TY - JOUR

T1 - Nonlinear effects in trapped modes of standing waves on the surface of shallow water

AU - Indeǐtsev, D. A.

N1 - Funding Information: ACKNOWLEDGMENTS This work was partially supported by the Russian Foundation for Basic Research (grant no. 99-01-00693). Copyright: Copyright 2018 Elsevier B.V., All rights reserved.

PY - 2000/12

Y1 - 2000/12

N2 - It was shown that traveling waves may coexist with standing waves in a planar infinitely long channel filled by ideal liquid with a free surface. The standing waves are localized near a dynamic inclusion - a massive die on an elastic base. The amplitude of the traveling waves may be turned to zero by appropriately selecting the vibration frequency of the die. The standing waves arise because the vibration eigenfrequencies have a mixed spectrum; that is, the discrete and continuous spectra superpose. Nonlinear effects were observed for the first time when standing waves form in shallow water. In particular, a relationship between the die weight necessary to excite trapped modes, die dimensions, and vibration frequency was derived. It was shown that the nonlinear effects cause double-frequency traveling waves with amplitudes of the next order of smallness. These traveling waves vanish if the die geometry is properly chosen, as for the waves of the zeroth order.

AB - It was shown that traveling waves may coexist with standing waves in a planar infinitely long channel filled by ideal liquid with a free surface. The standing waves are localized near a dynamic inclusion - a massive die on an elastic base. The amplitude of the traveling waves may be turned to zero by appropriately selecting the vibration frequency of the die. The standing waves arise because the vibration eigenfrequencies have a mixed spectrum; that is, the discrete and continuous spectra superpose. Nonlinear effects were observed for the first time when standing waves form in shallow water. In particular, a relationship between the die weight necessary to excite trapped modes, die dimensions, and vibration frequency was derived. It was shown that the nonlinear effects cause double-frequency traveling waves with amplitudes of the next order of smallness. These traveling waves vanish if the die geometry is properly chosen, as for the waves of the zeroth order.

UR - http://www.scopus.com/inward/record.url?scp=0034338298&partnerID=8YFLogxK

U2 - 10.1134/1.1333186

DO - 10.1134/1.1333186

M3 - Article

AN - SCOPUS:0034338298

VL - 45

SP - 1513

EP - 1517

JO - Technical Physics

JF - Technical Physics

SN - 1063-7842

IS - 12

ER -