Such conclusion is, however, inconsistent with the experimental data obtained for relatively deep parts of the Arctic Ocean [3–6] and also contradicts the theoretical results [7, 8], according to which internal waves may be reflected in the fluctuations of the ice cover at frequencies comparable with the Brunt-V？is？l？ frequency. Scientists from the Shirshov Institute of Oceanology (Russian Academy of Sciences) and The University Centre in Svalbard (UNIS) carried out marine studies in the shallow Van Mijen Fjord in Svalbard to perform experimental tests of the theoretical conclusion concerning the possible influence of short internal waves on the fluctuations of the compact ice cover. 2. Brief Theory of Internal Waves under an Ice Cover In the theoretical approach, the ice cover of the ocean surface can be considered as a thin elastic plate floating on the sea surface. The theoretical description of the ice cover fluctuations should take into account the elastic properties of the ice plate, the compression forces, and the ice inertia. If the processes inside the ice cover are ignored the main equations and boundary conditions of the ice cover should be similar to the equations and conditions in the situation when the sea surface is free of ice. The only exception is the dynamic condition that may be expressed under the constant ice thickness h in the following form [7–11]: Here, is the pressure, the ice surface deflection, the acceleration due to gravity, the seawater density at the boundary
References
[1]
E. G. Morozov, V. G. Neiman, S. V. Pisarev, and S. Yu. Erofeeva, “Internal tidal waves in the Barents Sea,” Doklady Earth Sciences, vol. 393, no. 8, pp. 1124–1127, 2003.
[2]
E. G. Morozov and S. V. Pisarev, “Internal waves and polynya formation in the Laptev sea,” Doklady Earth Sciences, vol. 398, no. 7, pp. 983–986, 2004.
[3]
P. V. Czipott, M. D. Levine, C. A. Paulson, D. Menemenlis, D. M. Farmer, and R. G. Williams, “Ice flexure forced by internal wave packets in the Arctic ocean,” Science, vol. 254, no. 5033, pp. 832–835, 1991.
[4]
V. N. Smirnov, “Oscillations of the ice cover induced by internal waves in an icy ocean,” Doklady Akademii Nauk SSSR, vol. 206, no. 5, pp. 1106–1108, 1972.
[5]
V. N. Smirnov, Dynamic Processes in Sea Ice, Gidrometeoizdat, St. Petersburg, Russia, 1996.
[6]
V. N. Smirnov, A. N. Shushlebin, and V. G. Korostelev, “Results of experimental measurements of the parameters of surface and internal waves in the Arctic ocean and the sea of Okhotsk,” in Surface and Internal Waves in the Arctic Seas, I. V. Lavrenov and E. G. Morozov, Eds., Gidrometeoizdat, St. Petersburg, Russia, 2002.
[7]
S. V. Muzylev, “Internal waves under an ice cover,” Doklady Earth Sciences, vol. 418, no. 1, pp. 145–148, 2008.
[8]
S. V. Muzylev and L. N. Oleinikova, “On the theory of internal waves under ice cover,” Oceanology, vol. 47, no. 2, pp. 172–177, 2007.
[9]
L. D. Landau and E. M. Lifshitz, Theory of Elasticity, Pergamon, Oxford, UK, 1967.
[10]
A. K. Liu and E. Mollo-Christensen, “Wave propagation in a solid ice pack,” Journal of Physical Oceanography, vol. 18, no. 11, pp. 1702–1712, 1988.
[11]
S. V. Muzylev, “Edge waves under ice cover at a straight coast with a sloping beach,” Oceanology, vol. 46, no. 4, pp. 465–471, 2006.
[12]
V. V. Bogorodsky and V. P. Gavrilo, Ice: Physical Properties, Modern Methods in Glaciology, Gidrometeoizdat, Leningrad, Russia, 1983.
[13]
M. Coon, D. C. Echert, and G. S. Knoke, “Ice in surface waters,” in Proceedings of the 14th International Symposium on Ice, H. T. Shen, Ed., pp. 1049–1055, Balkema, 1999.
[14]
A. Marchenko, “Parametric excitation of flexural-gravity edge waves in the fluid beneath an elastic ice sheet with a crack,” European Journal of Mechanics B, vol. 18, no. 3, pp. 511–525, 1999.
[15]
A. V. Marchenko, “Flexural gravity waves,” Trudy Instituta Obshchei Fiziki, vol. 56, pp. 65–111, 1999.
[16]
A. Marchenko, I. Langen, and A. Shestov, “Hydrological characteristics of the strait separating Braganzavagen from Sveabukta in Van Mijen Fjord,” in Coastal Technology—Coast 2008, NTNU, Trondheim, Norway, 2008.
[17]
A. Marchenko, A. Shestov, A. Karulin et al., “Field studies of sea water and ice properties in Svalbard fjords,” in Proceedings of the International Conference on Port and Ocean Engineering under Arctic Conditions (POAC '11), pp. 148–160, 2011.
[18]
“The Winter-Expedition of RV “Polarstern” to the Antarctic (ANT V/1–3),” Berichte zur Polarforschung, Nr. 39, Alfred-Wegener-Institut für Polar- und Meeresforschung, Bremerhaven, Germany, 1987.
[19]
J. R. Marko, “Observations and analyses of an intense waves-in-ice event in the Sea of Okhotsk,” Journal of Geophysical Research, vol. 108, no. 9, pp. 3296–3309, 2003.
[20]
I. V. Polyakov, L. A. Timokhov, V. A. Alexeev, et al., “Arctic ocean warming contributes to reduced polar ice cap,” Journal of Physical Oceanography, vol. 40, no. 12, pp. 2743–2756, 2010.
